Pariksha SaathiPedagogy
CTET Maths MCQ with Answers, Paper 2 (Classes VI-VIII)
234 practice questions on Mathematics, Classes VI-VIII (Paper II) for CTET Paper II (Mathematics and Science), with answers; most also have an explanation or a worked solution. Try each one before you open its answer.
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Q.101
Solve: (x − 2)/5 + 3 = (x + 4)/3.
- A 9.5
- B −11.5
- C 17.5
- D 19
Show answer
Correct answer: (A) 9.5
Multiply both sides by 15: 3(x − 2) + 45 = 5(x + 4), so 3x + 39 = 5x + 20, 2x = 19 and x = 9.5. Check: 7.5/5 + 3 = 4.5 and 13.5/3 = 4.5.
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Q.102
Two angles are complementary, and one of them is 18° more than the other. What is the larger angle?
- A 36°
- B 54°
- C 81°
- D 99°
Show answer
Correct answer: (B) 54°
x + (x + 18°) = 90°, so 2x = 72° and x = 36°. The larger angle is 36° + 18° = 54°; check: 36° + 54° = 90°.
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Q.103
Which of the following is NOT true for all integers a, b and c? (Assume there is no division by zero.)
- A a + (−a) = 0
- B a × (b + c) = a × b + a × c
- C a ÷ (b ÷ c) = (a ÷ b) ÷ c
- D a × (−1) = −a
Show answer
Correct answer: (C) a ÷ (b ÷ c) = (a ÷ b) ÷ c
Division is not associative: (−24) ÷ [(−4) ÷ 2] = (−24) ÷ (−2) = 12, but [(−24) ÷ (−4)] ÷ 2 = 6 ÷ 2 = 3. The other three are the additive inverse, the distributive property and multiplication by −1.
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Q.104
A polyhedron has 8 faces and 12 vertices. Using Euler's formula, how many edges does it have?
- A 6 edges
- B 18 edges
- C 20 edges
- D 22 edges
Show answer
Correct answer: (B) 18 edges
Euler's formula is F + V − E = 2, so 8 + 12 − E = 2 and E = 18. (A hexagonal prism has exactly these numbers.)
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Q.105
How many bricks, each 25 cm × 12.5 cm × 7.5 cm, are needed to build a wall 10 m long, 30 cm thick and 2.5 m high, if the space taken by mortar is ignored?
- A 320
- B 3200
- C 6400
- D 32000
Show answer
Correct answer: (B) 3200
Volume of the wall = 1000 × 30 × 250 = 7500000 cm³ and volume of one brick = 25 × 12.5 × 7.5 = 2343.75 cm³. Number of bricks = 7500000 ÷ 2343.75 = 3200.
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Q.106
Which of the following sets of four numbers, taken in the given order, is NOT in proportion?
- A 4, 6, 10, 15
- B 3, 5, 9, 15
- C 5, 8, 15, 20
- D 2, 7, 6, 21
Show answer
Correct answer: (C) 5, 8, 15, 20
Four numbers are in proportion when the product of the extremes equals the product of the means. For 5, 8, 15, 20: 5 × 20 = 100 but 8 × 15 = 120. The others pass (4 × 15 = 6 × 10, 3 × 15 = 5 × 9, 2 × 21 = 7 × 6).
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Q.107
8 tailors stitch 120 shirts in a day. Working at the same rate, how many shirts will 14 tailors stitch in a day?
- A 68.6
- B 126
- C 210
- D 1680
Show answer
Correct answer: (C) 210
One tailor stitches 120 ÷ 8 = 15 shirts a day, so 14 tailors stitch 14 × 15 = 210 shirts (direct proportion).
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Q.108
A shopkeeper buys a fan for ₹1,250 and sells it for ₹1,425. What is his profit per cent?
- A 12.3%
- B 14%
- C 17.5%
- D 114%
Show answer
Correct answer: (B) 14%
Profit = 1425 − 1250 = ₹175. Profit % = (175 ÷ 1250) × 100 = 14%, calculated on the cost price.
