Pedagogy

CTET Maths MCQ with Answers, Paper 1 (Classes I-V)

222 practice questions on Mathematics, Classes I-V (Paper I) for CTET Paper I, with answers; most also have an explanation or a worked solution. Try each one before you open its answer.

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1. Q.1

   How many paise make 3/4 of a rupee? (A) 30 paise (B) 75 paise (C) 25 paise (D) 34 paise

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   Answer: (B) 75 paise. ₹ 1 = 100 paise; 1/4 of 100 = 25, so 3/4 of 100 = 3 × 25 = 75 paise.

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2. Q.2

   Consider these statements:

   1. Every corner of a rectangle is a right angle.

   2. A triangle can have two right angles.

   3. At 6 o'clock the hands of a clock make a straight angle.

   Which of them are correct?

   1. A 1 and 2 only
   2. B 1 and 3 only
   3. C 2 and 3 only
   4. D 1, 2 and 3
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   Correct answer: (B) 1 and 3 only

   All four corners of a rectangle are right angles, and at 6:00 the hands lie in one straight line (180°). In a 'triangle' with two right angles, the two sides standing on the base would be parallel and never meet, so statement 2 is wrong.

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3. Q.3

   A pictograph of trees in four villages uses the key one symbol = 10 trees: P has 4 symbols, Q 6½, R 3 and S 5½. Which statement is NOT correct?

   1. A R has exactly half as many trees as Q.
   2. B Q has 65 trees.
   3. C P and R together have 70 trees.
   4. D S has 15 more trees than P.
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   Correct answer: (A) R has exactly half as many trees as Q.

   P = 40, Q = 65, R = 30 and S = 55 trees. Half of 65 is 32½, not 30, so the statement about R and Q is wrong; the others are true (40 + 30 = 70, 55 − 40 = 15).

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4. Q.4

   Since 9 = 10 − 1, nine times a number equals ten times the number minus the number. Using this pattern, 9 × 47 = ?

   1. A 437
   2. B 517
   3. C 423
   4. D 432
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   Correct answer: (C) 423

   9 × 47 = 470 − 47 = 423. Check: 9 × 40 + 9 × 7 = 360 + 63 = 423. (517 adds 47 instead of subtracting it.)

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5. Q.5

   A pattern for multiplying a two-digit number by 11: 11 × 23 = 253 (write 2 and 3, and put 2 + 3 = 5 between them). Using this pattern correctly, 11 × 68 = ?

   1. A 748
   2. B 6148
   3. C 648
   4. D 758
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   Correct answer: (A) 748

   6 + 8 = 14, so write 4 in the middle and carry 1 to the 6: 6 + 1 = 7, giving 748. Check: 68 × 10 + 68 = 680 + 68 = 748.

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6. Q.6

   Children count aloud from 1 to 100. Raju claps on every multiple of 3 and Rani claps on every multiple of 5. On how many numbers do both of them clap?

   1. A 20 numbers
   2. B 6 numbers
   3. C 5 numbers
   4. D 7 numbers
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   Correct answer: (B) 6 numbers

   Both clap on the common multiples of 3 and 5, that is, on multiples of 15: 15, 30, 45, 60, 75 and 90. That is 6 numbers.

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7. Q.7

   A triangle is placed on top of a square so that one side of the triangle exactly matches the top side of the square, like the outline of a hut. How many sides and corners does the outline of the new shape have?

   1. A 7 sides and 7 corners
   2. B 5 sides and 5 corners
   3. C 6 sides and 5 corners
   4. D 7 sides and 5 corners
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   Correct answer: (B) 5 sides and 5 corners

   The shared side goes inside and is no longer part of the outline. The outline has 3 sides of the square and 2 sides of the triangle, so 5 sides and 5 corners (2 at the bottom, 2 where the roof meets the walls and 1 at the top).

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8. Q.8

   There are 45 children in a class, and 2/5 of them come to school by bus. How many children do NOT come by bus?

   1. A 43 children
   2. B 27 children
   3. C 18 children
   4. D 9 children
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   Correct answer: (B) 27 children

   1/5 of 45 = 9, so 2/5 of 45 = 18 children come by bus. The remaining 45 - 18 = 27 children (3/5 of the class) do not.

