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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.151
In a quiz, +5 marks are given for a correct answer, −2 for a wrong answer and 0 for a question not attempted. Ritu attempted 18 questions and scored 41. How many of her answers were correct and how many wrong?
- A 9 correct and 9 wrong
- B 11 correct and 7 wrong
- C 13 correct and 5 wrong
- D 7 correct and 11 wrong
Show answer
Correct answer: (B) 11 correct and 7 wrong
11 correct and 7 wrong give 11 × 5 + 7 × (−2) = 55 − 14 = 41. The other choices give 45 − 18 = 27, 65 − 10 = 55 and 35 − 22 = 13, none of which is 41.
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Q.152
A train running at 75 km/h covers a distance in 4 hours. At what speed must it run to cover the same distance in 3 hours 20 minutes?
- A 62.5 km/h
- B 93.75 km/h
- C 100 km/h
- D 90 km/h
Show answer
Correct answer: (D) 90 km/h
Distance = 75 × 4 = 300 km, and 3 hours 20 minutes = 10/3 hours. Speed = 300 ÷ 10/3 = 90 km/h. Writing 3 h 20 min as 3.2 h is the slip that gives 93.75.
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Q.153
A water tank is 3/5 full. After 42 litres are drawn out, it is 1/4 full. What is the capacity of the tank?
- A 120 litres
- B 70 litres
- C 168 litres
- D 60 litres
Show answer
Correct answer: (A) 120 litres
The 42 litres drawn out are 3/5 − 1/4 = 12/20 − 5/20 = 7/20 of the tank, so the capacity is 42 × 20/7 = 120 litres. Check: 3/5 of 120 = 72, and 72 − 42 = 30 = 1/4 of 120.
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Q.154
What is the smallest number by which 1,323 must be divided so that the quotient is a perfect cube?
- A 7
- B 49
- C 3
- D 21
Show answer
Correct answer: (B) 49
1,323 = 3³ × 7². The factor 7² does not make a group of three, so dividing by 7² = 49 leaves 27 = 3³.
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Q.155
Consider the following statements:
1. (a − b)² = (b − a)² for all numbers a and b.
2. (a + b)² = a² + b² whenever ab = 0.
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: (C) Both 1 and 2
Both are correct. b − a = −(a − b), and a number and its negative have the same square. Also (a + b)² = a² + 2ab + b², which equals a² + b² when ab = 0.
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Q.156
Sarita is x years old. Her mother's age is 4 years more than three times Sarita's age. Which expression gives her mother's age in years?
- A 4x + 3
- B 3(x + 4)
- C 3x + 4
- D 7x
Show answer
Correct answer: (C) 3x + 4
Three times Sarita's age is 3x, and 4 years more than that is 3x + 4. Note that 3(x + 4) = 3x + 12, which is 12 more, not 4 more.
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Q.157
In the number 7,40,53,962, what is the difference between the place value of 4 and the place value of 5?
- A 3,95,000
- B 39,95,000
- C 39,50,000
- D 3,50,000
Show answer
Correct answer: (C) 39,50,000
The 4 is in the ten-lakhs place, so its place value is 40,00,000; the 5 is in the ten-thousands place, so its place value is 50,000. Difference = 40,00,000 − 50,000 = 39,50,000.
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Q.158
How many whole numbers lie between 437 and 1,026, not counting 437 and 1,026 themselves?
- A 590
- B 589
- C 588
- D 587
Show answer
Correct answer: (C) 588
Between a and b, excluding both, there are b − a − 1 whole numbers: 1,026 − 437 − 1 = 588. Writing 589 forgets to subtract 1.
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Q.159
Two numbers are in the ratio 5 : 8. If 6 is added to each of them, the ratio becomes 2 : 3. The numbers are:
- A 20 and 32
- B 25 and 40
- C 30 and 48
- D 35 and 56
Show answer
Correct answer: (C) 30 and 48
Let the numbers be 5k and 8k. Then (5k + 6)/(8k + 6) = 2/3, so 15k + 18 = 16k + 12 and k = 6. The numbers are 30 and 48; check: 36 : 54 = 2 : 3.
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Q.160
Two parallel lines are cut by a transversal. One of the interior angles on the same side of the transversal is 64°. What is the other interior angle on that side?
- A 26°
- B 64°
- C 116°
- D 296°
Show answer
Correct answer: (C) 116°
Interior angles on the same side of a transversal cutting two parallel lines are supplementary, so the other angle is 180° − 64° = 116°.
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Q.161
Two sides of a triangle are 6 cm and 15 cm. If the third side is a whole number of centimetres, how many different lengths are possible for it?
