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.101

   1 kg of besan costs ₹ 92. Consider: 1. 500 g of besan costs ₹ 46. 2. 250 g of besan costs ₹ 23. 3. 1 kg 750 g of besan costs ₹ 161. Which of these statements are correct?

   1. A 1 and 2 only
   2. B 2 and 3 only
   3. C 1 and 3 only
   4. D 1, 2 and 3
   Show answer

   Correct answer: (D) 1, 2 and 3

   500 g is half of 1 kg, so it costs 92 ÷ 2 = ₹ 46; 250 g is a quarter, so ₹ 23; 1 kg 750 g costs 92 + 46 + 23 = ₹ 161. All three are correct.

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2. Q.102

   A railway timetable gives distances from the starting station: A 0 km, B 142 km, C 287 km and D 455 km. How far is it from B to D?

   1. A 313 km
   2. B 597 km
   3. C 168 km
   4. D 145 km
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   Correct answer: (A) 313 km

   Distance from B to D = 455 − 142 = 313 km. (168 km is C to D and 145 km is B to C; 145 + 168 = 313 checks it.)

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3. Q.103

   On a map, 1 cm stands for 2 km. Two villages are 7 cm apart on the map. What is the actual distance between them?

   1. A 14 km
   2. B 9 km
   3. C 3.5 km
   4. D 7 km
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   Correct answer: (A) 14 km

   Each centimetre on the map stands for 2 km, so 7 cm stands for 7 × 2 = 14 km. Dividing (3.5 km) or adding (9 km) are common slips.

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4. Q.104

   A rectangular plot is 12 m long and 9 m wide. A square flower bed of side 3 m is made in one corner. What is the area of the plot outside the flower bed?

   1. A 96 sq m
   2. B 99 sq m
   3. C 105 sq m
   4. D 117 sq m
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   Correct answer: (B) 99 sq m

   Plot area = 12 × 9 = 108 sq m and flower bed = 3 × 3 = 9 sq m. Remaining area = 108 − 9 = 99 sq m.

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5. Q.105

   A solid has a square base and four triangular faces that meet at one point at the top. How many edges and corners does it have?

   1. A 8 edges, 5 corners
   2. B 5 edges, 8 corners
   3. C 8 edges, 4 corners
   4. D 12 edges, 5 corners
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   Correct answer: (A) 8 edges, 5 corners

   The base has 4 edges, and 4 more edges rise from the base corners to the top, so 8 edges. The corners are the 4 base corners plus the top point, so 5.

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6. Q.106

   In a pictograph of children who come to school by bus, the key is: one symbol = 4 children. Class 3 is shown by 6 whole symbols and a half symbol. How many children of Class 3 come by bus?

   1. A 24 children
   2. B 28 children
   3. C 25 children
   4. D 26 children
   Show answer

   Correct answer: (D) 26 children

   6 whole symbols = 6 × 4 = 24 children and half a symbol = 2 children, so 24 + 2 = 26 children. (25 wrongly reads the half symbol as 1 child.)

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7. Q.107

   A cone stands on its circular base on a table. When it is seen from directly above, it looks like:

   1. A A triangle standing on its base
   2. B A circle with a dot at its centre
   3. C A square with a dot at its centre
   4. D A semicircle with its flat side down
   Show answer

   Correct answer: (B) A circle with a dot at its centre

   From above, the circular base shows as a circle, and the pointed top (the corner of the cone) is seen exactly over its centre as a dot. The triangle is what is seen from the front.

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8. Q.108

   A bus leaves a town at 21:40 and reaches a city at 06:15 the next morning. How long does the journey take?

   1. A 8 hours 35 minutes
   2. B 15 hours 25 minutes
   3. C 9 hours 35 minutes
   4. D 8 hours 25 minutes
   Show answer

   Correct answer: (A) 8 hours 35 minutes

   From 21:40 to midnight (24:00) is 2 hours 20 minutes, and from midnight to 06:15 is 6 hours 15 minutes. Total = 8 hours 35 minutes.

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9. Q.109

   Asha sold her old mobile phone for ₹ 3,860 and made a loss of ₹ 1,145. For how much had she bought it?