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Q.109
How many diagonals does a polygon with 7 sides (a heptagon) have?
- A 4 diagonals
- B 14 diagonals
- C 21 diagonals
- D 28 diagonals
Show answer
Correct answer: (B) 14 diagonals
From each vertex, diagonals go to 7 − 3 = 4 other vertices (not to itself or its two neighbours). 7 × 4 = 28 counts each diagonal twice, so there are 28 ÷ 2 = 14 diagonals.
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Q.110
Consider the statements: 1. If a number is divisible by 3, it is divisible by 9. 2. If a number exactly divides each of two numbers, it exactly divides their difference. 3. If a number is divisible by both 3 and 5, it is divisible by 15. Which of these are true?
- A Only 1 and 2
- B Only 2 and 3
- C Only 3
- D 1, 2 and 3
Show answer
Correct answer: (B) Only 2 and 3
Statement 1 is false: 12 is divisible by 3 but not by 9. Statement 2 is a property of divisibility, and statement 3 is true because 3 and 5 are co-prime, so their product 15 divides the number.
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Q.111
The angles of a triangle are in the ratio 2 : 3 : 4. The triangle is:
- A Acute-angled and scalene
- B Right-angled and scalene
- C Obtuse-angled and scalene
- D Acute-angled and isosceles
Show answer
Correct answer: (A) Acute-angled and scalene
2x + 3x + 4x = 180°, so x = 20° and the angles are 40°, 60° and 80°. All are less than 90° and all are different, so the triangle is acute-angled and scalene.
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Q.112
Consider the following statements. 1. An equilateral triangle has rotational symmetry of order 6. 2. A circle has infinitely many lines of symmetry. Which of the statements is/are correct?
- A Only 1
- B Only 2
- C Both 1 and 2
- D Neither 1 nor 2
Show answer
Correct answer: (B) Only 2
An equilateral triangle looks the same after turns of 120°, 240° and 360°, so its order is 3, not 6; statement 1 is false. Every line through the centre of a circle is a line of symmetry, so statement 2 is true.
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Q.113
Which of the following numbers can NOT be a perfect square?
- A 4,48,900
- B 1,05,625
- C 64,000
- D 7,29,316
Show answer
Correct answer: (C) 64,000
A perfect square always ends in an even number of zeros, and 64,000 ends in three zeros, so it is not a square. The others are squares: 325² = 1,05,625, 670² = 4,48,900 and 854² = 7,29,316.
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Q.114
How many factors does 144 have?
- A 12
- B 14
- C 16
- D 15
Show answer
Correct answer: (D) 15
The factors of 144 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72 and 144, that is 15. The count is odd because 144 = 12 × 12 is a perfect square and 12 is counted only once.
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Q.115
1729, the Hardy-Ramanujan number, is the smallest number that can be written as the sum of two cubes in two different ways. Which are the two ways?
- A 1³ + 12³ and 9³ + 10³
- B 2³ + 12³ and 9³ + 10³
- C 1³ + 12³ and 8³ + 11³
- D 6³ + 11³ and 9³ + 10³
Show answer
Correct answer: (A) 1³ + 12³ and 9³ + 10³
1 + 1,728 = 1,729 and 729 + 1,000 = 1,729. The other pairs fail: 2³ + 12³ = 1,736, 8³ + 11³ = 1,843 and 6³ + 11³ = 1,547.
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Q.116
The HCF of two numbers is 16 and their LCM is 480. If one of the numbers is 96, what is the other number?
- A 160
- B 80
- C 120
- D 30
Show answer
Correct answer: (B) 80
For two numbers, HCF × LCM = product of the numbers, so the other number = (16 × 480) ÷ 96 = 80. Check: the HCF of 96 and 80 is 16 and their LCM is 480.
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Q.117
Which of the following figures has rotational symmetry of order 2 but no line of symmetry?
