CBSE Class 12

CBSE Sample Papers for Class 12 Maths Paper 2 are part of CBSE Sample Papers for Class 12 Maths. Here we have given CBSE Sample Papers for Class 12 Maths Paper 2.

CBSE Sample Papers for Class 12 Maths Paper 2

Students who are going to appear for CBSE Class 12 Examinations are advised to practice the CBSE sample papers given here which is designed as per the latest Syllabus and marking scheme as prescribed by the CBSE is given here. Paper 2 of Solved CBSE Sample Paper for Class 12 Maths is given below with free PDF download solutions.

Time: 3 Hours
Maximum Marks: 100

General Instructions:

• All questions are compulsory.
• Questions 1-4 in section A are very short answer type questions carrying 1 mark each.
• Questions 5-12 in section B are short answer type questions carrying 2 marks each.
• Questions 13-23 in section C are long answer I type questions carrying 4 marks each.
• Questions 24-29 in section D are long answer II type questions carrying 6 marks each.

SECTION A

Question 1.
Find λ when projection of \(\bar { a } =\lambda \hat { i } +\hat { j } +4\hat { k }\) on \(\bar { b } =2\hat { i } +6\hat { j } +3\hat { k }\) is 4 units.

Question 2.
Evaluate \(\int _{ 2 }^{ 3 }{ \frac { 1 }{ 2x } } dx\)

Question 3.
Write the cofactor of the element a₃₁ in \(A=\left( \begin{matrix} 3 & 2 & 6 \\ 5 & 0 & 7 \\ 3 & 8 & 5 \end{matrix} \right)\)

Question 4.
For which values of x, f(x) = \(\left| x-1 \right| +\left| x-2 \right|\) is not differentiable?

SECTION B

Question 5.
For what value of c, Mean Value theorem is applicable for the function f(x) = x + \(\frac { 1 }{ x }\) on [1, 3] ?

Question 6.
Find \(\frac { dy }{ dx }\), if y = \({ tan }^{ -1 }\left( \frac { 1-cosx }{ 1+cosx } \right)\)

Question 7.
For the matrix \(A=\begin{pmatrix} 3 & 1 \\ 7 & 5 \end{pmatrix}\) find the value of x and y so that A² + xI = yA

Question 8.
Using derivative, find the approximate percentage increase in the area of a circle if its radius is increased by 2%.

Question 9.
The random variable x has a probability distribution P(x) of the following form, where k is some number

Find the value of (i) k (ii) P(x ≥ 2)

Question 10.
Find the equation of line passing through the point with position vector \(\hat { i } +\hat { j } +\hat { k }\) and perpendicular to the plane \(\left( 2\hat { i } +\hat { j } +\hat { 3k } \right) \cdot \hat { r } =5\) in both vector form and Cartesian form.

Question 11.
Evaluate \(\int _{ 0 }^{ 1 }{ x{ e }^{ { x }^{ 2 } } } dx\)

Question 12.
Anil wants to invest at most ₹ 12000 in bonds A and B. He wants to invest atleast ₹ 2000 in bond A and atleast ₹ 4000 in bond B. If rate of interest on bond A is 8% per annum and rate of interest on bond B is 9% per annum. Formulate it as L.P.P. to find maximum yearly income.

SECTION C

Question 13.
Two balls are drawn at random from a bag containing 2 white, 3 red, 5 green and 4 black balls one by one without replacement. Find the probability that both the balls are of different colours.

Question 14.
The probabilities of two students A and B coming to the school in time are \(\frac { 3 }{ 7 }\) and \(\frac { 5 }{ 7 }\) respectively. Assuming that the events A coming in time and B coming in time are independent. Find the probability of only one of them coming to the school in time. Write atleast one advantage of coming to the school in time.

Question 15.

Question 16.

Question 17.

Question 18.
Evaluate \(\int { \frac { sin\phi d\phi }{ \sqrt { { sin }^{ 2 }\phi +2cos\phi +3 } } }\)

Question 19.
Evaluate \(\int _{ 0 }^{ \pi }{ \frac { x\quad tanx }{ secx+tanx } } dx\)
OR
Evaluate \(\int _{ 0 }^{ \frac { \pi }{ 2 } }{ log\quad sinx\quad dx }\)

Question 20.

Question 21.
Find the particular solution for the differential equation

Question 22.
If the sum of two unit vectors is a unit vector, prove that the magnitude of their difference is √3.

Question 23.
Solve the following L.P.P. graphically:
Minimize and maximize Z = 3x + 9y
Subject to constraint
x + 3y ≤ 60
x + y ≥ 10
x ≤ y
x, y ≥ 0

SECTION D

Question 24.
Find the distance of the point P(3, 4, 4) from the point where the line joining the points A (3, -4, -5) and B (2, -3, 1) intersect the plane 2x + y + z = 7.
OR
It lines \(\frac { x-1 }{ 1 } =\frac { y+1 }{ 3 } =\frac { z-1 }{ 4 }\) and \(\frac { x-3 }{ 1 } =\frac { y-k }{ 2 } =\frac { z }{ 1 }\) intersect, then find the value of k and hence find the equation of the plane containing these lines.

Question 25.
Let N denote the set of all natural numbers and R be the relation on N x N defined by (a, b) R (c, d) if ad (b + c) = bc (a + d)
Show that R is an equivalence relation.
OR
A binary operation * is defined on the set X = R – {-1} by x * y = x + y + xy ∀ x, y ∈ X. Check whether * is commutative and associative. Find the identity element and also find the inverse of each element of X.

Question 26.
Given the sum of the perimeter of a square and a circle. Show that sum of their areas is least when the side of the square is equal to the diameter of the circle.
OR
Show that the height of the cylinder of maximum volume that can be inscribed in a sphere of radius R is \(\frac { 2R }{ \surd 3 }\). Also find the maximum volume.

Question 27.
Determine the product \(\left( \begin{matrix} -4 & 4 & 4 \\ -7 & 1 & 3 \\ 5 & -3 & -1 \end{matrix} \right) \left( \begin{matrix} 1 & -1 & 1 \\ 1 & -2 & -2 \\ 2 & 1 & 3 \end{matrix} \right)\) and use it to solve the system of equations
x – y + z = 4
x – 2y – 2z = 9
2x + y + 3z = 1

Question 28.
Find the area of the region {(x, y): x² + y² ≤ 4, x + y ≥ 2} using integration.

Question 29.
Solve the following differential equation

Solutions

Solution 1.

Solution 2.

Solution 3.

Solution 4.
At x = 1 and x = 2, f(x) is not differentiable.

Solution 5.

Solution 6.

Solution 7.

Solution 8.

Solution 9.

Solution 10.

Solution 11.

Solution 12.
Let amount invested in bond A is ₹ x, and amount invested in bond B is ₹ y.
Objective function is maximise income Z = \(\frac { 8x }{ 100 } +\frac { 9y }{ 100 }\)
Subject to constraints are
x + y ≤ 12000 (Investment constraint)
x ≥ 2000
y ≥ 4000

Solution 13.
Bag contains- 2 White balls, 3 Red balls, 5 Green balls, 4 Black balls
Total balls = 14
2 balls are drawn without replacement.
P (both balls are of different colours) = 1 – P(both balls are of same colour)
= 1 – [P(both white) + P (both red) + P (both green) + P (both black)]

Solution 14.
Let E₁ is the event: A coming in time
and E₂ is the event: B coming in time

Solution 15.

Solution 16.
Using elementary row transformation
A = IA

Solution 17.

Solution 18.

Solution 19.

Solution 20.

Solution 21.

Solution 22.

Solution 23.

Solution 24.
Equation of line joining the points A (3, -4, -5) and B (2, -3, 1) is

Solution 25.
R be a relation on N x N defined by
(a, b) R (c, d) if ad (b + c) = bc (a + d)

Solution 26.

Solution 27.

Solution 28.

Solution 29.

We hope the CBSE Sample Papers for Class 12 Maths Paper 2 help you. If you have any query regarding CBSE Sample Papers for Class 12 Maths Paper 2, drop a comment below and we will get back to you at the earliest.