   1. A ₹ 2,715
   2. B ₹ 4,905
   3. C ₹ 5,105
   4. D ₹ 5,005
   Show answer

   Correct answer: (D) ₹ 5,005

   With a loss, cost price = selling price + loss = 3,860 + 1,145 = ₹ 5,005. Check: 5,005 − 1,145 = 3,860.

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10. Q.110

    A train leaves Station A at 10:40 p.m., reaches Station B at 1:15 a.m., stops there for 10 minutes and reaches Station C at 4:05 a.m. For how long does it run between B and C?

    1. A 2 h 50 min
    2. B 2 h 40 min
    3. C 2 h 30 min
    4. D 5 h 25 min
    Show answer

    Correct answer: (B) 2 h 40 min

    It leaves B at 1:15 + 10 min = 1:25 a.m. From 1:25 a.m. to 4:05 a.m. is 2 h 40 min. (2 h 50 min includes the halt; 5 h 25 min is A to C.)

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11. Q.111

    A timetable shows three morning trains from Patna to Gaya: Train X leaves 6:45, arrives 9:20; Train Y leaves 7:50, arrives 10:05; Train Z leaves 8:35, arrives 10:55. Which train takes the least time for the journey?

    1. A Train Z
    2. B Train Y
    3. C Train X
    4. D All three take the same time
    Show answer

    Correct answer: (B) Train Y

    X takes 2 h 35 min, Y takes 2 h 15 min (7:50 to 10:00 is 2 h 10 min, plus 5 min) and Z takes 2 h 20 min, so Y is quickest. Subtracting the times like decimals (10.05 − 7.50 = 2.55) wrongly makes Z look quickest.

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12. Q.112

    Which statement is true about a rectangle 6 cm × 4 cm and a rectangle 8 cm × 3 cm?

    1. A They have the same area but different perimeters
    2. B They have the same perimeter but different areas
    3. C They have the same area and the same perimeter
    4. D They have different areas and different perimeters
    Show answer

    Correct answer: (A) They have the same area but different perimeters

    Areas: 6 × 4 = 24 sq cm and 8 × 3 = 24 sq cm (equal). Perimeters: 2 × (6 + 4) = 20 cm and 2 × (8 + 3) = 22 cm (different).

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13. Q.113

    A school store had 2,345 notebooks. It bought 1,878 more and then gave away 2,569 to students. How many notebooks are left?

    1. A 1,754
    2. B 4,223
    3. C 1,654
    4. D 1,644
    Show answer

    Correct answer: (C) 1,654

    2,345 + 1,878 = 4,223 notebooks; 4,223 - 2,569 = 1,654 are left. Check: 1,654 + 2,569 = 4,223.

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14. Q.114

    How many millimetres are there in 3 m 4 cm?

    1. A 304 mm
    2. B 3004 mm
    3. C 3040 mm
    4. D 3400 mm
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    Correct answer: (C) 3040 mm

    3 m = 300 cm = 3000 mm and 4 cm = 40 mm, so 3 m 4 cm = 3000 + 40 = 3040 mm. Check: 3040 mm = 304 cm = 3 m 4 cm.

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15. Q.115

    Which of these solids can both roll and slide down a slope, depending on how it is placed?

    1. A Cube
    2. B Cylinder
    3. C Sphere
    4. D Cuboid
    Show answer

    Correct answer: (B) Cylinder

    A cylinder rolls on its curved surface and slides when placed on a flat face. A cube and a cuboid have only flat faces, so they slide, while a sphere has no flat face, so it only rolls.

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16. Q.116

    A basket has 56 mangoes, and 3/4 of them are ripe. How many mangoes are NOT ripe?

    1. A 28 mangoes
    2. B 16 mangoes
    3. C 14 mangoes
    4. D 42 mangoes
    Show answer

    Correct answer: (C) 14 mangoes

    1/4 of 56 = 14, so 3/4 of 56 = 42 mangoes are ripe. The rest, 56 - 42 = 14 mangoes (that is, 1/4), are not ripe.

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17. Q.117

    When 1,000 is divided by 7, what are the quotient and the remainder?