- A A parallelogram that is neither a rectangle nor a rhombus
- B An isosceles trapezium
- C A kite that is not a rhombus
- D A scalene triangle
Show answer
Correct answer: (A) A parallelogram that is neither a rectangle nor a rhombus
Such a parallelogram looks the same after a half turn about the point where its diagonals meet, but no fold makes its two halves match. An isosceles trapezium and a kite have one line of symmetry and no rotational symmetry of order more than 1; a scalene triangle has neither.
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Q.118
Consider the following statements:
1. 0.5% of a quantity is the same as half of that quantity.
2. If A's salary is 25% more than B's, then B's salary is 20% less than A's.
Which of these is/are correct?
- A Only 1
- B Only 2
- C Both 1 and 2
- D Neither 1 nor 2
Show answer
Correct answer: (B) Only 2
Statement 1 is wrong: 0.5% means 0.5/100 = 1/200 of the quantity, while half of it is 50%. Statement 2 is correct: if B = 100, then A = 125, and 25 is 20% of 125.
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Q.119
In a village of 1,260 voters, 3/7 voted for candidate A and 2/5 of the remaining voters voted for candidate B. How many voters voted for neither A nor B?
- A 720
- B 288
- C 216
- D 432
Show answer
Correct answer: (D) 432
A got 3/7 × 1,260 = 540 votes, leaving 720 voters. B got 2/5 × 720 = 288, so 720 − 288 = 432 voted for neither. Taking 2/5 of all 1,260 instead of the remaining voters gives 216.
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Q.120
A cuboidal water tank is 2.5 m long, 1.6 m wide and 1.2 m deep. How many litres of water can it hold when full?
- A 48 litres
- B 480 litres
- C 4,800 litres
- D 48,000 litres
Show answer
Correct answer: (C) 4,800 litres
Volume = 2.5 × 1.6 × 1.2 = 4.8 m³. Since 1 m³ = 1000 litres, the tank holds 4.8 × 1000 = 4,800 litres.
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Q.121
A cement company makes a profit of ₹9 on each bag of white cement and a loss of ₹6 on each bag of grey cement. In a month it sells 2,400 bags of white cement and 4,000 bags of grey cement. What is its result for the month?
- A Profit of ₹2,400
- B Loss of ₹2,400
- C Profit of ₹45,600
- D Profit of ₹21,600
Show answer
Correct answer: (B) Loss of ₹2,400
Taking profit as positive and loss as negative: 2,400 × 9 + 4,000 × (−6) = 21,600 − 24,000 = −2,400, a loss of ₹2,400. Adding the two amounts (₹45,600) ignores the signs, and ₹21,600 is only the profit on white cement.
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Q.122
Each of the two equal sides of an isosceles triangle is 5 cm longer than its base. If the perimeter of the triangle is 61 cm, what is the length of the base?
- A 17 cm
- B 20.3 cm
- C 22 cm
- D 28 cm
Show answer
Correct answer: (A) 17 cm
Let the base be b cm; each equal side is b + 5. Then b + 2(b + 5) = 61, so 3b + 10 = 61 and b = 17. Check: 17 + 22 + 22 = 61.
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Q.123
Which of the following is NOT a correct way of writing 36 as the sum of two prime numbers?
- A 11 + 25
- B 5 + 31
- C 7 + 29
- D 17 + 19
Show answer
Correct answer: (A) 11 + 25
5, 31, 7, 29, 17 and 19 are all prime, but 25 = 5 × 5 is composite, so 11 + 25 is not a sum of two primes.
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Q.124
In right triangles PQR and XYZ, angle Q = angle Y = 90°, PR = XZ = 13 cm and PQ = XY = 5 cm. Which of the following is correct?
- A They are congruent by RHS, and QR = YZ = 12 cm
- B They are congruent by SAS, and QR = YZ = 8 cm
- C They need not be congruent, since only two sides are known
- D They are congruent by RHS, and QR = YZ = 18 cm
Show answer
Correct answer: (A) They are congruent by RHS, and QR = YZ = 12 cm
The hypotenuses and one pair of sides are equal, so ΔPQR ≅ ΔXYZ by RHS. By Pythagoras, QR = √(13² − 5²) = √144 = 12 cm, and YZ is the same.