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9. Q.9

   Tally of vehicles passing a school gate: cars - 3 groups of five and 4 marks; buses - 1 group and 2 marks; two-wheelers - 6 groups and 1 mark; autos - 2 groups only. How many vehicles passed in all?

   1. A 55 vehicles
   2. B 67 vehicles
   3. C 57 vehicles
   4. D 19 vehicles
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   Correct answer: (B) 67 vehicles

   Cars 15 + 4 = 19, buses 5 + 2 = 7, two-wheelers 30 + 1 = 31, autos 10; total = 19 + 7 + 31 + 10 = 67. (55 comes from counting each group as 4.)

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10. Q.10

    Meena divides 754 by 9 and gets quotient 83 and remainder 7. Which calculation correctly checks her answer?

    1. A 9 × 7 + 83 = 754
    2. B 9 × 83 + 7 = 754
    3. C 9 × 83 + 9 = 754
    4. D (83 + 7) × 9 = 754
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    Correct answer: (B) 9 × 83 + 7 = 754

    Dividend = divisor × quotient + remainder: 9 × 83 = 747 and 747 + 7 = 754, so her answer is right. The other calculations give 756, 810 and 146, not 754.

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11. Q.11

    A poultry farm packs 1,000 eggs in trays of 30. What is the greatest number of trays that can be completely filled, and how many eggs are left over?

    1. A 33 trays, 10 eggs left over
    2. B 34 trays, 10 eggs left over
    3. C 32 trays, 40 eggs left over
    4. D 330 trays, 10 eggs left over
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    Correct answer: (A) 33 trays, 10 eggs left over

    30 × 33 = 990, and 1,000 - 990 = 10 eggs are left, too few for another tray. With 32 trays, 40 eggs would be left, enough to fill one more tray.

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12. Q.12

    In a magic triangle, the numbers 1 to 9 are placed on the sides, four on each side, so that every side has the same sum. If 1, 2 and 3 are at the corners, what is the sum of each side?

    1. A 17
    2. B 15
    3. C 18
    4. D 16
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    Correct answer: (A) 17

    Adding the three sides counts every number once and each corner twice: 45 + (1 + 2 + 3) = 51. So each side is 51 ÷ 3 = 17; one arrangement is 1, 6, 8, 2 / 2, 5, 7, 3 / 3, 4, 9, 1.

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13. Q.13

    Mount Everest is about 8,849 m high and Kanchenjunga is about 8,586 m high. By about how many metres is Everest higher?

    1. A 263 m
    2. B 343 m
    3. C 273 m
    4. D 17,435 m
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    Correct answer: (A) 263 m

    8,849 - 8,586 = 263 m. Check: 8,586 + 263 = 8,849. The answer 343 comes from taking the smaller digit from the larger in each column.

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14. Q.14

    A ribbon 2 m 40 cm long is cut into 6 equal pieces. How long is each piece?

    1. A 4 cm
    2. B 33 cm
    3. C 40 cm
    4. D 2 m 34 cm
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    Correct answer: (C) 40 cm

    2 m 40 cm = 240 cm, and 240 cm ÷ 6 = 40 cm. Check: 6 × 40 cm = 240 cm = 2 m 40 cm.

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15. Q.15

    A number rounded off to the nearest hundred becomes 6,400. Which of the following could be the number?

    1. A 6,540
    2. B 6,449
    3. C 6,349
    4. D 6,451
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    Correct answer: (B) 6,449

    Numbers from 6,350 to 6,449 round to 6,400. 6,349 rounds to 6,300, while 6,451 and 6,540 round to 6,500.

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16. Q.16

    A truck carries 48 bags of cement of 50 kg each and 26 boxes of tiles of 35 kg each. What is the total load?

    1. A 6,290 kg
    2. B 3,210 kg
    3. C 3,310 kg
    4. D 3,410 kg
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    Correct answer: (C) 3,310 kg

    Cement: 48 × 50 = 2,400 kg; tiles: 26 × 35 = 910 kg. Total = 2,400 + 910 = 3,310 kg. (6,290 kg wrongly multiplies all 74 items by 85 kg.)