    1. A Quotient 140, remainder 20
    2. B Quotient 14, remainder 2
    3. C Quotient 142, remainder 6
    4. D Quotient 142, remainder 5
    Show answer

    Correct answer: (C) Quotient 142, remainder 6

    7 × 142 = 994 and 1,000 - 994 = 6, which is less than 7. Check: 7 × 142 + 6 = 1,000.

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18. Q.118

    Which of the following is the largest amount of money?

    1. A ₹ 4.05
    2. B ₹ 4 and 45 paise
    3. C 450 paise
    4. D 448 paise
    Show answer

    Correct answer: (C) 450 paise

    Change all to paise: 450 paise, ₹ 4.05 = 405 paise, ₹ 4 and 45 paise = 445 paise, and 448 paise. The largest is 450 paise (₹ 4.50).

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19. Q.119

    A school library has 245 Hindi books, 180 English books, 320 story books and 135 science books. How many more story books are there than science books?

    1. A 185 books
    2. B 215 books
    3. C 140 books
    4. D 455 books
    Show answer

    Correct answer: (A) 185 books

    320 − 135 = 185 books (borrowing in the ones and tens). 215 comes from subtracting the smaller digit from the larger in each column.

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20. Q.120

    Each of these shapes has a perimeter of 20 cm. Which one encloses the greatest area?

    1. A A 9 cm × 1 cm rectangle
    2. B A 7 cm × 3 cm rectangle
    3. C A 6 cm × 4 cm rectangle
    4. D A 5 cm × 5 cm square
    Show answer

    Correct answer: (D) A 5 cm × 5 cm square

    Areas: 9 × 1 = 9, 7 × 3 = 21, 6 × 4 = 24 and 5 × 5 = 25 sq cm. Among rectangles with the same perimeter, the closer the shape is to a square, the larger the area.

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21. Q.121

    A carton holding 20 identical soap cakes weighs 2 kg 640 g. The empty carton weighs 240 g. What is the weight of one soap cake?

    1. A 12 g
    2. B 120 g
    3. C 132 g
    4. D 144 g
    Show answer

    Correct answer: (B) 120 g

    Soap cakes alone = 2640 g − 240 g = 2400 g, so one cake = 2400 ÷ 20 = 120 g. Forgetting to remove the carton gives 2640 ÷ 20 = 132 g.

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22. Q.122

    Children want to draw a pictograph of votes for four games: 45, 60, 35 and 50 votes. Which key lets every number be shown with whole symbols only, using the fewest symbols?

    1. A One symbol = 10 votes
    2. B One symbol = 5 votes
    3. C One symbol = 15 votes
    4. D One symbol = 1 vote
    Show answer

    Correct answer: (B) One symbol = 5 votes

    All four numbers are multiples of 5, and 5 is the largest number that divides all of them (10 fails for 45 and 35; 15 fails for 35 and 50). One symbol = 1 vote also uses whole symbols but needs 190 symbols instead of 38.

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23. Q.123

    How many pieces, each 25 cm long, can be cut from a wire 4 m long?

    1. A 16 pieces
    2. B 20 pieces
    3. C 100 pieces
    4. D 160 pieces
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    Correct answer: (A) 16 pieces

    4 m = 400 cm, and 400 ÷ 25 = 16. Check: 1 m gives 4 pieces of 25 cm, so 4 m gives 4 × 4 = 16 pieces.

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24. Q.124

    A class has 42 children. Attendance from Monday to Saturday was 38, 41, 36, 40, 39 and 35. How many absences were there in the week in all?

    1. A 229 absences
    2. B 23 absences
    3. C 7 absences
    4. D 19 absences
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    Correct answer: (B) 23 absences

    Absent each day: 4, 1, 6, 2, 3 and 7, which add up to 23. Check: 6 × 42 = 252 and 252 − 229 (total present) = 23.

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25. Q.125

    A milkman had 25 L 500 mL of milk. He sold 18 L 750 mL. How much milk is left?