- A 11
- B 12
- C 13
- D 20
Show answer
Correct answer: (A) 11
The third side must be more than 15 − 6 = 9 cm and less than 15 + 6 = 21 cm, so it can be 10, 11, ..., 20 cm: 11 lengths. (20 cm is the longest possible side, not the number of choices.)
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Q.162
Which of the following is an equation?
- A 4m − 1 = 11
- B 7y − 3
- C 2x + 5 > 9
- D x + 8 < 10
Show answer
Correct answer: (A) 4m − 1 = 11
An equation states that two expressions are equal, so it must contain the equals sign: 4m − 1 = 11. 7y − 3 is only an expression, and the other two are inequalities.
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Q.163
The maximum temperatures (in °C) of a town on the seven days of a week were 34, 37, 31, 39, 35, 33 and 38. What is the range of these temperatures?
- A 8 °C
- B 35 °C
- C 39 °C
- D 70 °C
Show answer
Correct answer: (A) 8 °C
Range = highest value − lowest value = 39 − 31 = 8 °C. (35 °C is the median, and 70 comes from adding instead of subtracting.)
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Q.164
Houses are made in a row with matchsticks. 1 house needs 6 matchsticks, 2 houses need 11, 3 houses need 16, and the pattern continues in the same way. How many houses are there in a row that uses exactly 191 matchsticks?
- A 31
- B 37
- C 38
- D 39
Show answer
Correct answer: (C) 38
Each new house adds 5 matchsticks, so n houses need 5n + 1. Solving 5n + 1 = 191 gives 5n = 190 and n = 38 (check: 5 × 38 + 1 = 191).
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Q.165
Which of the following is the greatest: 2⁶, 3⁴, 4³ or 6²?
- A 3⁴
- B 2⁶
- C 4³
- D 6²
Show answer
Correct answer: (A) 3⁴
2⁶ = 64, 3⁴ = 81, 4³ = 64 and 6² = 36, so 3⁴ is the greatest. A bigger base alone or a bigger exponent alone does not decide which power is larger.
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Q.166
What is the difference between the compound interest (compounded annually) and the simple interest on ₹15,000 for 2 years at 8% per annum?
- A ₹48
- B ₹96
- C ₹192
- D ₹2,496
Show answer
Correct answer: (B) ₹96
SI = 15000 × 8 × 2 ÷ 100 = ₹2,400. Amount at CI = 15000 × 1.08 × 1.08 = ₹17,496, so CI = ₹2,496. Difference = ₹96, which is 8% of the first year's interest of ₹1,200.
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Q.167
Which of the following is a Pythagorean triplet whose smallest member is 14?
- A 14, 24, 28
- B 14, 49, 50
- C 14, 50, 52
- D 14, 48, 50
Show answer
Correct answer: (D) 14, 48, 50
Using 2m, m² − 1, m² + 1 with 2m = 14 gives m = 7 and the triplet 14, 48, 50. Check: 14² + 48² = 196 + 2,304 = 2,500 = 50².
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Q.168
The perimeter of a triangle is 9x² − 4x + 11. Two of its sides are 2x² + 3x − 1 and 4x² − 5x + 6. The third side is:
- A 3x² − 6x + 6
- B 3x² − 2x + 16
- C 15x² − 6x + 16
- D 3x² − 2x + 6
Show answer
Correct answer: (D) 3x² − 2x + 6
The two sides add to 6x² − 2x + 5. Third side = (9x² − 4x + 11) − (6x² − 2x + 5) = 3x² − 2x + 6; check: the three sides add back to 9x² − 4x + 11.
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Q.169
Which of the following expressions is a trinomial (has exactly three terms)?
- A 2x × 3y + z
- B 3a + 2b − c + 7
- C 4x²y × 3
- D p²q − 5pq + 9
Show answer
Correct answer: (D) p²q − 5pq + 9
p²q − 5pq + 9 has three terms. 2x × 3y + z = 6xy + z has two terms, 4x²y × 3 = 12x²y is a single term, and 3a + 2b − c + 7 has four terms.
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Q.170
Which of the following statements about rational numbers is FALSE?
- A 0 is the additive identity for rational numbers
- B Rational numbers are closed under subtraction
- C Rational numbers are closed under division
- D Between any two rational numbers there are infinitely many rational numbers
Show answer
Correct answer: (C) Rational numbers are closed under division
Division by 0 is not defined, so a ÷ b is not a rational number when b = 0; hence rational numbers are not closed under division (non-zero rational numbers are). The other three statements are true.