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17. Q.17

    Data to be shown in a bar graph: 120, 340, 260 and 180. The graph paper is 20 squares tall. Which scale makes every bar end exactly on a grid line and still lets the longest bar fit?

    1. A 1 square = 10 units
    2. B 1 square = 20 units
    3. C 1 square = 40 units
    4. D 1 square = 50 units
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    Correct answer: (B) 1 square = 20 units

    With 1 square = 20 the bars are 6, 17, 13 and 9 squares, all whole and within 20. With 10 the longest bar needs 34 squares; with 40 or 50 some bars end between grid lines (340 ÷ 40 = 8.5, 120 ÷ 50 = 2.4).

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18. Q.18

    A rectangle is 8 cm long and 5 cm wide. What is its perimeter?

    1. A 13 cm
    2. B 21 cm
    3. C 26 cm
    4. D 40 cm
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    Correct answer: (C) 26 cm

    Perimeter = 8 + 5 + 8 + 5 = 2 × (8 + 5) = 26 cm. 13 cm counts only two sides, and 40 is the area in square cm.

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19. Q.19

    In a class survey of favourite fruits, the tally for mango shows 6 complete groups of five and 2 more marks. How many children chose mango?

    1. A 26 children
    2. B 62 children
    3. C 8 children
    4. D 32 children
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    Correct answer: (D) 32 children

    Each complete group stands for 5, so 6 groups = 30, and 2 more marks make 30 + 2 = 32 children. (26 comes from wrongly counting a group as 4.)

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20. Q.20

    Which of the following capital letters of the English alphabet, written as plain block letters, has exactly two lines of symmetry?

    1. A A
    2. B H
    3. C M
    4. D T
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    Correct answer: (B) H

    H has a vertical and a horizontal line of symmetry. A, M and T each have only one line of symmetry, the vertical one.

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21. Q.21

    Observe the pattern: 9 × 9 + 7 = 88; 98 × 9 + 6 = 888; 987 × 9 + 5 = 8888. Which is the next line of the pattern?

    1. A 9875 × 9 + 4 = 88888
    2. B 9876 × 9 + 3 = 88888
    3. C 9876 × 9 + 4 = 88888
    4. D 9876 × 9 + 4 = 8888
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    Correct answer: (C) 9876 × 9 + 4 = 88888

    The first number gains the next digit (9876), the number added drops by 1 (4), and the answer gains one more 8. Check: 9876 × 9 = 88,884 and 88,884 + 4 = 88,888.

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22. Q.22

    Which of the following is equal to 2.5?

    1. A 250 tenths
    2. B 2 ones and 5 hundredths
    3. C 25 tenths
    4. D 25 hundredths
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    Correct answer: (C) 25 tenths

    2.5 = 2 ones and 5 tenths = 20 tenths + 5 tenths = 25 tenths, i.e. 25/10. 25 hundredths = 0.25, 250 tenths = 25, and 2 ones and 5 hundredths = 2.05.

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23. Q.23

    A cuboid is built from 1 cm cubes. It is 5 cubes long, 3 cubes wide and 2 cubes high. How many cubes are used?

    1. A 10 cubes
    2. B 15 cubes
    3. C 30 cubes
    4. D 60 cubes
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    Correct answer: (C) 30 cubes

    One layer has 5 × 3 = 15 cubes, and there are 2 layers, so 15 × 2 = 30 cubes. Adding 5 + 3 + 2 = 10 is a common mistake.

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24. Q.24

    How many even numbers lie between 47 and 125?

    1. A 39
    2. B 38
    3. C 40
    4. D 77
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    Correct answer: (A) 39

    The even numbers are 48, 50, ..., 124. Their count is (124 - 48) ÷ 2 + 1 = 38 + 1 = 39. There are 77 numbers in all between 47 and 125.

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25. Q.25

    Which of the following decimals is the greatest?

    1. A 0.65
    2. B 0.09
    3. C 0.69
    4. D 0.7
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    Correct answer: (D) 0.7

    Compare tenths first: 0.7 has 7 tenths, 0.65 and 0.69 have 6 tenths and 0.09 has 0 tenths. So 0.7 (= 0.70) is the greatest, even though it has fewer digits.

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26. Q.26

    Which fraction with denominator 35 is equivalent to 3/5?