    1. A 6 L 750 mL
    2. B 7 L 250 mL
    3. C 7 L 750 mL
    4. D 6 L 250 mL
    Show answer

    Correct answer: (A) 6 L 750 mL

    25 L 500 mL = 25500 mL and 18 L 750 mL = 18750 mL, so 25500 − 18750 = 6750 mL = 6 L 750 mL. Check: 18 L 750 mL + 6 L 750 mL = 25 L 500 mL.

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26. Q.126

    Two brothers have ₹ 5,000 in all. The elder brother has ₹ 2,768. How much more money does the elder brother have than the younger?

    1. A ₹ 2,232
    2. B ₹ 636
    3. C ₹ 546
    4. D ₹ 536
    Show answer

    Correct answer: (D) ₹ 536

    Younger brother: 5,000 - 2,768 = ₹ 2,232. Difference: 2,768 - 2,232 = ₹ 536 (check: 2,232 + 536 = 2,768).

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27. Q.127

    A pictograph shows fruits sold by a vendor in a day, with the key one symbol = 6 fruits. Apples: 5 symbols, bananas: 9 symbols, guavas: 3½ symbols, oranges: 6 symbols. How many more bananas than guavas were sold?

    1. A 33 fruits
    2. B 5½ fruits
    3. C 36 fruits
    4. D 30 fruits
    Show answer

    Correct answer: (A) 33 fruits

    Bananas have 9 − 3½ = 5½ more symbols, and 5½ × 6 = 33. So 33 more bananas were sold (54 − 21 = 33).

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28. Q.128

    A standard seven-piece tangram is cut from one big square. What fraction of the big square does the small square piece cover?

    1. A 1/4
    2. B 1/7
    3. C 1/8
    4. D 1/16
    Show answer

    Correct answer: (C) 1/8

    The two large triangles cover 1/4 each. The other half is split into the medium triangle, the square and the parallelogram (1/8 each) and two small triangles (1/16 each). Check: 1/4 + 1/4 + 3 × 1/8 + 2 × 1/16 = 1.

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29. Q.129

    In a certain year, 5 March is a Monday. What day of the week is 31 March of the same year?

    1. A Friday
    2. B Saturday
    3. C Sunday
    4. D Monday
    Show answer

    Correct answer: (B) Saturday

    Mondays fall on 5, 12, 19 and 26 March, so 27 is Tuesday, 28 Wednesday, 29 Thursday, 30 Friday and 31 Saturday. Check: 31 − 5 = 26 days = 3 weeks 5 days, and Monday + 5 days = Saturday.

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30. Q.130

    A square has a perimeter of 36 cm. What is its area?

    1. A 9 sq cm
    2. B 36 sq cm
    3. C 324 sq cm
    4. D 81 sq cm
    Show answer

    Correct answer: (D) 81 sq cm

    Side = 36 ÷ 4 = 9 cm, so area = 9 × 9 = 81 sq cm. Check: perimeter = 4 × 9 = 36 cm.

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31. Q.131

    How many minutes are there in 3 1/4 hours?

    1. A 195 minutes
    2. B 205 minutes
    3. C 315 minutes
    4. D 325 minutes
    Show answer

    Correct answer: (A) 195 minutes

    3 hours = 3 × 60 = 180 minutes and 1/4 hour = 60 ÷ 4 = 15 minutes, so 180 + 15 = 195 minutes. Taking 1/4 hour as 25 minutes, or an hour as 100 minutes, gives the other options.

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32. Q.132

    What is the place value of 7 in 4,73,256?

    1. A 70,000
    2. B 7,000
    3. C 7,00,000
    4. D 7
    Show answer

    Correct answer: (A) 70,000

    In 4,73,256 the 7 is in the ten-thousands place, so its place value is 7 × 10,000 = 70,000. Its face value is just 7.

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33. Q.133

    A film starts at 10:50 a.m. and lasts 2 hours 25 minutes. At what time does it end?

    1. A 12:75 p.m.
    2. B 1:15 a.m.
    3. C 1:15 p.m.
    4. D 12:15 p.m.
    Show answer

    Correct answer: (C) 1:15 p.m.

    10:50 + 2 hours = 12:50 p.m.; adding 25 minutes gives 12:75, i.e. 1 hour 15 minutes past 12, which is 1:15 p.m. The time has passed noon, so it is p.m., not a.m.