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Q.171
Two lines are cut by a transversal. Which of the following does NOT by itself show that the two lines are parallel?
- A A pair of corresponding angles are equal
- B A pair of alternate interior angles are equal
- C The interior angles on the same side of the transversal add up to 180°
- D A pair of vertically opposite angles are equal
Show answer
Correct answer: (D) A pair of vertically opposite angles are equal
Vertically opposite angles are equal whenever two lines cross, whether or not the lines are parallel. Each of the other three conditions is a test for parallel lines.
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Q.172
What is the value of (2⁻¹ + 3⁻¹)⁻¹?
- A 6/5
- B 5
- C 5/6
- D 1/5
Show answer
Correct answer: (A) 6/5
2⁻¹ + 3⁻¹ = 1/2 + 1/3 = 5/6, and (5/6)⁻¹ = 6/5. Treating 2⁻¹ + 3⁻¹ as (2 + 3)⁻¹ is a common error.
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Q.173
What is the order of rotational symmetry of a regular pentagon, and the smallest angle through which it must be turned about its centre to look exactly the same?
- A Order 4; 90°
- B Order 5; 108°
- C Order 5; 72°
- D Order 10; 36°
Show answer
Correct answer: (C) Order 5; 72°
A regular pentagon fits onto itself 5 times in one full turn, so its order is 5 and the smallest angle is 360° ÷ 5 = 72°. (108° is its interior angle, not the angle of rotation.)
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Q.174
What is 0.000000307 in standard form?
- A 3.07 × 10⁷
- B 3.07 × 10⁻⁶
- C 307 × 10⁻⁹
- D 3.07 × 10⁻⁷
Show answer
Correct answer: (D) 3.07 × 10⁻⁷
Moving the decimal point 7 places to the right gives 3.07, so 0.000000307 = 3.07 × 10⁻⁷. 307 × 10⁻⁹ has the same value but is not in standard form, which needs a number from 1 up to (but less than) 10.
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Q.175
A cubical box has a volume of 17,576 cm³. What is the length of each of its edges?
- A 24 cm
- B 26 cm
- C 36 cm
- D 34 cm
Show answer
Correct answer: (B) 26 cm
Edge = ∛17,576. The number ends in 6, so its cube root ends in 6; and 17 lies between 2³ = 8 and 3³ = 27, so the tens digit is 2. Edge = 26 cm, since 26³ = 17,576.
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Q.176
Which numeral stands for 'five crore three lakh six thousand forty'?
- A 5,03,60,040
- B 5,30,06,040
- C 5,03,06,040
- D 5,03,06,400
Show answer
Correct answer: (C) 5,03,06,040
Five crore = 5,00,00,000, three lakh = 3,00,000, six thousand = 6,000 and forty = 40; together 5,03,06,040. Zeros must fill the empty ten-lakhs, ten-thousands, hundreds and ones places.
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Q.177
Consider the following statements. 1. The diagonals of a rhombus bisect each other at right angles. 2. The diagonals of a rectangle are equal in length. 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: (C) Both 1 and 2
A rhombus is a parallelogram with all sides equal, so its diagonals bisect each other and are perpendicular. The diagonals of a rectangle are equal. Both statements are true.
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Q.178
Consider the following statements about data. 1. The range of a set of data is its highest value minus its lowest value. 2. A set of data can have more than one mode. 3. For an even number of observations arranged in order, the median is the mean of the two middle observations. Which of the statements are correct?
- A 1 and 2 only
- B 2 and 3 only
- C 1 and 3 only
- D 1, 2 and 3
Show answer
Correct answer: (D) 1, 2 and 3
All three are true. For example, 2, 3, 3, 5, 5, 8 has range 8 − 2 = 6, two modes (3 and 5), and median (3 + 5) ÷ 2 = 4.
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Q.179
A poster measures 0.6 m by 0.45 m. What is its area in square centimetres?
- A 27 cm²
- B 270 cm²
- C 2,700 cm²
- D 27,000 cm²
Show answer
Correct answer: (C) 2,700 cm²
In centimetres the poster is 60 cm by 45 cm, so its area is 60 × 45 = 2,700 cm². Equivalently, 0.27 m² × 10,000 = 2,700 cm², since 1 m² = 10,000 cm².
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Q.180
A shopkeeper marks his goods 40% above the cost price and then allows a discount of 25% on the marked price. What is his profit or loss per cent?
