ICSE

ML Aggarwal Class 8 Solutions for ICSE Maths Model Question Paper 6

Questions 1 to 8 is of 1 mark each.
Question 1.
If x + y = 11 and xy = 24, then x² + y² =
(a) 121
(b) 73
(c) 48
(d) none of these
Solution:

Question 2.
Factors of a³ – 64a are
(a) a(a – 8)²
(b) (a + 8) (a – 8)
(c) a(a + 8) (a – 8)
(d) a(a + 8)²
Solution:

Question 3.
If 3(y – 3) = 5(2y + 1) then y is equal to
(a) 3
(b) -3
(c) 2
(d) -2
Solution:

Question 4.
If one angle of a parallelogram is 30° less than other angles, then the larger angle is
(a) 150°
(b) 75°
(c) 105°
(d) 210°
Solution:

Question 5.
A polyhedron has 7 faces, 10 vertices and 15 edges. Name of the polyhedron is
(a) hexagonal prism
(b) pentagonal prism
(c) hexagonal pyramid
(d) none of these
Solution:

Question 6.
The base of a triangle is twice its height. If the area of the triangle is 25 cm², then the base is
(a) 10 cm
(b) 20 cm
(c) 5 cm
(d) 25 cm
Solution:

Question 7.
From a well-shuffled deck of 52 playing cards, one card is drawn at random then the probability that card drawn is a blackjack

Solution:

Question 8.
Amongst the following digits, the one having exactly one line of symmetry is
(a) 0
(b) 3
(c) 6
(d) 8
Solution:

Section-B
Questions 9 to 14 are of 2 marks each.
Question 9.
Using a suitable identity, evaluate (9.7)².
Solution:

Question 10.
Factorize x²y²(a⁴ + b⁴) + a²b²(x⁴ + y⁴).
Solution:

Question 11.
Sum of three consecutive odd numbers is 153. Find the numbers.
Solution:

Question 12.
If each interior angle of a regular polygon is 108°, then find the number of sides of the polygon.
Solution:

Question 13.
Verify Euler’s formula for a decagonal pyramid.
Solution:

Question 14.
A cuboid is of dimensions 24 cm × 30 cm × 36 cm. How many small cubes with side 6 cm can be placed in the cuboid?
Solution:

Section-C
Questions 15 to 24 are of 4 marks each.
Question 15.
Simplify the following expressions and evaluate it when x = 1, y = -1
(5xy – 3x² + 2y²) × (5y² – 8xy + 3x²) + 9x³y – 8y⁴ + 12x⁴
Solution:

Question 16.
Factorize: 15(2x – 3y)² – 4(4x – 6y) – 16
Solution:

Question 17.
Two years ago Ramesh was three times as old as his son. Two years later, twice of his age will be equal to the five times that of his son’s age. Find their present ages.
Solution:

Question 18.
In the given figure ABCD is a parallelogram in which ∠DAP = 40°, ∠BAP = 25° and ∠CPD = 105°, find
(i) ∠ABP
(ii) ∠PDC
(iii) ∠ACB
(iv) ∠CBD
Solution:

Question 19.
Construct a rhombus TRUE whose one side TR = 4 cm and diagonal TU = 6.5 cm.
Solution:

Question 20.
Construct a parallelogram GOLD in which diagonal GL = 3.8 cm, diagonal OD = 4.6 cm and angle between diagonals is 60°.
Solution:

Question 21.
In the given figure, O is the centre of the circle. If PT is tangent to the circle at point T, find the size of each lettered angle.

Solution:

Question 22.
A rectangular sheet of tin foil of size 30 cm × 18 cm can be rolled to form a cylinder two ways along length and breadth. Find the ratio of volumes of the two cylinders thus formed.
Solution:

Question 23.
Construct a histogram for the following data:

Solution:

Question 24.
Height of a room is half of its length and its breadth is \(\frac{3}{2}\) of the height. If the cost of painting its four walls at the rate of ₹1.75 per m² is ₹ 196, then find the cost of tiling the floor of the room at the rate of ₹8.50 per m².
Solution:

Section-D
Questions 25 to 29 are of 6 marks each.
Question 25.
If \(x+\frac{1}{x}=5\), them find

Solution:

Question 26.
In the given figure, ABCD is a rhombus and DCFE is a square, If ∠ABC = 56°, find
(i) ∠DAG
(ii) ∠FEG
(iii) ∠AGC

Solution:

Question 27.
The figure given below shows a field with the measurement given in metres. Find the area of the field.