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Q.125
A bag contains 3.75 kg of rice, 1.6 kg of dal and 850 g of sugar. What is the total weight of the bag's contents?
- A 13.85 kg
- B 6.2 kg
- C 5.435 kg
- D 4.76 kg
Show answer
Correct answer: (B) 6.2 kg
850 g = 0.85 kg. Lining up the decimal points: 3.75 + 1.60 + 0.85 = 6.20 kg. Writing 850 g as 8.5 kg or 0.085 kg is a conversion error, and 4.76 kg comes from adding 1.6 as if it were 0.16.
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Q.126
The length of a rectangle is 7 cm more than its breadth, and its perimeter is 90 cm. What is its length?
- A 26 cm
- B 19 cm
- C 45 cm
- D 48.5 cm
Show answer
Correct answer: (A) 26 cm
Let the breadth be b. Then 2(b + 7 + b) = 90, so 2b + 7 = 45 and b = 19; the length is 26 cm. Check: 2 × (26 + 19) = 90.
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Q.127
Consider the following statements:
1. If x and y are in direct proportion, then x + y has the same value for every pair of values.
2. If x and y are in inverse proportion and x is doubled, then y is also doubled.
Which of these is/are correct?
- A Only 1
- B Only 2
- C Both 1 and 2
- D Neither 1 nor 2
Show answer
Correct answer: (D) Neither 1 nor 2
Both are wrong. In direct proportion it is x/y, not x + y, that stays constant (for y = 3x, the pairs 1, 3 and 2, 6 have sums 4 and 8). In inverse proportion xy is constant, so when x is doubled, y is halved.
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Q.128
Which decimal is equal to 7/16?
- A 0.4375
- B 0.716
- C 0.4357
- D 0.375
Show answer
Correct answer: (A) 0.4375
7/16 = (7 × 625)/(16 × 625) = 4,375/10,000 = 0.4375; dividing 7 by 16 gives the same result. 0.375 is 3/8.
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Q.129
When written as capital block letters, which of the following has rotational symmetry of order 2 but no line of symmetry?
- A Z
- B E
- C V
- D A
Show answer
Correct answer: (A) Z
Z looks the same after a half turn (180°) but has no line of symmetry. E has a horizontal line of symmetry, V and A have a vertical one, and none of these three looks the same after a half turn.
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Q.130
Which expression stands for 'one-third of the sum of y and 8'?
- A y/3 + 8
- B (y + 8)/3
- C 3(y + 8)
- D 3y + 8
Show answer
Correct answer: (B) (y + 8)/3
First form the sum y + 8, then take one-third of the whole sum: (y + 8)/3. The expression y/3 + 8 takes one-third of y only.
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Q.131
In a table, x takes the values 4, 6 and 10, and the corresponding values of y are 30, 20 and 12. Which statement is correct?
- A x and y are in direct proportion
- B x and y are in inverse proportion, with xy = 120
- C x and y are in inverse proportion, with xy = 60
- D x and y are in neither direct nor inverse proportion
Show answer
Correct answer: (B) x and y are in inverse proportion, with xy = 120
4 × 30 = 6 × 20 = 10 × 12 = 120, so the product xy is constant and x and y are in inverse proportion. The ratio x/y is not constant (4/30 is not equal to 6/20), so they are not in direct proportion.
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Q.132
A rectangular park is 63 m long and 16 m wide. Asha walks from one corner to the opposite corner along the diagonal instead of along two sides. How many metres does she save?
- A 14 m
- B 16 m
- C 65 m
- D 79 m
Show answer
Correct answer: (A) 14 m
Diagonal = √(63² + 16²) = √(3969 + 256) = √4225 = 65 m. Along two sides she would walk 63 + 16 = 79 m, so she saves 79 − 65 = 14 m.
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Q.133
If 49x² + kx + 16 is a perfect square and k is positive, the value of k is:
- A 11
- B 28
- C 56
- D 112
Show answer
Correct answer: (C) 56
49x² = (7x)² and 16 = 4², so the expression is (7x + 4)² = 49x² + 2 × 7x × 4 + 16 = 49x² + 56x + 16; hence k = 56.