- A 15% profit
- B 5% loss
- C 10% profit
- D 5% profit
Show answer
Correct answer: (D) 5% profit
Take CP = ₹100. Marked price = ₹140, and after a 25% discount the selling price is 140 × 0.75 = ₹105. So he makes a 5% profit (not 40 − 25 = 15%).
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Q.181
A ladder 25 m long leans against a wall, and its top reaches a window 24 m above the ground. How far is the foot of the ladder from the wall?
- A 1 m
- B 7 m
- C 34.7 m
- D 49 m
Show answer
Correct answer: (B) 7 m
The wall, the ground and the ladder form a right triangle with the ladder as hypotenuse. Distance = √(25² − 24²) = √(625 − 576) = √49 = 7 m.
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Q.182
What is the cube root of −5,832?
- A −18
- B −28
- C −12
- D −16
Show answer
Correct answer: (A) −18
5,832 = 2³ × 3⁶ = (2 × 3²)³ = 18³, and the cube root of a negative number is negative, so ∛(−5,832) = −18. 28³ = 21,952 is far too large.
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Q.183
To construct the perpendicular bisector of a line segment AB with ruler and compasses, arcs of the same radius are drawn from A and from B on both sides of AB. This radius must be:
- A Less than half of AB
- B Exactly one-third of AB
- C Exactly equal to AB, and no other length
- D More than half of AB
Show answer
Correct answer: (D) More than half of AB
Arcs of the same radius from A and B meet only if the radius is more than half of AB; joining their two meeting points gives the perpendicular bisector. A radius equal to AB also works, but it is not the only choice.
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Q.184
What is the least length of a rope that can be cut exactly into whole pieces of 90 cm, or of 1 m, or of 1 m 20 cm, with nothing left over in each case?
- A 6 m
- B 9 m
- C 3 m 60 cm
- D 18 m
Show answer
Correct answer: (D) 18 m
The length must be a common multiple of 90 cm, 100 cm and 120 cm. 90 = 2 × 3² × 5, 100 = 2² × 5² and 120 = 2³ × 3 × 5, so the LCM = 2³ × 3² × 5² = 1,800 cm = 18 m.
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Q.185
Observe the pattern: 9 × 9 + 7 = 88, 98 × 9 + 6 = 888, 987 × 9 + 5 = 8,888 and 9,876 × 9 + 4 = 88,888. What is 98,765 × 9 + 3?
- A 8,88,888
- B 88,888
- C 88,88,888
- D 8,88,883
Show answer
Correct answer: (A) 8,88,888
Each step adds one more 8, so the next result has six 8s: 8,88,888. Check: 98,765 × 9 = 8,88,885 and 8,88,885 + 3 = 8,88,888.
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Q.186
Which of the following numbers is divisible by 11?
- A 6,19,520
- B 6,91,520
- C 6,19,250
- D 9,61,250
Show answer
Correct answer: (A) 6,19,520
Find the difference between the sums of alternate digits: for 6,19,520 it is (0 + 5 + 1) − (2 + 9 + 6) = −11, a multiple of 11. For the other numbers the difference is 5, 17 and 7, which is neither 0 nor a multiple of 11.
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Q.187
The complete factorisation of 3x² − 27 is:
- A 3(x − 3)²
- B 3(x + 9)(x − 9)
- C (3x + 3)(x − 9)
- D 3(x + 3)(x − 3)
Show answer
Correct answer: (D) 3(x + 3)(x − 3)
Take out the common factor 3 to get 3(x² − 9). Then x² − 9 = (x + 3)(x − 3), so 3x² − 27 = 3(x + 3)(x − 3).
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Q.188
Which property of whole numbers is used in 47 × 98 + 47 × 2 = 47 × (98 + 2) = 4,700?
- A Commutativity of multiplication
- B Distributivity of multiplication over addition
- C Associativity of addition
- D Closure under multiplication
Show answer
Correct answer: (B) Distributivity of multiplication over addition
Taking out the common factor 47, that is a × b + a × c = a × (b + c), is the distributive property. It turns the sum into the easy product 47 × 100.
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Q.189
The students of a class collected ₹2,601 for a relief fund. Each student gave as many rupees as there were students in the class. How many students are in the class?
- A 49 students
- B 51 students
- C 61 students
- D 41 students
Show answer
Correct answer: (B) 51 students
If there are n students, n × n = 2,601, so n = √2,601 = 51 (51 × 51 = 2,601). For comparison, 49² = 2,401, 61² = 3,721 and 41² = 1,681.
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Q.190
A parallelogram has sides 12 cm and 8 cm. The height on the 12 cm side is 6 cm. What is the height on the 8 cm side?