Solution:

Question 28.
A bag contains 5 red, 6 black and 4 white balls. A ball is drawn at random from the bag. Find the probability that the ball drawn is
(i) white
(ii) not black
(iii) red or black
Solution:

Question 29.
A school decided to award prizes to their students for three values, honesty, punctuality and obedience. The value of prize for punctuality is \(\frac{5}{6}\) of the value of prize for honesty and value of prize for obedience is \(\frac{4}{5}\) of the value of prize for punctuality. If the total value of the three prizes is ₹1500, find the value of each prize. Which quality you prefer to be rewarded most and why? What values are being promoted?
Solution:

ML Aggarwal Class 8 Solutions for ICSE Maths

ML Aggarwal Class 8 Solutions for ICSE Maths Model Question Paper 5

Choose the correct answer from the given four options (1-2):
Question 1.
In a pentagonal pyramid number of faces, vertices and edges are
(a) F = 6, V = 6, E = 10
(b) F = 7, V = 7, E = 12
(c) F = 6, V = 8, E = 12
(d) none of these.
Solution:

Question 2.
If the lateral surface area of a cube is 144 cm, then its volume is
(a) 36cm³
(b) 216 cm³
(c) 288 cm³
(d) none of these
Solution:

Question 3.
Draw the top, front and side views of the given solid.

Solution:

Question 4.
The area of a trapezium is 96 cm². If the lengths of its two parallel sides are 14 cm and 10 cm, then find the perpendicular distance between parallel sides.
Solution:

Question 5.
In the given figure, C is the centre of the circle. The tangent to the circle of radius 6 cm from a point P outside the circle is of length 8 cm. Find the distance of the point P from the farthest point of the circumference.

Solution:

Question 6.
Construct a quadrilateral PQRS in which PQ = 5.5 cm, RS = 6.5 cm, PS = 4.4 cm, PR = 6.5 cm and QS = 7.1 cm.
Solution:

Question 7.
The length, breadth and height of cuboidal water tank is 7 m, 6 m and 2 m respectively. If 4200 litre of water is pumped out from the tank. Find the fall in water level in the tank.
Solution:

Question 8.
Construct a rhombus PQRS such that PQ = 5.4 cm and ∠P = 60°. Also, draw its lines of symmetry.
Solution:

Question 9.
A road roller has a diameter 84 cm and its width is 1.2 m. If it takes 500 complete revolutions to level a playground. Find the area of the playground. Also, find the cost of levelling the playground at a rate of 50 paise per m².
Solution:

Question 10.
Construct a rectangle ABCD, such that AB = 6.4 cm and BD = 7.6 cm.
Solution:

ML Aggarwal Class 8 Solutions for ICSE Maths

ML Aggarwal Class 8 Solutions for ICSE Maths Model Question Paper 3

Questions 1 to 8 is of 1 mark each.
Question 1.
Product of rational number \(\frac{-4}{7}\) and itsadditive inverse is
(a) \(\frac{16}{49}\)
(b) \(\frac{-16}{49}\)
(c) 1
(d) 0
Solution:

Question 2.
What should be subtracted from \(\frac{-3}{5}\) to get \(\frac{-2}{3}\)?