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Q.134
How is the number 30,507,040 (written with international commas) read in the international system?
- A Three hundred five million seven thousand forty
- B Three million fifty thousand seven hundred forty
- C Thirty million fifty-seven thousand forty
- D Thirty million five hundred seven thousand forty
Show answer
Correct answer: (D) Thirty million five hundred seven thousand forty
The international periods are millions, thousands and ones: 30 | 507 | 040, so the number is thirty million five hundred seven thousand forty. In the Indian system the same number is 3,05,07,040, three crore five lakh seven thousand forty.
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Q.135
How many natural numbers lie between 37² and 38², not counting 37² and 38² themselves?
- A 37
- B 75
- C 73
- D 74
Show answer
Correct answer: (D) 74
Between n² and (n + 1)² there are 2n natural numbers, none of which is a perfect square. For n = 37 this is 2 × 37 = 74; check: 1,444 − 1,369 − 1 = 74.
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Q.136
Subtract 4x² − 3x + 2 from 7x² + x − 5.
- A 3x² + 4x − 7
- B 3x² − 2x − 3
- C 11x² − 2x − 3
- D 3x² + 4x − 3
Show answer
Correct answer: (A) 3x² + 4x − 7
(7x² + x − 5) − (4x² − 3x + 2) = 7x² + x − 5 − 4x² + 3x − 2 = 3x² + 4x − 7. Every sign of the expression being subtracted must change.
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Q.137
A kite is a quadrilateral with two pairs of equal adjacent sides. Which of the following is NOT necessarily true for a kite?
- A Its diagonals are perpendicular to each other
- B One of its diagonals bisects the other
- C It has at least one line of symmetry
- D Its opposite sides are equal
Show answer
Correct answer: (D) Its opposite sides are equal
In a kite, the diagonal joining the two vertices where equal sides meet is a line of symmetry; it is perpendicular to the other diagonal and bisects it. The equal sides are adjacent, not opposite, so opposite sides need not be equal.
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Q.138
Two tankers hold 850 litres and 680 litres of kerosene. What is the greatest capacity of a container that can measure the kerosene of each tanker an exact number of times?
- A 85 litres
- B 170 litres
- C 340 litres
- D 3,400 litres
Show answer
Correct answer: (B) 170 litres
The capacity must be a common factor of 850 and 680, and the greatest such factor is the HCF. 850 = 2 × 5² × 17 and 680 = 2³ × 5 × 17, so HCF = 2 × 5 × 17 = 170 litres (3,400 is the LCM).
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Q.139
If a : b = 2 : 3 and b : c = 4 : 5, then a : b : c is:
- A 2 : 3 : 5
- B 6 : 12 : 15
- C 8 : 12 : 15
- D 2 : 12 : 5
Show answer
Correct answer: (C) 8 : 12 : 15
Make the b terms equal: a : b = 8 : 12 (multiplying by 4) and b : c = 12 : 15 (multiplying by 3). So a : b : c = 8 : 12 : 15.
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Q.140
Ramesh spends 2/5 of his monthly salary on rent and 1/3 of the remaining amount on food. He saves the rest, which is ₹13,200. What is his monthly salary?
- A ₹33,000
- B ₹49,500
- C ₹22,000
- D ₹19,800
Show answer
Correct answer: (A) ₹33,000
After rent 3/5 of the salary is left, and food takes 1/3 of that, i.e. 1/5 of the salary. Savings = 3/5 − 1/5 = 2/5 of the salary = ₹13,200, so the salary is 13,200 × 5/2 = ₹33,000. Taking food as 1/3 of the whole salary wrongly gives ₹49,500.
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Q.141
By selling a chair for ₹1,316, a carpenter suffers a loss of 6%. What was the cost price of the chair?
- A ₹1,237
- B ₹1,395
- C ₹1,400
- D ₹1,450
Show answer
Correct answer: (C) ₹1,400
Selling price = 94% of cost price, so CP = 1316 × 100 ÷ 94 = ₹1,400. Check: 6% of 1400 is 84, and 1400 − 84 = 1316.