CBSE Sample Papers for Class 12 Physics Paper 1 are part of CBSE Sample Papers for Class 12 Physics. Here we have given CBSE Sample Papers for Class 12 Physics Paper 1.

CBSE Sample Papers for Class 12 Physics Paper 1

• Time Allowed : 3 Hours
  Max. Marks : 70
  General Instructions 

  • All questions are compulsory. There are 26 questions in all.
  • This question paper has five sections: Section A, Section B, Section C, Section D and Section E.
  • Section A contains five questions of 1 mark each. Section B contains five questions of 2 marks each. Section C contains twelve questions of 3 marks each. Section D contains one value based question of 4 marks and Section E contains three questions of 5 marks each.
  • There is no overall choice. However, an internal choice has been provided in 1 question of 2 marks, 1 question of 3 marks and all the 3 questions of 5 marks weightage. You have to attempt only 1 of the choices in such questions.
  • You may use the following values of physical constants wherever necessary :

  

Questions :
SECTION : A

Question 1.
Define the term self-inductance of a coil. Write its S.I. unit

Question 2.
Which basic mode of communication is used for telephonic communication?

Question 3.
Why do the electrostatic field lines not form closed loops?

Question 4.
1-V graph for a metallic wire at two different temperatures, T₁ and T₂ is as shown in the figure. Which of the two temperature is lower and why?

Question 5.
Why does bluish colour predominate in a clear sky?

SECTION : B

Question 6.
Use Kirchhoff’s rules to determine the potential difference between the points A and D when no current flows in the arm BE.

Question 7.
When an electron in hydrogen atom jumps from the excited state to the ground state, how would the de-Broglie wavelength associated with the electron change? Justify your answer.

Question 8.
You are given two converging lenses of focal lengths 1.25 cm and 5 cm to design a compound microscope. If it is desired to have a magnification of 30, find out the separation between the objective and the eyepiece.

OR

A small telescope has an objective lens of focal length 150 cm and eyepiece of focal length 5 cm. What is the magnifying power of the telescope for viewing distant objects in normal adjustment? If this telescope is used to view a 100 m tall tower 3 km away, what is the height of the image of the tower formed by the objective lens?

Question 9.
Calculate the shortest wavelength in the Balmer series of hydrogen atom. In which region (infra-red, visible, ultraviolet) of hydrogen spectrum does this wavelength lie?

Question 10.
Write two factors which justify the need of modulation.

SECTION : C

Question 11.
Draw a circuit diagram of a C.E. transistor amplifier. Briefly explain its working and write the expression for
(i) current gain
(ii) voltage gain of the amplifier.

Question 12.
State clearly how an unpolarised light gets linearly polarized when passed through a Polaroid.
(i) Unpolarised light of intensity I₀ is incident on a Polaroid P₁ which is kept near another Polaroid P₂ whose pass axis is parallel to that of P₁. How will the intensities of light, I₁ and I₂, transmitted by the Polaroids P₁ and P₂ respectively, change on rotating P₁ without disturbing P₂?
(ii) Write the relation between the intensities  I₁ and I₂.

Question 13.
Define modulation index. Why is its value kept, in practice, less than one? A carrier wave of frequency 1.5 MHz and amplitude 50 V is modulated by a sinusoidal wave of frequency 10 kHz producing 50% amplitude modulation. Calculate the amplitude of the AM wave and frequencies of the side bands produced.

Question 14.
A uniform magnetic field B is set up along the positive X – axis. A particle of charge ‘q’ mass ‘m’ moving with a velocity v enters the field at the origin in X – Y plane such that it has velocity components both along and perpendicular to the magnetic field B. Trace, giving reason, the trajectory followed by the particle. Find out the expression for the distance moved by the particle along the magnetic field in one rotation.

Question 15.
Find the relation between drift velocity and relaxation time of charge carriers in a conductor. A conductor of length L is connected to a d.c. source of emf ‘E’. If the length of the conductor is tripled by stretching it, keeping ‘E’ constant, explain how its drift velocity would be affected.

Question 16.
(a) Determine the value of phase difference between the current and the voltage in the given series LCR circuit.

(b) Calculate the value of the additional capacitor which may be joined suitably to the capacitor C that would make the power factor of the circuit unity.

Question 17.
Write the expression for the generalized form of Amperes Circuital law. Discuss its significance and describe briefly how the concept of displacement current is explained through charging/ discharging of a capacitor in an electric circuit. 

Question 18.
(a) Describe briefly three experimentally observed features in the phenomenon of photoelectric effect.
(b) Discuss briefly how wave theory of light cannot explain these features.

OR

(a) Write the important properties of photons which are used to establish Einstein’s photoelectric equation.
(b) Use this equation to explain the concept
(i) threshold frequency and
(ii) stopping potential.

Question 19.
Use Huygens principle to show how a plane wavelength propagates from a denser to rarer medium. Hence verify Snell’s law of refraction.

Question 20.
Identify the gates P and Q shown in the figure . Write the truth table for the combination of the gates shown.

Name the equivalent gate representing this circuit and write its logic symbol. 

Question 21.
(a) Write three characteristic properties of nuclear force.
(b) Draw a plot of potential energy of a pair of nucleons as a function of their separation. Write two important conclusions that can be drawn from the graph.

Question 22.
Calculate the potential difference and the energy stored in the capacitor C₂ in the circuit shown in the figure. Given potential at A is 90 V, C₁ = 20 µF, C₂ = 30 µF and C₃ = 15 µF.

SECTION : D

Question 23.
One morning an old lady tried bare-footed to replace the fuse wire fitted with power supply mains for her house. Suddenly she cried and collapsed on the floor. Her family members cried loudly for help. Her neighbour heard the cries and rushed to the spot wearing rubber soul shoes on. He took a wooden stick and used it to switch off the main supply.
Answer the folio wing questions :

1. What are the voltage and frequency of mains supply in India?
2. These days most of the electrical devices we use require a.c. voltage. Why?
3.  Can a transformer be used to step up d.c. voltage ?
4. Write two qualities displayed by neighbour by his action.

SECTION : E

Question 24.
(a) Define electric flux. Write its S.I. unit. “Gauss’s law in electrostatics is true for any closed surface, no matter what its shape or size is”. Justify this statement with the help of a suitable example.
(b) Use Gauss’s law to prove that electric field inside a uniformly charged spherical shell is zero.

OR

(a) Derive the expression for the energy stored in a parallel plate capacitor. Hence obtain the expression for the energy density of the electric field.
(b) A fully charged parallel plate capacitor is connected across an uncharged identical capacitor. Show that the energy stored in the combination is less than that stored initially in the single capacitor.

Question 25.
Explain, using a labelled diagram, the principle and working of a moving coil galvanometer. What is the function of
(i) uniform radial magnetic field,
(ii) soft iron core?
Define the terms :
(i) current sensitivity and
(ii) voltage sensitivity of a galvanometer. Why does increasing the current sensitivity not necessarily increase voltage sensitivity?

OR

Question 26.
(a) Consider two coherent sources S₁ and S₂ producing monochromatic waves to produce interference pattern. Let the displacement of the wave produced by S₁ be given by y₁ = a cos mt and the displacement by S₂ be y₂ = a cos (ωt + Φ). Find out the expression for the amplitude of the resultant displacement at a point and show that the intensity at that point will be I = 4a² cos² Φ/2. Hence establish the conditions for constructive and destructive interference.
(b) What is the effect on the interference fringes in Young’s double slit experiment when
(i) the width of the source slit is increased,
(ii) the monochromatic source is replaced by a source of white light.

OR

(a) A ray ‘PQ’ of light is incident on the face AB of a glass prism ABC (as shown in the figure) and emerges out of the face AC. Trace the path of the ray. Show that ∠i + ∠e = ∠A + ∠δ. Where δ and e denote the angle of deviation and angle of emergence respectively.
Plot a graph showing the variation of the angle of deviation as a function of angle of incidence. State the condition under which ∠δ is minimum.
(b) A ray of light passing through an equilateral triangular prism from air undergoes minimum deviation when angle of incidence is 3/4th of the angle of prism. Calculate the speed of light in the prism.