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34. Q.134

    At which of these times do the hands of a clock make an obtuse angle (more than a right angle but less than a straight angle)?

    1. A 2:00
    2. B 3:00
    3. C 6:00
    4. D 5:00
    Show answer

    Correct answer: (D) 5:00

    Neighbouring hour marks are 30° apart. At 2:00 the angle is 60° (acute), at 3:00 it is 90° (right), at 5:00 it is 150° (obtuse) and at 6:00 it is 180° (straight).

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35. Q.135

    In a tile pattern, Figure 1 is 1 white tile with a border of 8 blue tiles, Figure 2 is a 2 × 2 white square with 12 blue border tiles, and Figure 3 is a 3 × 3 white square with 16. How many blue tiles are in the border of Figure 10?

    1. A 44 tiles
    2. B 40 tiles
    3. C 48 tiles
    4. D 100 tiles
    Show answer

    Correct answer: (A) 44 tiles

    The border grows by 4 tiles each time (8, 12, 16, ...), so Figure 10 has 8 + 9 × 4 = 44 blue tiles (also 12 × 12 − 10 × 10 = 44).

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36. Q.136

    Consider these statements:

    1. A closed figure can be made with just two straight line segments.

    2. A circle is a closed curve with no corners.

    3. The capital letter C is an open curve.

    Which of them are correct?

    1. A 1 and 2 only
    2. B 2 and 3 only
    3. C 1 and 3 only
    4. D 1, 2 and 3
    Show answer

    Correct answer: (B) 2 and 3 only

    Two straight line segments cannot enclose a region; at least three are needed (a triangle), so 1 is wrong. A circle is closed and has no corners, and C does not close up, so 2 and 3 are correct.

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37. Q.137

    How many days are there from 15 August to 2 October of the same year, counting both these dates?

    1. A 47 days
    2. B 48 days
    3. C 49 days
    4. D 50 days
    Show answer

    Correct answer: (C) 49 days

    August: 15 to 31 = 17 days (counting both); September: 30 days; October: 1 and 2 = 2 days. Total = 17 + 30 + 2 = 49 days.

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38. Q.138

    The outline of a pond is drawn on paper ruled in 1 cm squares. It covers 14 full squares and 6 squares that are about half covered; tiny bits less than half are ignored. What is the approximate area of the drawing?

    1. A 8 sq cm
    2. B 14 sq cm
    3. C 20 sq cm
    4. D 17 sq cm
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    Correct answer: (D) 17 sq cm

    The full squares give 14 sq cm, and two half squares make one square, so 6 half squares give 3 sq cm. Area ≈ 14 + 3 = 17 sq cm.

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39. Q.139

    Mohan bought a bicycle for ₹ 2,350 and later sold it for ₹ 1,975. What was the result of the deal?

    1. A A profit of ₹ 375
    2. B A loss of ₹ 375
    3. C A loss of ₹ 1,625
    4. D A loss of ₹ 425
    Show answer

    Correct answer: (B) A loss of ₹ 375

    The selling price is less than the cost, so there is a loss: 2,350 − 1,975 = ₹ 375. (1,625 comes from subtracting the smaller digit from the larger in each column.)

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40. Q.140

    A crate holds 24 bottles. How many bottles are there in 135 such crates?

    1. A 810
    2. B 3,420
    3. C 3,140
    4. D 3,240
    Show answer

    Correct answer: (D) 3,240

    135 × 24 = 135 × 20 + 135 × 4 = 2,700 + 540 = 3,240. The answer 810 comes from treating the 2 of 24 as 2 instead of 20 (540 + 270).

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41. Q.141

    A jug holds 1 L 500 mL of lassi. How many glasses of 250 mL each can be filled from it?

    1. A 2 glasses
    2. B 4 glasses
    3. C 6 glasses
    4. D 60 glasses
    Show answer

    Correct answer: (C) 6 glasses

    1 L 500 mL = 1500 mL, and 1500 ÷ 250 = 6 glasses. Check: 6 × 250 mL = 1500 mL; using only the 1 L would wrongly give 4.

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42. Q.142

    In the addition 3□8 + 46□ = 825, what are the two missing digits (first box, second box)?