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Q.142
Without adding term by term, find 1 + 3 + 5 + ... + 29, the sum of the consecutive odd numbers from 1 to 29.
- A 435
- B 196
- C 256
- D 225
Show answer
Correct answer: (D) 225
The sum of the first n odd numbers is n². From 1 to 29 there are (29 + 1) ÷ 2 = 15 odd numbers, so the sum is 15² = 225. (435 is the sum of all the numbers from 1 to 29.)
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Q.143
₹8,000 is invested for 1 year at 10% per annum, compounded half-yearly. What is the amount at the end of the year?
- A ₹8,400
- B ₹8,800
- C ₹8,820
- D ₹9,680
Show answer
Correct answer: (C) ₹8,820
Compounding half-yearly means a rate of 5% for each of the 2 half-years: 8000 × 1.05 × 1.05 = ₹8,820.
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Q.144
Find the value of 2a² − 3ab + b when a = −2 and b = 3.
- A −7
- B 13
- C 37
- D 29
Show answer
Correct answer: (D) 29
2a² = 2 × 4 = 8, −3ab = −3 × (−2) × 3 = 18 and b = 3, so the value is 8 + 18 + 3 = 29.
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Q.145
Solve: 3(2y − 5) − 4(y − 6) = 30.
- A 5.5
- B 10.5
- C 19.5
- D 34.5
Show answer
Correct answer: (B) 10.5
Open the brackets: 6y − 15 − 4y + 24 = 30, so 2y + 9 = 30 and y = 10.5. Note that −4 × (−6) = +24.
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Q.146
A milk vendor supplies 32 litres of milk in the morning and 68 litres in the evening. If milk costs ₹45 per litre, how much money does he receive in a day?
- A ₹4,500
- B ₹3,092
- C ₹1,508
- D ₹5,400
Show answer
Correct answer: (A) ₹4,500
Money = 32 × 45 + 68 × 45 = (32 + 68) × 45 = 100 × 45 = ₹4,500, using the distributive property. ₹3,092 comes from wrongly working out 32 + 68 × 45 without brackets.
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Q.147
₹5,200 is divided among three friends in the ratio 1/2 : 1/3 : 1/4. What is the largest share?
- A ₹1,200
- B ₹1,600
- C ₹2,400
- D ₹2,600
Show answer
Correct answer: (C) ₹2,400
Multiply each fraction by 12 (the LCM of 2, 3 and 4): 1/2 : 1/3 : 1/4 = 6 : 4 : 3. One part = 5200 ÷ 13 = ₹400, so the largest share is 6 × 400 = ₹2,400.
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Q.148
The number of bacteria in a culture doubles every 20 minutes. If there are 500 bacteria at the start, how many will there be after 3 hours?
- A 5,12,000
- B 1,28,000
- C 2,56,000
- D 9,000
Show answer
Correct answer: (C) 2,56,000
3 hours = 180 minutes = 9 doubling periods, so the number becomes 500 × 2⁹ = 500 × 512 = 2,56,000. Counting 8 or 10 doublings gives 1,28,000 or 5,12,000, and 500 × 18 = 9,000 confuses 2⁹ with 2 × 9.
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Q.149
If 9 : x = 15 : 35, what is the value of x?
- A 15
- B 21
- C 29
- D 41
Show answer
Correct answer: (B) 21
In a proportion the product of the extremes equals the product of the means: 15x = 9 × 35 = 315, so x = 21. Check: 9 : 21 = 3 : 7 = 15 : 35.
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Q.150
The angles of a triangle are (x + 10)°, (2x − 20)° and (3x − 50)°. What is the largest angle of the triangle?
- A 40°
- B 50°
- C 60°
- D 70°
Show answer
Correct answer: (D) 70°
(x + 10) + (2x − 20) + (3x − 50) = 180 gives 6x − 60 = 180, so x = 40. The angles are 50°, 60° and 70°, and the largest is 70°.
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