 Answers :
SECTION : A

Answer 1.
L = Φ / I . If I = 1 then L = Φ i.e self inductance L of a coil is numerically equal to the amount of magnetic flux (Φ) linked with the coil when unit current flows through the coil. The S.I. unit of self inductance is henry (H) or weber per ampere.

Answer 2.
The basic mode of communication used in telephony is the point-to-point communications mode, which takes place through a link between a single transmitter and receiver.

Answer 3.
Electrostatic field lines originate from positive charge and terminate at negative charge.

Answer 4.
For the given figure the slope of a V – I graph is I/V = 1/R . Here the smaller the slope larger is the resistance . As the resistance of a metal increases with the increase in temperature, so resistance at T₂ is more and T₁ is lower.

Answer :
The light is scattered by air molecules. According to Lord Rayleigh the intensity of scattered light I ∝ 1/λ⁴. As λ_blue < λ_red Therefore blue colour scattered more in sky.

SECTION : B

Answer 6.

According to Kirchhoff’s junction law at B
i₃ = i₁ + i₂
i₃ = i₁
As  i₃ = 0  (given)
Applying second law to loop AFEB, electronic network shown in the figure.

∴   i₃ x 2 + i₃ x 3 + i₂ R₁ = 1+3 + 6
∴   i₃ = i₁ = 2A

From A to D along AFD
∴  V_AD = 2 i₃ – 1 + 3 x i₃
= (4 – 1 + 6)V
= 9V

Answer 7.
In an hydrogen atom, the negatively charged electron revolves in a circular orbit around the heavy positively charged nucleus. The centripetal force required by the electron is produced by the attractive force exerted by the nucleus on it. The energy is radiated, when an electron jumps from higher to lower energy orbit and the energy is absorbed, when jumps from lower to higher energy orbit.

It is called Bohr’s frequency condition.

Answer 8.
Given, f₀ = 5 cm , f_e = 1.25 cm and m = 30
Let S be tube length (distance between the objective and the eyepiece).

Thus, the height of the image would be 31.58 m.

Answer 9.
The formula for wavelength (λ) by Balmer series is :

Answer 10.
Two factors that justify the need for modulation of low frequency signals to high frequency signals are :

• increase in range of communication base band signals suffer from attenuation and so cannot be transmitted over long distances, and
• the antenna height and aperture is inversely proportional to the radiated signal frequency, implying that higher frequencies result in smaller antennas.

SECTION : C

Answer 11.

The purpose of this circuit is to amplify a small a.c input signal, such as an audio or radio signal. A small a.c. voltage is applied to the input through a coupling capacitor. The ratio of the a.c. component of the output to the a.c. component of the input, is known as gain.

Answer 12.
Polaroid filters are made of a special material that is capable of blocking of the two planes of vibration of an electromagnetic wave. In this sense, a Polaroid serves as a device that filter out one-half of the vibrations upon transmission of the light through the filter. When unpolarised light is transmitted through a Polaroid filter, it emerge with one-half the intensity and with vibrations in a single plane; it emerges as polarized light.

Answer 13.
The modulation index p, can be defined as the ratio between the amplitude of the modulating signal and the amplitude of the carrier signal. A modulation index above 1 causes over-modulation, causing the carrier to experience 180° phase reversals. These reversals give rise to additional side and audio signal will be distorted during reception.
Given,
carrier wave frequency = 1.5 MHz, amplitude (V _m) = 50 V
sinusoidal wave frequency = 10 kHz
amplitude modulation = 50%

Thus, amplitude of the AM wave = 250 volt
Now,
f _USB = 1.5 x 1000+ 10 kHz
⇒ 1500 + 10 = 1510 kHz
f _LSB = 1.5 x 1000 -10 = 1490 kHz

Answer 14.
Field at an axial point of a circular coil.

Where N is the number of turns of the circular coil. If M =iA is the magnetic moment of the coil, then

∵ a = 0, For small loop,

Where p is electric dipole  moment.

Answer 15.
The drift velocity of electrons can be formulated as :

Answer 16.

Answer 17.
Generalized form of Ampere Circuital Law :

It signifies that the source of magnetic field is not just due to the conduction of electric current due to flow of charge but also due to the time rate of change of electric field called displacement current.

Displacement current :
During charging and discharging of a capacitor the electric field between the plates will change so there will be a change of electric flux (displacement current) between the plates.

Answer 18.
(a)
(i) The photoelectric effect will not occur when the frequency of the incident light is less than the threshold frequency. Different materials have different threshold frequencies and most elements have threshold frequencies in the ultraviolet region of the electromagnetic spectrum.
(ii) The maximum KE of a stream of photo electrons increases linearly with the frequency of the incident light above the threshold frequency.
(iii) The rate at which photo electrons are emitted from a photosensitive surface is directly proportional to the intensity of incident light when the frequency is constant.

(b) Classical wave theory cannot explain :
(i) The existence of threshold frequency because it predicts that electrons would absorb enough energy to escape and there would not be any threshold frequency.
(ii) The almost immediate emission of photo electrons as, according to this theory, electrons require a period of time before sufficient energy is absorbed by it to escape from the metal; however such a thing does not happen practically; and
(iii) The independence of KE of photo electrons on intensity and dependence on frequency because it cannot explain why maximum KE is dependent on frequency and independent of intensity.

OR

(i) The important property of photons that is useful in establishing Einstein’s photoelectric equation is their ability to hold on to the electrons of an atom by their forces of attraction.
(ii) Einstein’s photoelectric equation states that :

Answer 19.
Medium 1

Answer 20.
Logic gate P is AND gate and logic Q is NOT gate.

The combination is NAND

Answer 21.
(a)
(i) Nuclear forces are short range forces.
(ii) Nuclear forces are primarily attractive and extremely strong.
(iii) Nuclear forces are charge independent

(b) Nuclear forces is of attractive nature when separation between the nuclei is greater than 1 fm and of repulsive nature when separation is less than 1 fm.

Answer 22.

SECTION : D

Answer 23.

1. The voltage and frequency of mains supply in India are 220 V and 50 Hz respectively.
2. Most electrical devices require a.c. voltage because a.c. is available by default through the mains supply and also because d.c., is actually a one-way current, is available only through batteries.
3. No, a transformer cannot be used to set-up d.c. voltage because a transformer works on the magnetic effect of current and d.c. voltage does not produces any magnetic field.
4. The two qualities displayed by neighbour are :
   (a) preventing himself from being the earthing conductor by putting on his shoes and
   (b) switching off the mains connection to prevent the old lady from acting as an earthing conductor

SECTION : E

Answer 24.
(a) The electric flux through an area is defined as the electric field multiplied by the area of the surface projected on a plane, perpendicular to the field. Its S.I. unit is volt-metres (Vm) or Newton metres square per coulomb (Nm² C^-1 ). The given statement is justified because while measuring the flux, the surface area is more important than its volume or its size.
(b) To prove that the electric field inside a uniformly charged spherical shell is zero, we place a single positive point charge ‘q’ at the centre of an imaginary spherical surface with radius R. The field lines of this point radiate outside equally in all directions. The magnitude E of the electric field at every point on the surface is given by

OR

(a) When charging parallel plate capacitor, whose plate area is A and distance between the plate is d. When charge on capacitor is q, potential difference increase 0 to V. Hence average

(b) Let the capacitance of the charged capacitor C₁ by and the voltage be ∆V₁

Answer 25.
The basic principle of a moving coil galvanometer is that when a current carrying coil is placed in a magnetic field, it experiences a torque.

When the current I is passed through the coil, the torque experienced is given by
τ = NIAB sinθ
Where
N = no. of turns of the coil,
A =  area of the coil
B = magnetic field and
θ = angle between normal of coil and magnetic field
(i) The uniform radial magnetic field allows the coil to rotate and
(ii) The soft iron core makes the magnetic field linked with the coil to be radial.
The current sensitivity is defien as the deflection produced in the galvanometer, while passing a current of 1 ampere (1amp).
Thus,

The voltage sensitivity is defined as the deflection produced in the galvanometer when a potential difference of IV is applied to the coil.
Thus,

Where, R is the resistance.
Increasing the current sensitivity does not necessarily increase the voltage sensitivity as there is an increase in the resistance as well.