    1. A 4 and 7
    2. B 5 and 7
    3. C 6 and 7
    4. D 5 and 3
    Show answer

    Correct answer: (B) 5 and 7

    Ones: 8 + □ must end in 5, so □ = 7 (15, carry 1). Tens: □ + 6 + 1 must end in 2, so □ = 5 (12, carry 1); hundreds: 3 + 4 + 1 = 8. Check: 358 + 467 = 825.

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43. Q.143

    Beads are strung in the repeating order red, yellow, yellow, green, blue, red, yellow, yellow, green, blue, ... What is the colour of the 74th bead?

    1. A Red
    2. B Yellow
    3. C Green
    4. D Blue
    Show answer

    Correct answer: (C) Green

    The pattern repeats every 5 beads. 74 = 14 × 5 + 4, so the 74th bead is the 4th bead of the pattern, which is green.

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44. Q.144

    A doctor prescribes 5 mL of syrup three times a day for 6 days. How much syrup is needed in all?

    1. A 15 mL
    2. B 30 mL
    3. C 180 mL
    4. D 90 mL
    Show answer

    Correct answer: (D) 90 mL

    Each day needs 3 × 5 mL = 15 mL, so 6 days need 6 × 15 mL = 90 mL. 15 mL is only one day's dose.

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45. Q.145

    Which of the following capital letters, written as plain block letters, has NO line of symmetry?

    1. A V
    2. B D
    3. C X
    4. D N
    Show answer

    Correct answer: (D) N

    V has a vertical line of symmetry, D a horizontal one and X has two. N has no line of symmetry; it only looks the same after a half turn.

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46. Q.146

    What is the next number in the pattern 2, 5, 10, 17, 26, ...?

    1. A 35
    2. B 39
    3. C 52
    4. D 37
    Show answer

    Correct answer: (D) 37

    The differences are 3, 5, 7, 9, so the next difference is 11: 26 + 11 = 37. (Each term is one more than a square number: 36 + 1 = 37.)

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47. Q.147

    Pooja walks 750 m to the bus stop, travels 4 km 600 m by bus and then walks 380 m to her school. What total distance does she cover?

    1. A 5 km 730 m
    2. B 5 km 73 m
    3. C 4 km 730 m
    4. D 6 km 730 m
    Show answer

    Correct answer: (A) 5 km 730 m

    Walking: 750 + 380 = 1,130 m = 1 km 130 m. Adding the bus journey: 4 km 600 m + 1 km 130 m = 5 km 730 m.

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48. Q.148

    Arjun saves ₹ 5 in the first week, ₹ 8 in the second week, ₹ 11 in the third week, and so on. How much has he saved in all after 8 weeks?

    1. A ₹ 26
    2. B ₹ 98
    3. C ₹ 153
    4. D ₹ 124
    Show answer

    Correct answer: (D) ₹ 124

    Weekly savings are 5, 8, 11, 14, 17, 20, 23, 26 (3 more each week). Their sum is 124, so he has saved ₹ 124; ₹ 26 is only the 8th week's saving.

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49. Q.149

    Neha has ₹ 200. She buys 3 notebooks at ₹ 38.50 each and a pen for ₹ 24.75. How much money is left with her?

    1. A ₹ 60.75
    2. B ₹ 136.75
    3. C ₹ 140.25
    4. D ₹ 59.75
    Show answer

    Correct answer: (D) ₹ 59.75

    Notebooks cost 3 × 38.50 = ₹ 115.50; with the pen she spends 115.50 + 24.75 = ₹ 140.25. Money left = 200 − 140.25 = ₹ 59.75.

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50. Q.150

    460 children are going on a school trip. Each bus can carry 45 children. What is the least number of buses needed?

    1. A 12 buses
    2. B 9 buses
    3. C 11 buses
    4. D 10 buses
    Show answer

    Correct answer: (C) 11 buses

    460 ÷ 45 = 10, remainder 10. Ten buses carry 450 children, and the 10 children left over need one more bus, so 11 buses are needed.

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