    1. A 21/35
    2. B 15/35
    3. C 33/35
    4. D 18/35
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    Correct answer: (A) 21/35

    35 = 5 × 7, so multiply both numerator and denominator by 7: 3/5 = (3 × 7)/(5 × 7) = 21/35. Writing 33/35 adds 30 to the numerator instead of multiplying.

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27. Q.27

    A rectangle 3 cm × 2 cm is cut off from one corner of a rectangle 8 cm × 6 cm, along the sides of the big rectangle. What is the perimeter of the remaining shape?

    1. A 18 cm
    2. B 23 cm
    3. C 28 cm
    4. D 33 cm
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    Correct answer: (C) 28 cm

    The original perimeter is 2 × (8 + 6) = 28 cm. Cutting the corner removes 3 cm and 2 cm of boundary but adds two new edges of 3 cm and 2 cm, so the perimeter stays 28 cm (though the area falls from 48 to 42 sq cm).

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28. Q.28

    How many factors does 36 have?

    1. A 7 factors
    2. B 9 factors
    3. C 8 factors
    4. D 10 factors
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    Correct answer: (B) 9 factors

    The factor pairs of 36 are 1 × 36, 2 × 18, 3 × 12, 4 × 9 and 6 × 6. Counting 6 only once, the factors are 1, 2, 3, 4, 6, 9, 12, 18 and 36: 9 factors.

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29. Q.29

    Which of the following is a common factor of 96 and 144 but NOT a factor of 120?

    1. A 12
    2. B 36
    3. C 48
    4. D 24
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    Correct answer: (C) 48

    48 divides 96 (48 × 2) and 144 (48 × 3) but not 120 (120 ÷ 48 = 2, remainder 24). 24 and 12 divide all three numbers, and 36 does not divide 96.

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30. Q.30

    If 845 - □ = 378, what number goes in the box?

    1. A 1,223
    2. B 477
    3. C 533
    4. D 467
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    Correct answer: (D) 467

    The missing number is 845 - 378 = 467, because subtraction can be undone this way. Check: 845 - 467 = 378.

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31. Q.31

    A shopkeeper buys 3 dozen eggs at ₹ 69 per dozen and sells every egg at ₹ 7 each. What is his total profit?

    1. A ₹ 45
    2. B ₹ 15
    3. C ₹ 207
    4. D ₹ 252
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    Correct answer: (A) ₹ 45

    Cost = 3 × 69 = ₹ 207. He sells 36 eggs for 36 × 7 = ₹ 252. Profit = 252 − 207 = ₹ 45 (₹ 15 on each dozen).

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32. Q.32

    Riya ate 2/8 of a pizza and Sonu ate 1/4 of another pizza of the same size. Which statement is correct?

    1. A Riya ate more, since 2 is more than 1
    2. B Sonu ate more, since 4 is less than 8
    3. C They cannot be compared, as the denominators differ
    4. D Both ate the same amount, since 2/8 equals 1/4
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    Correct answer: (D) Both ate the same amount, since 2/8 equals 1/4

    2/8 = (2 ÷ 2)/(8 ÷ 2) = 1/4, so the two amounts are equal: two eighths of a pizza make one quarter.

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33. Q.33

    A wall 2 m long and 1 m 60 cm high is to be covered with square tiles of side 20 cm. How many tiles are needed?

    1. A 18 tiles
    2. B 36 tiles
    3. C 80 tiles
    4. D 1600 tiles
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    Correct answer: (C) 80 tiles

    Along the length 200 ÷ 20 = 10 tiles fit, and along the height 160 ÷ 20 = 8 tiles, so 10 × 8 = 80 tiles. Check: wall area 32000 sq cm ÷ tile area 400 sq cm = 80.

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34. Q.34

    Using each of the digits 0, 3, 5, 7 and 9 exactly once, the greatest and the smallest 5-digit numbers are formed. What is their difference?

    1. A 66,961
    2. B 66,951
    3. C 93,951
    4. D 67,049
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    Correct answer: (B) 66,951

    Greatest = 97,530. Smallest = 30,579, because 0 cannot be the first digit of a 5-digit number. 97,530 - 30,579 = 66,951 (check: 30,579 + 66,951 = 97,530).