OR

The direction of dB is perpendicular to the plane formed by dl and r. It has an x-component dB_x. When the components perpendicular to the x-axis are summed over, they cancel out and we obtain null result. Thus only the x-component survives.

If the coil has N turns, then each turn will contribute equally to B. Then


Where μ₀ in the permeability of free space. Ampere’s circuital law in electromagnetism is analogous to Gauss’ law in electrostatics.

Answer 26.
(a) Let S be a narrow slit illuminated by a monochromatic source of light, and Sj and S₂ two similar parallel slits very close together and equidistant from S.

Displacement of the wave produced by S₁ is given by
y₁ = a cos ωt and
the displacement of the Wave produced by S₂ is given by
y₂ = a cos (ωt + Φ)
The resultant displacement is given by
y = y₁ + y₂ = a cos(ωt + Φ) + a cos (ωt + Φ)
⇒ y = 2a cos Φ/2 cos (ωt + Φ/2)
The amplitude of the resultant displacement is 2a cos Φ/2. The intensity of light is directly proportional to the square of amplitude of the wave.
The resultant intensity in given by
I = 4a cos² Φ/2

(b)  (i) As the width of the slits is increased, the fringe width decreases. It is because,

(ii) The different colours of white light will produce different interference patterns but the central bright fringes due to all colours are at the same positions. Therefore, the central bright fringe is white in colour. Since the wavelength of the blue light is smallest, the fringe close to the either side of the central white fringe is blue and farthest is red.
OR

(a) Let the incident ray meet refracting face AB of the prism at point P. Ray PQ is the refracted ray inside the prism and δ₁ and r₁, are the angle of the deviation and refraction at interface AB. At interface AC the ray goes out of the prism. Let e be the angle of emergence. The angle of deviation at point Q is δ₂ as shown in figure. Using geometry, we see that at point P,



So angle of deviation produced by a prism depends upon the angle of incidence, refracting angle of prism, and the material of the prism.

CBSE Sample Papers for Class 12 Maths Paper 1 are part of CBSE Sample Papers for Class 12 Maths. Here we have given CBSE Sample Papers for Class 12 Maths Paper 1.

CBSE Sample Papers for Class 12 Maths Paper 1

Students who are going to appear for CBSE Class 12 Examinations are advised to practice the CBSE sample papers given here which is designed as per the latest Syllabus and marking scheme as prescribed by the CBSE is given here. Paper 1 of Solved CBSE Sample Paper for Class 12 Maths is given below with free PDF download solutions.

Time: 3 Hours
Maximum Marks: 100

General Instructions:

• All questions are compulsory.
• Questions 1-4 in section A are very short answer type questions carrying 1 mark each.
• Questions 5-12 in section B are short answer type questions carrying 2 marks each.
• Questions 13-23 in section C are long answer I type questions carrying 4 marks each.
• Questions 24-29 in section D are long answer II type questions carrying 6 marks each.

SECTION A

Question 1.

Question 2.
Check the continuity of the function

Question 3.
Integrate

Question 4.
Find a vector in the direction of vector \(\vec { a } =2\hat { i } -3\hat { j } +4\hat { k }\) that has magnitude 5 units.

SECTION B

Question 5.
Find the value of x + y + z if

Question 6.
Differentiate log (1 + θ) with respect to sin^-1 θ.

Question 7.
A balloon which always remains spherical has a variable radius. Find the rate at which its volume is increasing with the radius when the radius is 10 cm.

Question 8.
Show that the function f(x) = tan x – x is always increasing in X ∈ R.

Question 9.
Find the equation of the plane passing through the point (1, 4, -2) and it is parallel to the plane -2x + y + 3z = 0.

Question 10.
Event E and F are such that P (not E or not F) = 0.25. State whether E and F are mutually exclusive.

Question 11.
A manufacturing company makes two types of teaching aids A and B of Mathematics for class XII. Each type of A requires 9 labour hours for fabricating and 1 labour hours for finishing. Each type of B requires 12 labour hours for fabricating and 3 labour hours for finishing. For fabricating and finishing the maximum labour hours available per week are 180 and 30 respectively. The company makes a profit of ₹ 80 on each type of A and ₹ 120 on each type of B. Formulate it as L.P.P. to make a maximum profit.

Question 12.
Evaluate

SECTION C

Question 13.
Prove that

Question 14.
Using properties of determinant prove that

OR
Using properties of determinant prove that

Question 15.

Question 16.
Evaluate

Question 17.
Evaluate

OR
Evaluate

as limit of sums

Question 18.
Solve the differential equation

Question 19.

Question 20.

Question 21.
On a multiple choice examination with three possible answers (out of which only one is correct) for each of the five questions, what is the probability that a candidate would get four or more correct answers just by guessing? Is examination necessary for success in the life of student?

Question 22.
There are two bags, bag I and bag II. Bag I contains 4 white and 3 red balls while another bag II contains 3 white and 7 red balls. One ball in drawn at random from one of the bags and it is found to be white. Find the probability that it was drawn from bag I.

Question 23.
Solve the following L.P.P.
Maximize profit Z = 17.5 x + 7y
Subject to constraints are x + 3y ≤ 12 3x + y ≤ 12, x, y ≥ 0

SECTION D

Question 24.
If \(A=\left( \begin{matrix} 1 & -1 & 1 \\ 2 & 1 & -3 \\ 1 & 1 & 1 \end{matrix} \right)\) Find A-1 and hence solve the system of equations
x + 2y + z = 4
-x + y + z = 0
x – 3y + z = 2

Question 25.
Let x be non-empty set. P(x) be its power set. Let * be an operation defined on element of P(x) by,
A*B = A ∩ B \(\forall\) A, B ∈ P(x). Then
(i) Prove that * is a binary operation in P(x)
(ii) Is * commutative?
(iii) Is * associative?
(iv) Find the identity element in P(x) w.r.t. *
(v) Find all the invertible elements of P(x)
(vi) If o is another binary operation defined on P(x) as AοB = A ∪ B then verify that o distributes itself over *
OR
Consider f : R₊ → [-5, ∞) given by f(x) = 9x² + 6x – 5. Show that f is invertible. Find the inverse of f.

Question 26.
Using integration find the area bounded by the lines x + 2y = 2, y – x = 1, 2x + y = 7.
OR
Using integration find the area bounded by the curves (x – 1)² + y² = 1 and x² + y² = 1

Question 27.
Find the maximum area of the isosceles triangle inscribed in the ellipse \(\frac { { x }^{ 2 } }{ { a }^{ 2 } } +\frac { { y }^{ 2 } }{ { b }^{ 2 } } =1\) with its vertex at one end of major axis.

Question 28.
Solve the following differential equation:

Question 29.
Find the equation of plane passing through the point (-1, -1, 2) and perpendicular to each of the following planes:
2x + 3y – 3z = 2 and 5x – 4y + z = 6
OR
Find the equation of the plane passing through the points (3, 4, 1) and (0, 1, 0) and parallel to the line \(\frac { x+3 }{ 2 } +\frac { y-3 }{ 7 } +\frac { z-2 }{ 5 }\)

Solutions

Solution 1.

Solution 2.

Solution 3.

Solution 4.

Solution 5.

Solution 6.

Solution 7.

Solution 8.
f(x) = tan x – x
f'(x) = sec²x – 1
\(\forall\) x ∈ R, The range of sec² x is [1, ∞)
So for all x ∈ R, f'(x) ≥ 0
Hence f(x) is always increasing function.

Solution 9.
Equation of plane passing through the point (1, 4, -2) is a(x – 1) + b(y – 4) + c (z + 2) = 0 …… (i)
where a, b, c are direction ratio of plane.
Plane (i) is parallel to the plane -2x + y + 3z = 0, so direction ratio of both planes will be in ratio

Solution 10.
P(not E or not F) = 0.25 or P(E’ ∪ F’) = 0.25
P(E ∩ F)’ = 0.25
P(E ∩ F)’ = 1 – P(E ∩ F)
0.25 = 1 – P (E ∩ F)
P(E ∩ F) = 1 – 0.25 = 0.75 ≠ 0
So E and F are not mutually exclusive.