Solution:

Question 3.
The value of \(\left(\frac{2}{3}\right)^{0}+\left(\frac{2}{3}\right)^{-1}\) is

Solution:

Question 4.
Standard form of 0.00000000234 is
(a) 2.34 × 10^-8
(b) 23.4 × 10^-10
(c) 2.34 × 10^-9
(d) 234 × 10^-1
Solution:

Question 5.
The volume of a cube is 216 m³. Length of its side is
(a) 3 m
(b) 6 m
(c) 9 m
(d) 12 m
Solution:

Question 6.
When the difference of a 2-digit number ab (a > b) and the number obtained by reversing the digits is divided by 9, then quotient is
(a) a + b
(b) b – a
(c) a – b
(d) none of these
Solution:

Question 7.
Amar buys a toy for ₹ 120 and sells it for ₹ 144, his profit % is
(a) 5%
(b) 10%
(c) 20%
(d) 24%
Solution:

Question 8.
If 567×8 is divisible by 9, then value of x is
(a) 1
(b) 2
(c) 3
(d) 4
Solution:

Section-B
Questions 9 to 14 are of 2 marks each.
Question 9.
Ramesh bought a fan for ₹ 1320 including 10% VAT. Find the price of the fan before VAT was added.
Solution:

Question 10.
Find A in the addition

Solution:

Question 11.
Find the value of x for which \(\left(-\frac{4}{5}\right)^{2} \times\) \(\left(-\frac{5}{4}\right)^{2 x}=\frac{625}{256}\).
Solution:

Question 12.
Using appropriate properties of operations of rational numbers, evaluate:

Solution:

Question 13.
What number should be subtracted from the sum of \(\frac{-5}{12}\) and \(\frac{2}{3}\) to get \(\frac{5}{4}\) ?
Solution:

Question 14.
If n(ξ) = 40, n(A) = 23, n(B’) = 28 and n(A ∪ B’) = 9, find n(A ∩ B).
Solution:

Section-C
Questions 15 to 24 are of 4 marks each.
Question 15.
In an auditorium, the number of rows is equal to the number of chairs in each row. If there are 5184 chairs in the auditorium, find the number of rows.
Solution:

Question 16.
Insert 5 rational numbers between \(\frac{1}{3}\) and \(\frac{1}{2}\).
Solution:

Question 17.
Find the smallest number by which 10584 should be multiplied so that product is a perfect cube. Also find the cube root of the product.
Solution:

Question 18.
In a 3-digit number unit’s digit is 2 less than hundred’s digit and hundred’s digit is 3 less than the ten’s digit. If the sum of the original number and number obtained by reversing the digits is 968, find the number.
Solution:

Question 19.
Rohit purchased some oranges at 3 for ₹5 and sold them at 5 for ₹12. Thus he gained ₹143 in all. How many oranges did he purchase?
Solution:

Question 20.
How much per cent above the cost price should a shopkeeper mark his goods so that after allowing a discount of 20% he still earns a profit of 20%?
Solution:

Question 21.
Find the difference between S.I. and C.I. on ₹2000 for \(1 \frac{1}{2}\) years at 6% p.a., compound interest being reckoned half-yearly.
Solution:

Question 22.
If 5 men or 7 women can earn ₹903 in a day, how much will 10 men and 5 women earn in a day?
Solution:

Question 23.
A hostel had rations for 150 students for 60 days. After 12 days, 30 more students join the hostel. How long will the remaining rations last?
Solution:

Question 24.
Simplify the following expression and write in the exponential form:
3^-5 × 3² ÷ 3⁶ × (2² × 3)² + \(\left(\frac{2}{3}\right)^{-1}\) + 2^-1 + \(\left(\frac{1}{19}\right)^{-1}\).
Solution:

Section-D
Questions 25 to 29 are of 6 marks each.
Question 25.
Ramesh scored 30% marks in an exam and failed by 20 marks, while Suresh scored 40% marks and got 40 marks more than the minimum marks required to pass the exam. Find the maximum marks and pass percentage.
Solution:

Question 26.
If ξ = {x | x ϵ W, x < 20}, A = {factors of 18} and B = {multiples of 3}, find
(i) A ∪ B
(ii) A ∩ B
(iii) (A ∪ B)’.
Also verify that n(A ∪ B) = n(A) + n(B) – n(A ∩ B).
Solution:

Question 27.
A and B together can do a piece of work in 15 days; B and C together can do it in 12 days; C and A can do it in 20 days. How long will they take to finish the work, working together? Also find the number of days taken by each to do the same work, working alone.
Solution:

Question 28.
Is 31104 a perfect square number? If not then find the smallest number by which 31104 should be divided so that quotient is a perfect square. Also, find the square root of the quotient.
Solution:

Question 29.
Three numbers are in the ratio 1:3:5 and sum of their cubes is 52479. Find the numbers.
Solution:

ML Aggarwal Class 8 Solutions for ICSE Maths

ML Aggarwal Class 8 Solutions for ICSE Maths Model Question Paper 2

Choose the correct answer from the given four options (1-2):
Question 1.
If 295×703 is divisible by 11, then value of x is
(a) 5
(b) 6
(c) 7
(d) 8
Solution:

Question 2.
If C.P. of an article is ₹500 and S.P. is ₹600, then, his profit % is
(a) 10%
(b) 15%
(c) 20%
(d) 25%
Solution:

Question 3.
Find the values of the letters in the following and give reasons for the steps involved:

Solution:

Question 4.
Ramu bought a fan for ₹1080 including 8% VAT. Find the price of fan before VAT was added.
Solution:

Question 5.
Find the amount and compound interest on ₹2000 for 2 years at 5% per annum, interest payable yearly.
Solution:

Question 6.
If P = {letters of the word HYDERABAD} and Q= {letters ofthewordALLAHABAD}, find
(i) P ∪ Q
(ii) P ∩ Q
Also verify that
n(P ∪ Q) = n(P) + n(Q) – n(P ∩ Q).
Solution:

Question 7.
A blanket was marked for ₹500. A shopkeeper allows a discount of 10%. But due to partial damage in the blanket he has to give an extra discount of 20%. Find the S.P. of the blanket.
Solution:

Question 8.
In a 3 digit number unit’s digit, ten’s digit and hundred’s digit are in the ratio 3 : 5 : 7. If the difference of original number and number obtained by reversing the digits is 396, find the number.
Solution:

Question 9.
In an exam atleast 40% marks are required to pass the exam. Rohit uses unfair means to pass the exam but fails by 20 marks. If he scored 220 marks, then find the maximum marks.
Is using unfair means in exam is good? Why should we not use unfair means?
Solution:

Question 10.
Find the sum invested for \(1 \frac{1}{2}\) years compounded half-yearly at the rate of 8% p.a. that will amount to ₹ 17576.
Solution:

ML Aggarwal Class 8 Solutions for ICSE Maths

ML Aggarwal Class 8 Solutions for ICSE Maths Model Question Paper 1

Choose the correct answer from the given four options (1-2):
Question 1.
Sum of rational number \(\frac { 5 }{ 7 }\) and its additiveinverse is
(a) 1
(b) 0
(c) -1
(d) none of these
Solution:

Question 2.
Product of two rational numbers is 1. If one of them is \(\frac { 4 }{ 5 }\), then other is

Solution:

Question 3.
Find the value of x for which \(\left(\frac{4}{9}\right)^{x} \times\left(\frac{3}{2}\right)^{-1}\) = \(\frac{8}{27}\).
Solution:

Question 4.
Express the following numbers in standard form:
(i) 0.0000000000578
(ii) 345700000000000
Solution:

Question 5.
Insert ten rational numbers between \(\frac{-4}{5}\) and \(\frac{2}{3}\).
Solution:

Question 6.
Find the cube root of 50653.
Solution:

Question 7.
Find the smallest number by which 3645 should be divided so that quotient is a perfect cube.
Solution:

Question 8.
If p = \(\frac{-3}{5}\), q = \(\frac{1}{2}\), r= \(\frac{-7}{9}\),then verify p × (q + r) = p × q + p × r.
Solution:

Question 9.
Find the square root of 7056 by prime factorisation method.
Solution:

Question 10.
Find the least number which must be added to 59000 to make it a perfect square.
Solution:

ML Aggarwal Class 8 Solutions for ICSE Maths