- A 4 cm
- B 6 cm
- C 9 cm
- D 16 cm
Show answer
Correct answer: (C) 9 cm
Area = base × height = 12 × 6 = 72 cm². Using the other side as base, 8 × h = 72, so h = 9 cm.
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Q.191
A student is asked to construct triangle PQR with QR = 7 cm, angle Q = 75° and angle R = 120°. What will happen?
- A It cannot be constructed, as angle Q + angle R is more than 180°
- B A unique triangle will be obtained
- C Two different triangles are possible
- D It can be drawn only if PQ is also given
Show answer
Correct answer: (A) It cannot be constructed, as angle Q + angle R is more than 180°
75° + 120° = 195°, which is more than 180°, so the arms drawn at Q and R will not meet on that side of QR. No triangle can have these two angles.
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Q.192
Which of the following describes the expression 5 − 2z in words?
- A Twice z subtracted from 5
- B 5 subtracted from twice z
- C Twice the difference of 5 and z
- D 2 less than 5 times z
Show answer
Correct answer: (A) Twice z subtracted from 5
5 − 2z means start with 5 and take away 2z (twice z). '5 subtracted from twice z' is 2z − 5, 'twice the difference' is 2(5 − z) and '2 less than 5 times z' is 5z − 2.
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Q.193
What is the value of (−15) + 28 + (−9) + (−11)?
- A −63
- B 23
- C −7
- D 15
Show answer
Correct answer: (C) −7
The positive part is 28 and the negative part is −15 − 9 − 11 = −35, so the sum is 28 − 35 = −7.
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Q.194
In a bar graph showing how many students chose each fruit, the bar for mango is 4 cm long and stands for 18 students. On the same scale, how many students does a bar 6 cm long stand for?
- A 20 students
- B 27 students
- C 30 students
- D 108 students
Show answer
Correct answer: (B) 27 students
The scale is 18 ÷ 4 = 4.5 students per cm, so a 6 cm bar stands for 6 × 4.5 = 27 students. (20 adds the extra 2 cm to 18, and 108 is 18 × 6.)
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Q.195
What is the place value of the digit 7 in 63.578?
- A 7
- B 0.7
- C 0.007
- D 0.07
Show answer
Correct answer: (D) 0.07
In 63.578 the digits after the decimal point are 5 tenths, 7 hundredths and 8 thousandths, so the place value of 7 is 7/100 = 0.07.
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Q.196
What is the HCF of 168, 252 and 420?
- A 2,520
- B 42
- C 21
- D 84
Show answer
Correct answer: (D) 84
168 = 2³ × 3 × 7, 252 = 2² × 3² × 7 and 420 = 2² × 3 × 5 × 7. Taking the common primes with their lowest powers: 2² × 3 × 7 = 84. (2,520 is the LCM.)
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Q.197
Each letter E made with matchsticks uses 5 matchsticks. How many matchsticks are needed to make n such letters E placed separately in a row?
- A n + 5
- B 5n
- C 5n + 1
- D n⁵
Show answer
Correct answer: (B) 5n
Each letter needs 5 matchsticks and the letters do not share any stick, so n letters need 5 × n = 5n matchsticks (for example, 3 letters need 15).
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Q.198
Which of the following CANNOT be the probability of an event?
- A 3/2
- B 0
- C 1
- D 0.7
Show answer
Correct answer: (A) 3/2
The probability of any event lies from 0 (an impossible event) to 1 (a certain event). 3/2 = 1.5 is greater than 1, so it cannot be a probability.
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Q.199
The supplement of an angle is five times its complement. What is the angle?
- A 22.5°
- B 45°
- C 67.5°
- D 112.5°
Show answer
Correct answer: (C) 67.5°
180° − x = 5(90° − x) gives 180° − x = 450° − 5x, so 4x = 270° and x = 67.5°. Check: the complement is 22.5° and the supplement is 112.5° = 5 × 22.5°.
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Q.200
Lines l and m are cut by a transversal. A pair of alternate interior angles measure (2x + 16)° and (4x − 20)°. If l is parallel to m, what is the measure of each of these angles?
- A 18°
- B 36°
- C 52°
- D 128°
Show answer
Correct answer: (C) 52°
For parallel lines, alternate interior angles are equal: 2x + 16 = 4x − 20, so 2x = 36 and x = 18. Each angle is 2(18) + 16 = 52°, and 4(18) − 20 = 52° checks.
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How these questions were made
Authored by an AI assistant (Claude) from its own general knowledge of stable, well-established facts (no live lookup) - not reviewed by a subject-matter expert; verify against an official source before relying on any fact.