Solution 11.
Let x teaching aids of type A andy teaching aids of type B are manufactured.
Objective function is maximize profit Z = ₹ (80x + 120y)
Subject to constraints are
9x + 12y ≤ 180 (fabricating constraint)
x + 3y ≤ 30 (finishing constraint)
x, y ≥ 0 (non-negative constraint)

Solution 12.

Solution 13.

Solution 14.

Solution 15.

Solution 16.

Solution 17.

Solution 18.

Solution 19.

Solution 20.

Solution 21.
Total questions = n = 5

Yes. In the life of students examination are necessary. By this, student keep his/her knowledge up-to-date.

Solution 22.
E₁ is the event. Bag I is selected.
E₂ is the event. Bag II is selected.

Solution 23.

Solution 24.

Solution 25.




Solution 26.

Solution 27.

Solution 28.

Solution 29.
Equation of plane passing through the point (-1, -1, 2) is
a (x + 1) + b (y + 1) + c (z – 2) = 0 …(1)
Here a, b, c are direction ratio of this plane.
Plane (1) is perpendicular to the planes
2x + 3y – 3z =2 and
5x – 4y + z = 6 so
2a + 3b – 3c = 0
5a – 4b + c = 0

We hope the CBSE Sample Papers for Class 12 Maths Paper 1 help you. If you have any query regarding CBSE Sample Papers for Class 12 Maths Paper 1, drop a comment below and we will get back to you at the earliest.

NCERT Exemplar Solutions for Class 12 Biology chapter 15 Biodiversity and Conservation

These Solutions are part of NCERT Exemplar Solutions for Class 12 Biology. Here we have given NCERT Exemplar Solutions for Class 12 Biology chapter 15 Biodiversity and Conservation

Multiple Choice Questions

Question 1.
Which of the following countries has the hiqhest biodiversity?
(a) Brazil
(b) South Africa
(c) Russia
(d) India
Answer:
(a) : The environment of Brazil is characterised by high biodiversity. Brazil’s large area comprises different ecosystems, which together sustain some of the world’s greatest biodiversity. It has the most known species of plants (55,000), freshwater fish (3,000) and mammals (700). Birds and reptiles are also found in abundance.

Question 2.
Which of the following is not a cause for loss of biodiversity?
(a) Destruction of habitat
(b) Invasion by alien species
(c) Keeping animals in zoological parks
(d) Over-exploitation of natural resources
Answer:
(c) : Keeping animals in zoological parks is not a cause for loss of biodiversity rather it is a method of conservation of biodiversity.

Question 3.
Which of the following is not an invasive alien species in the Indian context?
(a) Lantana
(b) Cynodon
(c) Parthenium
(d) Eichhornia
Answer:
(b) : Lantana, Eichhornia and Parthenium are all exotic species, which had been introduced in India. Lantana camara has  replaced many species in forests of Uttar Pradesh and Madhya Pradesh. Eichhornia (water hyacinth) has clogged water bodies including wetlands resulting in death of several aquatic plants and animals. Parthenium has pushed out several herbs and shrubs from open places in the plains.

Question 4.
Where among the following will you find pitcher plant?
(a) Rain forest of North-East India
(b) Sunderbans
(c) Thar Desert
(d) Western Ghats
Answer:
(a) : Pitcher plant is mainly found in rain forest of North-East India. This plant grows in the soil which has low nitrate. Hence, they obtain their nitrogen nutrition by trapping insects.

Question 5.
Which one of the following is not a feature of biodiversity hotspots?
(a) Large number of species
(b) Abundance of endemic species
(c) Mostly located in the polar regions
(d) Mostly located in the tropics
Answer:
(c) : Hotspots are areas of high endemism and high species richness. All over the world, some 34 such spots have been identified, including 3 in India (Western Ghats, Indo- Burma and Himalayas). The environmental conditions in polar regions do not favour large number of species or species richness.

Question 6.
Match the animals given in Column A with their location in Column B.

Choose the correct match from the following.
(a) i-A, ii-C, iii-B, iv-D
(b) i-D, ii-C, iii-A, iv-B
(c) i-C, ii-A, iii-B, iv-D
(d) i-C, ii-A, iii-D, iv-B
Answer:
(d)

Question 7.
What is common to the following plants: Nepenthes, Psilotum, Rauwolfa and Aconitum?
(a) All are ornamental plants.
(b) All are phylogenic link species.
(c) All are prone to over exploitation.
(d) All are exclusively present in the Eastern Himalayas.
Answer:
(c) : Nepenthes, Psilotum, Rauwolfia and Aconitum have either medicinal or ornamental importance. Hence, they are prone to over exploitation.

Question 8.
The one-horned rhinoceros is specific to which of the following National Parks?
(a) BhitarKanika
(b) Bandipur
(c) Kaziranga
(d) Corbett park
Answer:
(c)

Question 9.
Amongst the animal groups given below, which one has the highest percentage of endangered species?
(a) Insects
(b) Mammals
(c) Amphibians
(d) Reptiles
Answer:
(c) : The percentage number of endangered species in the list of threatened ones is 19% mammals, 17%birds, 21% reptiles, 22% amphibians.

Question 10.
Which one of the following is an endangered plant species of India?
(a) Rauwolfia serpentina
(b) Santalum album (Sandal wood)
(c) Cycas beddqmei
(d) All of the above
Answer:
(d)

Question 11.
What is common to Lantana, Eichhornia and African catfish?
(a) All are endangered species of India.
(b) All are key stone species.
(c) All are mammals found in India.
(d) All the species are neither threatened nor indigenous species of India.
Answer:
(d) : Lantana, Eichhornia and African catfish are exotic species or non-native species. Exotic species are often introduced for their economic and other uses. They often become invasive .and drive away the local species. These species are considered to be second major cause of extinction of species. Exotic species have proved harmful to both aquatic and terrestrial ecosystems.

Question 12.
The extinction of passenger pigeon was due to
(a) increased number of predatory birds
(b) over exploitation by humans
(c) non-availability of the food
(d) bird flu virus infection.
Answer:
(b) : Passenger pigeons (Ectopistes migratorious) were once one of the most abundant birds on our planet, living in North
AmeVica. But hunting on a very massive scale as well as deforestation, lead to their extinction. Many cruel ways were used for their hunting. The last individual of this species died in 1914 in Cincinnati Zoo.

Question 13.
Which of the following statements is correct?
(a) Parthenium is an endemic species of our country.
(b) African catfish is not a threat to indigenous catfishes.
(c) Steller’s sea cow is an extinct animal.
(d) Lantana is popularly known as carrot grass.
Answer:
(c) : Steller’s sea cow became extinct due to over exploitation by humans.

Question 14.
Among the ecosystem mentioned below, where can one find maximum biodiversity?
(a) Mangroves
(b) Desert
(c) Coral reefs
(d) Alpine meadows
Answer:
(c) : Coral reefs have the highest biodiversity with its macrobiota representing about 4-5% of the described global biota.

Question 15.
Which of the following forests is known as the ‘lungs of the planet Earth’?
(a) Taiga forest
(b) Tundra forest
(c) Amazon rainforest
(d) Rain forests of North East India
Answer:
(c) : Amazon rainforests are also called as the lungs of the planet earth. This rainforest in South America is the largest and most diverse tropical rain forest on our planet. It contributes around 20% of the total oxygen in our planet.

Question 16.
The active chemical drug reserpine is obtained from
(a) Datura
(b) Rauwolfia
(c) Atropa
(d) Papaver.
Answer:
(b) : Reserpine is an alkaloid that has been used as an anti hypertensive drug i.e., drug to lower blood pressure. It is obtained from the dried roots of Raiavolfia serpentina (Sarpagandha).

Question 17.
Which of the following groups exhibits more species diversity?
(a) Gymnosperms
(b) Algae
(c) Bryophytes
(d) Fungi
Answer:
(d)

Question 18.
Which of the below mentioned regions exhibit less seasonal variations?
(a) Tropics
(b) Temperates
(c) Alpines
(d) Both (a) & (b)
Answer:
(a) : There are no unfavourable seasons in tropics. Continued favourable environment has helped tropical organisms to gain more niche specialisation and increased diversity. Hence, tropics exhibit lesser seasonal variations.