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35. Q.35

    A number divided by 6 gives quotient 47 and remainder 5. What are the quotient and remainder when the same number is divided by 8?

    1. A Quotient 35, remainder 7
    2. B Quotient 35, remainder 5
    3. C Quotient 36, remainder 1
    4. D Quotient 34, remainder 15
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    Correct answer: (A) Quotient 35, remainder 7

    The number is 6 × 47 + 5 = 287. Since 8 × 35 = 280, we get 287 = 8 × 35 + 7, so the quotient is 35 and the remainder is 7.

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36. Q.36

    A piece of cloth is 6.08 m long. What is its length in metres and centimetres?

    1. A 60 m 8 cm
    2. B 6 m 0.8 cm
    3. C 6 m 8 cm
    4. D 6 m 80 cm
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    Correct answer: (C) 6 m 8 cm

    1 cm = 1/100 m, so 0.08 m = 8/100 m = 8 cm. Hence 6.08 m = 6 m 8 cm, while 6 m 80 cm would be 6.80 m.

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37. Q.37

    What is the sum of the first 9 odd numbers, 1 + 3 + 5 + ... + 17?

    1. A 81
    2. B 90
    3. C 99
    4. D 72
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    Correct answer: (A) 81

    The sum of the first n odd numbers is n × n: 1 + 3 = 4, 1 + 3 + 5 = 9, and so on. So the first 9 odd numbers add up to 9 × 9 = 81.

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38. Q.38

    A ration shop has 6 sacks of wheat of 50 kg each. Each family is given 35 kg. How many families get their full share, and how much wheat is left over?

    1. A 8 families; 15 kg left
    2. B 8 families; 20 kg left
    3. C 9 families; 5 kg left
    4. D 8 families; 30 kg left
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    Correct answer: (B) 8 families; 20 kg left

    Total wheat = 6 × 50 = 300 kg. 300 ÷ 35 = 8 remainder 20, since 8 × 35 = 280. So 8 families are served and 20 kg is left.

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39. Q.39

    Which is the correct way to record the number 23 using tally marks?

    1. A 4 groups of five and 3 single marks
    2. B 2 groups of ten and 3 single marks
    3. C 5 groups of four and 3 single marks
    4. D 3 groups of five and 8 single marks
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    Correct answer: (A) 4 groups of five and 3 single marks

    In tally marks every fifth mark is drawn across four marks to make a group of five. 23 = 4 × 5 + 3, so it is 4 groups of five and 3 single marks; single marks are never left at 5 or more.

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40. Q.40

    In the number 73.46, what is the value of the digit 6?

    1. A 6 thousandths
    2. B 6 hundredths
    3. C 6 tenths
    4. D 6 ones
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    Correct answer: (B) 6 hundredths

    In 73.46, the 4 is in the tenths place and the 6 is in the hundredths place, so the 6 stands for 6/100 = 0.06.

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41. Q.41

    Without adding, decide which of the following sums is odd.

    1. A 11 + 15 + 21 + 33
    2. B 46 + 52 + 64
    3. C 17 + 23 + 35
    4. D 19 + 27 + 34
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    Correct answer: (C) 17 + 23 + 35

    A sum is odd only when it has an odd count of odd numbers: 17 + 23 + 35 has three odd numbers, so it is odd (75). The others have two, four or no odd numbers: 80, 80 and 162 are even.

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42. Q.42

    Which of the following is NOT equal to 47 mm?

    1. A 4.7 cm
    2. B 4 cm 7 mm
    3. C 47/10 cm
    4. D 0.47 m
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    Correct answer: (D) 0.47 m

    Since 10 mm = 1 cm, 47 mm = 4 cm 7 mm = 4.7 cm = 47/10 cm. But 0.47 m = 47 cm = 470 mm, ten times as long.

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43. Q.43

    Four packets of the same rice are on sale: 400 g for ₹ 52, 1 kg for ₹ 125, 250 g for ₹ 35 and 500 g for ₹ 60. Which packet gives rice at the cheapest rate (the lowest price for the same weight)?