Question 19.
The historic convention on Biological Diversity held in Rio de Janeiro in 1992 is known as
(a) CITES Convention
(b) The Earth Summit
(c) G-16 Summit
(d) MAB Programme.
Answer:
(b) : Earth Summit at Rio de Janeiro (1992), Brazil, promoted Convention on Biological Diversity (CBD) which was signed by 152 nations. Its recommendations came into effect on 29th December 1993. India became a party to this Convention on Biological Diversity in May, 1994.

Question 20.
What is common to the techniques (1) in vitro fertilisation, (2) Cryo preservation and (3) tissue culture?
(a) All are in situ conservation methods.
(b) All are ex situ conservation methods.
(c) All require ultra modern equipment and large space.
(d) All are methods of conservation of extinct organisms.
Answer:
(b) : Conservation of biodiversity can be broadly classified into two types : in situ (on-site) and ex situ (off site). Examples of in situ strategies include National parks, sanctuaries, Biosphere reserves etc. It is the preferred method to maintain species of wild animals in their natural habitats. This approach helps in conservation of total ecosystem. Ex situ approaches include conservation of those organisms, whose species may become extinct or decline heavily in number (due to a variety of reasons) in their natural habitat. This includes seed banks, cryopreservation, tissue culture, in vitro fertilisation etc.

 Very Short Answer Type Questions

Question 1.
What characteristics make a community stable?
Answer:
Characteristics which make community stable are :

1. Resistance to occasional disturbance (natural or man made).
2. Resistance to invasion by alien species.

Question 2.
What could have triggered mass extinctions of species in the past?
Answer:
The exact reason for mass extinctions of species in the past is not known. Scientists however assume that drastic environmental changes that followed events such as asteroid or meteorite impact or volcanic eruptions lead to mass extinctions.

These environmental changes include fall in temperature causing global cooling that trapped sea water in polar ice caps leading to lowering of sea level; or rise in temperature leading to disrupted ocean circulation patterns, green house effect and depletion of ozone layer etc.

Question 3.
What accounts for the greater ecological diversity of India?
Answer:
Greater ecological biodiversity in India is due to greater geographical and topographical diversity in the form of rainforest, deciduous forests, temperate forests, deserts, mangroves, wet lands alpine meadows etc.

Question 4.
According to David Tilman, greater the diversity, greater is the primary productivity. Can you think of a very low diversity man-made ecosystem that has high productivity?
Answer:
Man made ecosystems like agricultural cropfields of wheat, maize, sorghum, paddy etc., show high productivity but low diversity.

Question 5.
What does ‘Red’ indicate in the IUCN Red list (2004)?
Answer:
Red’ being the sign of danger, in IUCN Red list (2004) indicates threatened species. These species are under various degrees of extinction risk.

Question 6.
Explain as to how protection of biodiversity hotspots alone can reduce up to 30% of the current rate of species extinction.
Answer:
Hotspots are the areas that are rich in species, have high endemism, and are under constant threat. Although it bears only 2.4% of land area of the world, but by protecting hotspots the current rate of extinction of species can be reduced upto 30%.

Question 7.
What is the difference between endemic and exotic species?
Answer:
Endemic species refers to plant or animal species that is restricted to one or a few localities in its distribution. Endemic species are usually confined to islands and are vulnerable to extinction whereas exotic species is a species of organism that is not native to a locality having been moved there from its natural range by humans or other agents. Some alien species, such as rats, are introduced mainly by accident in cargoes or transport vessels, while others are transferred intentionally, often for their ornamental or economic value.

Question 8.
How does species diversity differ from ecological diversity?
Answer:
Species diversity is the variety in the number and richness of the species of a region. Species diversity is product of both species richness or evenness or equitability, i.e., species richness weighed by species evenness. For example, big cats, like tiger (Panthera tigris), and lion (Panthera leo) belong to the same genus Panthera but they all differ at the species level.

Ecosystem diversity explains the diverse number of niches, trophic levels and various ecological processes that sustain energy flow, food webs and recycling of nutrients. Within the geographical area, there may be variable number of ecosystems/habitats.

Question 9.
Why is genetic variation important in the plant Rauwolfia vomitoria
Answer:
Rnumnifin vomitoria grows in different ranges of Himalaya. This plant is a source of an alkaloid ‘reserpine’ which has medicinal value. Genetic variation is important for potency and concentration of active chemical reserpine present in it.

Question 10.
What is Red Data Book?
Answer:
International Union of Conservation of Nature and Natural Resources which which is now called World Conservation Union (WCU) maintains a red data book or red list which is a catalogue of taxa facing risk of extinction.
Red list has eight categories of species:

1. extinct
2. extinct in wild
3. critically endangered
4. endangered
5. vulnerable
6. lower risk
7. data deficiency
8. not evaluated.

Question 11.
Define gene pool.
Answer:
The sum total of all the genes found in an inbreeding population is known as gene pool.

Question 12.
What does the term ‘frugivorous’ mean?
Answer:
The term frugivorous is used for fruit eating animals.

Question 13.
What is the expanded form of IUCN?
Answer:
IUCN stands for ‘International Union of Conservation of Nature and Natural Resources’.

Question 14.
Define the terms (1) Bioprospecting (2) Endemism
Answer:

1. Bioprospecting refers to exploring molecular, genetic and species level products of economic importance.
2. Endemism refers to presence of some species in particular region only and nowhere else.

Question 15.
What is common to the species shown in figures A and B?

Answer:
Both are invasive weed species.

Question 16.
What is common to the species shown in figure A and B?

Answer:
Both are keystone species.

Short Answer Type Questions

Question 1.
How is the presently occurring species extinction different from the earlier mass extinctions?
Answer:
In earlier time, extinction of species occurred mainly due to natural causes or calamities like volcanic eruption, asteroid impact which lead to drastic environmental changes, etc., while at present human activities like deforestation, over-exploitation, pollution, intensive agriculture, introduction of alien species, etc., are the major causes of species extinction.

Question 2.
Of the four major causes for the loss of biodiversity alien species invasion, habitat loss and fragmentation, over-exploitation and co-extinctions which according to you is the major cause for the loss of biodiversity? Give reasons in support.
Answer:
Out of thy four causes for the loss of biodiversity, habitat loss and fragmentation seems to be the major cause of biodiversity losses. Loss of habitats result in annihilation of plants, microorganisms and forcing out of animals which in alien lands die out after some time. Fragmentation of habitats results in disruption of complex interactions amongst species, destruction of species in the cleared regions, annihilation of species restricted to deeper undisturbed parts of forests and decreased biodiversity in the habitat fragments. Animals requiring large territories (e.g., mammals, birds) are badly affected. Migrating animals would go astray and get killed.

Question 3.
Discuss one example, based on your day-to-day observations, showing how loss of one species may lead to the extinction of another.
Answer:
It has been observed that certain mutualistic relationships exist in nature. Extinction of one will automatically cause extinction of other. E.g., if the host fish becomes extinct, all the parasites exclusively found on it will also become extinct.

Question 4.
A species-area curve is drawn by plotting the number of species against the area. How is it that when a very large area is considered the slope is steeper than that for smaller areas?
Answer:
species-area relationship graph, Z is slope of line or regression coefficient which generally is 0.1-0.2 regardless of taxonomic group or region. When species area relationship is considered for a large area the slope of line becomes steeper having a value of 0.6-1.2. This is because the larger area has more food availability and other resources, so obviously more species can thrive there.

Question 5.
It is possible that productivity and diversity of a natural community remain constant over a time period of, say one hundred years?
Answer:
Although a typical community maintains itself, more or less in equilibrium with the prevailing conditions of the environment, in nature, communities are never stable; rather, they are dynamic, changing more or less regularly over time and space. They are never found permanently in complete balance with their component species, or with the physical environment. Environment is always changing over a period of time due to

1. variations in climatic and physiographic factors, and
2. The activities of the species of the communities themselves.
   These influences bring about marked changes in the dominants of the existing community, which is thus, sooner or later replaced by another community at the same place.

Question 6.
There is greater biodiversity in tropical/ subtropical regions than in temperate region. Explain.
KPlffl
Higher diversity in tropical areas is because of the following reasons:

1. Speciation is a function of time. Temperate areas have undergone frequent glaciation in the past. It killed most of the species. No such disturbance occurred in tropics where species continued to flourish and evolve undisturbed for millions of years.
2. There are no unfavourable seasons in tropics. Continued favourable environment has helped tropical organisms to gain more niche specialisation and increased diversity.
3. More solar energy is available in tropics. This promotes higher productivity and increased biodiversity.
4. Resource availability is higher in tropics.
5. There is reduced competition in tropics due to favourable environment.
6. Rate of extinction is low in tropics.

Question 7.
Why are the conventional methods not suitable for the assessment of biodiversity of bacteria?
Answer:
All forms of bacteria cannot be cultured in normal laboratory conditions which creates a problem in studying their morphological and biochemical characteristics. Biodiversity can be studied by examining morphological and biochemical characters. Such conventional methods cannot be applied for assessment of biodiversity of bacteria.

Question 8.
What criteria should one use in categorising a species as threatened?
Answer:
A threatened species is one which is unable to realise its full biotic potential and is, therefore, liable to become extinct. The inability of realising full biotic potential is due to depletion of food, habitat deterioration, over-exploitation, alien species, etc.

Question 9.
What could be the possible explanation for greater vulnerability of amphibians to extinction as compared to other animal groups?
Answer:
Amphibians are the group of animals which can live both on land and in water. They do not have scales and their skin is permeable to gases. A vast majority of amphibian species have to maintain moist skin surfaces because a significant amount of breathing occurs through skin. They easily get affected by the fluctuations in the surrounding environment.

Their eggs lack shell and hence are prone to dessication in an unprotective environment. Variations in environmental patterns can affect their physiological and reproductive features thereby affecting the survival and continuation of their race which accounts for their greater vulnerability to extinctions as compared to other animal groups.

Moreover, as amphibians need both aquatic and terrestrial habitats to survive, threats to either habitat can affect their population. Hence, amphibians are more vulnerable to habitat modification than the organisms which require only one habitat type.

Question 10.
Howido scientists extrapolate the total number of species on Earth?
Answer:
Scientists make a statistical comparison of the temperate-tropical species richness of an exhaustively studied group of insects and extrapolate this ratio to other groups of animals and plants to come up with a gross estimate of the total number of species on earth.

Question 11.
Humans benefit from diversity of life. Give two examples.
Answer:
Humans derive numerous benefits from diversity of living organisms. These are discussed as follows:
(1) Useful products : Plant species provide a variety of useful products such as timber, crops, fruits and vegetables, gums, resins, dyes, fragrance, perfumes, waxes, lubricants, hydrocarbons, rubber, latex, tannins, paper, tea, coffee, dry-fruits etc. Animals like goat, hen etc., serve as good source of food to humans. Milk, flesh, honey, egg, etc. are all useful animal products. Similarly, animal species provide, wool, fur, skin, leather, lac, silk, waxes, lubricants, pearls, ivory, horns, antlers etc. Large number of substances with therapeutic properties are obtained from variety of plant species. For example, quinine is obtained from the bark of plant Cinchona to combat malaria; taxol from the bark of trees Taxus brevifolia, Taxus baccata for treating cancer; reserpine from Rauwolfia serpentina for treating blood pressure and schizophrenia.

(2) Indirect benefits : Oxygen which made the earth hospitable and is indispensable for survival of almost all living organisms comes from plants which release it in the earth’s atmosphere by the process of photosynthesis. Plants also help in maintaining water cycle, replenishment of water table, bringing rains, preventing soil erosion and flood etc.
Aesthetic values of various natural ecosystems provide the opportunity of ecotourism and hence means of earning to humans.

Question 12.
List any two major causes other than anthropogenic causes for the loss of biodiversity.
Answer:
Loss of biodiversity may be due to:
(1) Natural extinction – Species with small population are always in danger of extinction due to natural causes like inbreeding depression, increased number of predators, development of more competitive species and environmental fluctuations like severe drought, severe winter, harsh summer, excess rain, floods, etc.

(2) Mass extinction – Many species dis-appeared due to catastrophes like glaciation, volcanoes, meteoriteimpact etc. Mass extinction has occurred many times in geological history. E.g., disappearance of dinosaurs coupled with loss of more than 50% of the existing species at the end of cretaceous period.

Question 13.
What is an endangered species? Give an example of an endangered plant and animal species each?
Answer:
Endangered species are those species which are facing high risk of extinction in the near future due to decrease in their habitat and excessive predation or poaching. Example of endangered animal is red panda (Ailurus fulgens). Example of endangered plant is Lycopodium nutans.

Question 14.
What are sacred groves and their role in biodiversity conservation?
Answer:
Sacred groves are forest patches around places of worship which are held in high esteem by tribal communities. They are the most undisturbed forest patches (island of pristine forests) which are often surrounded by highly degraded landscapes.
Some examples of sacred groves are-

1. Khasi and Jaintia Hills in Meghalaya.
2. Aravalli Hills of Rajasthan.
3. Sarguja, Chand and Batsar areas of Madhya pradesh.
4. Western Ghats of Maharashtra and Madhya pradesh.

Role , of sacred groves in biodiversity conservation are as follows:
Sacred groves are serving as refugia for a number of rare, endangered and endemic species. Not a single branch is allowed to be cut from these forests. As a result many endemic species which are rare or have become extinct ‘ elsewhere can be seen to flourish here.

Question 15.
Suggest a place where one can go to study coral reefs, mangrove vegetation and estuaries.
Answer:
Place suggested for studying coral reefs is Andaman and Nicobar island. Mangrove vegetation can be well studied in West Bengal sunderbans and estuaries can be studied in coastal areas of Kerala.

Question 16.
1s it true that there is more solar energy available in the tropics? Explain briefly.
Answer:
Tropics lie on either side of equator between 30° south latitudes. It is limited in latitude by the tropic of cancer in the northern hemisphere and the tropic of capricorn in the southern hemisphere. The tropics include the areas on earth surrounding the equator where the sun reaches a subsolar point (a point directly overhead). These regions receive the most direct sunlight and heat energy from the sun and are the hottest.

Question 17.
What is co-extinction? Explain with a suitable example?
Answer:
When a species becomes extinct, the plant or animal species associated with it in an obligatory way also becomes extinct. This is called co-extinction. E.g., if the host fish becomes extinct, all the parasites exclusively found on it will also become extinct.

Long Answer Type Questions

Question 1.
Elaborate how invasion by an alien species reduces the species diversity of an area.
Answer:
Non-native or alien species are often introduced inadvertently for their economic and other uses. They often become invasive and drive away the local species. These species are considered to be second major cause of extinction of species. Exotic species have proved harmful to both aquatic and terrestrial ecosystems. This can be explained as follows:

Water hyacinth (Eichhornia crassipes) was introduced in Indian waters to reduce pollution. It has clogged water bodies including wetlands at many places resulting in death of several aquatic plants and animals. Nile Perch (a predator fish) was introduced in lake Victoria of South Africa. It killed and eliminated ecologically unique assemblage of over 200 native species of small cliched fish.

Question 2.
How can you, as an individual, prevent the loss of biodiversity?
Answer:
Biodiversity has great importance to mankind. But certain human activities are leading to biodiversity losses. In order to maintain biodiversity we all need to put an effort to save our ecosystem. Following measures can be undertaken to prevent biodiversity losses:

1. Educate people about the importance of wildlife and their conservation.
2. Implementing laws imposed by the government to protect biodiversity.
3. Avoiding over-exploitation of natural re-sources.
4. Promoting afforestation.
5. Avoiding the introduction of alien species.
6. Checking habitat loss and fragmentation of species.
7. Reducing pollution, etc.

Question 3.
Can you think of a scientific explanation, besides analogy used by Paul Ehrlich, for the direct relationship Answer:
Species diversity is formally measured as an index combining numbers and proportion of each species present in an ecosystem. A species diversity index reflects the number of links in a food web. The relationship between species diversity and ecosystem stability has been the most studied and debated topic since 1950.