    1. A 400 g for ₹ 52
    2. B 500 g for ₹ 60
    3. C 1 kg for ₹ 125
    4. D 250 g for ₹ 35
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    Correct answer: (B) 500 g for ₹ 60

    Cost of 100 g: 52 ÷ 4 = ₹ 13, 125 ÷ 10 = ₹ 12.50, (35 × 2) ÷ 5 = ₹ 14 and 60 ÷ 5 = ₹ 12. The 500 g packet is cheapest at ₹ 12 per 100 g.

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44. Q.44

    What is the sum 1 + 2 + 3 + ... + 20?

    1. A 210
    2. B 200
    3. C 420
    4. D 190
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    Correct answer: (A) 210

    Pair the numbers from the two ends: 1 + 20, 2 + 19, ..., 10 + 11 make 10 pairs of 21 each, so the sum is 10 × 21 = 210.

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45. Q.45

    Which of these arrangements of six equal squares, joined edge to edge, can be folded into a cube?

    1. A A row of 4 squares, with one square above the 2nd and one below the 3rd
    2. B A row of 4 squares, with one square above the 1st and one above the 2nd
    3. C A single row of 6 squares
    4. D Two rows of 3 squares each, forming a rectangle
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    Correct answer: (A) A row of 4 squares, with one square above the 2nd and one below the 3rd

    A row of 4 folds into the four side faces of the cube; a square above any of them becomes the top and a square below any of them becomes the bottom. With both extra squares above the row, two faces overlap on top and the bottom stays open; a row of 6 or a 2 × 3 rectangle also leaves faces overlapping or open.

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46. Q.46

    How many faces, edges and corners does a cube have?

    1. A 6 faces, 8 edges, 12 corners
    2. B 6 faces, 12 edges, 8 corners
    3. C 8 faces, 12 edges, 6 corners
    4. D 4 faces, 12 edges, 8 corners
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    Correct answer: (B) 6 faces, 12 edges, 8 corners

    A cube (like a die) has 6 square faces, 12 edges where two faces meet, and 8 corners where three edges meet. Swapping the numbers of edges and corners is a common slip.

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47. Q.47

    Ravi multiplies 47 × 36 in columns. His first partial product is 47 × 6 = 282. What should the second partial product be?

    1. A 1,692
    2. B 2,820
    3. C 1,410
    4. D 141
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    Correct answer: (C) 1,410

    The 3 in 36 stands for 3 tens, so the second partial product is 47 × 30 = 1,410. Then 282 + 1,410 = 1,692 is the final product.

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48. Q.48

    A shop opens at 9:30 a.m. and closes at 8:15 p.m. It is shut for 1 hour 15 minutes for lunch. For how long is it open in a day?

    1. A 9 hours 30 minutes
    2. B 10 hours 45 minutes
    3. C 12 hours
    4. D 9 hours 45 minutes
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    Correct answer: (A) 9 hours 30 minutes

    From 9:30 a.m. to 8:15 p.m. (20:15) is 10 hours 45 minutes. Taking away the lunch break leaves 10 h 45 min − 1 h 15 min = 9 hours 30 minutes.

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49. Q.49

    Tea is made for 36 guests at a school function. Each cup needs 150 mL of milk, and milk is sold only in 500 mL packets costing ₹ 28 each. What is the least amount that must be spent on milk?

    1. A ₹ 280
    2. B ₹ 302.40
    3. C ₹ 308
    4. D ₹ 151.20
    Show answer

    Correct answer: (C) ₹ 308

    Milk needed = 36 × 150 = 5,400 mL. 10 packets give only 5,000 mL, so 11 packets are needed. Cost = 11 × 28 = ₹ 308. (₹ 280 buys 10 packets, which is not enough.)

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50. Q.50

    Runs scored in five matches - Anil: 34, 0, 57, 21, 48; Sohan: 12, 66, 45, 30, 25. Who scored more runs in all, and by how many?

    1. A Anil, by 18 runs
    2. B Sohan, by 28 runs
    3. C Sohan, by 18 runs
    4. D Sohan, by 8 runs
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    Correct answer: (C) Sohan, by 18 runs

    Anil: 34 + 0 + 57 + 21 + 48 = 160. Sohan: 12 + 66 + 45 + 30 + 25 = 178. Sohan scored 178 − 160 = 18 runs more.

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