Paul Ehrlich in his rivet popper hypothesis tried to prove the dependence of ecosystem stability on species diversity. Another scientific explanation to his theory is as follows :
If we imagine that only one food chain is operating in an ecosystem where only one species is occupying each trophic level then this type of food chain is most susceptible to destruction as loss or extinction of any species can lead to destruction of other species dependent on it for food. On the other hand, if many alternatives are available at each trophic level in the food sequence a food web will be formed decreasing the dependence of a species on a particular species for food. Then even extinction of one species will not affect any other species due to availability of alternative food. That is why, in nature food chains never operate singly rather many food chains are interconnected to form food web which gives stability to the ecosystem.

Question 4.
Though the conflict between humans and wildlife started with the evolution of man, the intensity of conflict has increased due to the activities of modern man. Justify your answer with suitable examples.
Answer:
Since the humans evolved on earth, they have been exploiting wildlife for their survival and continuity. Initially the degree of exploitation of wildlife was very less but with increasing civilisation and modernisation, the humans are becoming more demanding. Their ever increasing population is inventing new ways for better survival and existence which at times are interferring with the ways of nature leading to extinction of wildlife species. Hence, the conflict between humans and wildlife continues and has been worsened.
This can be explained as follows:
(1) Destruction of habitat and fragmentation : Over-population, urbanisation and industrialisation require additional land every year. It can come through destruction or fragmentation of natural habitats of wild animals through filling wetlands, ploughing grasslands, cutting down trees, burning a forest and clearing some area of vegetation. Loss of habitat results in annihilation of plants, microorganisms and forcing out of animals Which in alien lands die out after some time. Fragmentation of habitats results in disruption of complex interactions amongst species, destruction of species in the cleared regions, annihilation of species restricted to deeper undisturbed parts of forests and decreased biodiversity in the habitat fragments.

(2) Indiscriminate hunting : Hunting of animals for food, hide, tusks, horn, at excessive levels may lead to species extinction. Dodo bird and passenger pigeon have already become extinct. Many species of fish, molluscs, sea turtle and whales are facing the risk of extinction.

(3) Introduction of alien species:

• Non-native or alien species are often introduced inadvertantly for their economic and other uses. They often become invasive and drive away the local species. These species are considered to be second major cause of extinction of species.
• Carrot grass has replaced herbs and shrubs of open spaces.
• Water hyacinth has become dominant species in pools and ponds.
• Pollution : Excessive use of pesticides has polluted both groundwater and surface 6. water bodies. Many sensitive species have disappeared.
• Intensive agriculture : Spread of agriculture is at the cost of wetlands, grasslands and forests. Destruction of habitats results in extinction of species. Intensive agriculture is also based on a few high yielding varieties. As a result, there is reduction in the genetic diversity. It increases vulnerability of the crop plants to sudden attack by pathogens and pests.

Question 5.
What is an ecosystem service? List any four important ecosystem services provided by the natural ecosystems. Are you in favour or against levying a charge on the service provided by the ecosystem?
Answer:
A wide range of economic, environmental and aesthetic benefits provided by ecolpgical process of an ecosystem are called ecosystem services. Services of healthy forest ecosystem are –

1. Forests provide food in the form of roots, tubers, leaves fruits etc.
2. They provide timber for building purposes of houses, ships, railway sleepers, sport good, agriculture tools etc.
3. Number of useful products like camphor, essential oils, tannins dyes gums, resins, drugs are obtained from forests.
4. Trees in forests produce oxygen during photosynthesis and keep environment cool by regulating transpiration and precipitation.
5. Trees prevent soil erosion floods and provide shelter.
6. Many insect pollinators help in pollination of plants thereby bring about flower and fruits formation.
7. Microbes help in decomposition of waste products and recycling of nutrients. Ecosystem provides lots of services. Instead of putting a price tag or levying a charge against service a sincere effort should be made to protect ecosystem to continue its services.

Question 6.
Describe the consumptive use value of biodiversity as food, drugs and medicines, fuel and fibre with suitable examples.
Answer:
The consumptive use value of biodiversity as food, drugs and medicines, fuel and fibre has been described as follows :
(1) Source of food : Several thousand species of edible plants and animals are known. However, 85% of the world’s food production is met by cultivating less than 20 plant species. Three carbohydrate-rich crops namely, wheat, corn (maize) and rice alone yield nearly two-third of the food production. To meet the demands of increasing human population, man is not only exploring new varieties of plants but also animal food. Biodiversity is also used as a source material for breeding improved varieties. To improve the desired traits, commercial/domesticated. species are crossbred with their wild relatives.

In this way, disease resistant and high yielding varieties of crops (e.g.,wheat, rice, maize, sugarcane) and fruits have been developed. For example, cross breeding of wild rice species has helped ! in developing new varieties which are resistant to four main rice diseases. Similarly, potato has been made resistant to late blight disease, potato mosaic virus, five races of cyst nematodes etc., through crossbreeding experiments. Also, hybrid animals varieties have been produced to increase the production of milk, meat, eggs etc. This indicates the need for protecting biodiversity for breeding programmes in agriculture, horticulture, floriculture, animal husbandry, apiculture, sericulture, lac culture, piggery, poultry and fishery.

(2) Fibers : A variety of plant species such as cotton, flax, hemp, jut, Agave, etc., are the major sources of fibers. More and more variety of plants are being explored for obtaining superior fibers.

(3) Useful products : Plant species provide a variety of useful products such as gums, resins, dyes, fragrance, perfumes, waxes, lubricants, hydrocarbons, rubber, latex, tannins, paper, tea, coffee, dry-fruits etc. Similarly, animal species provide, wool, fur, skin, leather, honey, lac, silk, waxes, lubricants, pearls, ivory, horns, antlers etc.

(4) Drugs and medicines : Large number of substances with therapeutic properties are obtained from variety of plant species. For example, quinine is obtained from the bark of plant Cinchona to combat
malaria ; taxol from the bark of Taxus for treating cancer; morphine from Papaver somniferum for pains; reserpine from Rauwolfia serpentina for treating blood pressure and schizophrenia. Ayurvedic medicines available in the market for treating innumerous diseases in man are based on plant product.

(5) As fuel wood : 80% of forest wood (most trees) are used as fuel wood. E.g., Acacia nilotica, Albizzia sp. Mangifera indica etc.

Question 7.
Species diversity decreases as we move away from the equator towards the poles. What could be the possible reasons?
Answer:
Species diversity decreases as we move away from the equator towards the poles, because of the following reasons :

1. Temperature decreases and conditions become harsh.
2. Both the amount and intensity of solar radiation decreases.
3. Limited resource availability.
4. Higher competition due to unfavourable environment.
   Speciation is generally a function of time and environmental stability, so if conditions are too harsh, it is difficult for species to survive.

Question 8.
Explain briefly the ‘rivet popper hypothesis’ of Paul Ehrlich.
Answer:
According to this hypothesis proposed by Paul Ehrlich (1981), the relationship between species richness and ecosystem functioning is non-linear, and may follow a variety of possible trajectories. The loss of a few species (or rivets holding together an aeroplane) will create no problem in the beginning, but beyond a certain point losses will cause catastrophic effect. Loss of rivets or key species that drive major ecosystem functions is a more serious threat for the ecosystem. Besides, the rich biodiversity is not only essential for ecosystem health, but imperative for the very survival of the human beings.

Question 9.
The relation between species richness and area for a wide variety of taxa turns out to be a rectangular hyperbola. Give a brief explanation.
Answer:
German naturalist and geographer Alexander von Humboldt while exploring the wilderness of South American jungles found that within a region the species richness increased with increasing area but upto a certain limit. The relationship between species richness and area turned out to be rectangular hyperbola for a wide variety of taxa Whether they are birds, bats, freshwater fishes or flowering plants. On a logarithmic scale it is a straight line and is represented by equation: log S = log C + Z log A

Here S is species richness, Z is slope of line or regression coefficient, C is Y intercept while A is area. The relationship between area and species richness in most cases is represented by a rectangular hyperbola which indicates that if we take a larger area under consideration then the number of species increases because more individuals get included in the sample and large areas are environmentally more heterogenous than small areas. But this increase in number is neither uniform nor unlimited. Ecologists have proposed wide range of factors determining the slope and elevation of species area curve. These factors include relative balance between immigration and extinction, rate and magnitude of disturbance predator-prey dynamics, etc.

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