Grade 10 : CBSE : Mathematics Sample question paper (MCQ) with detailed answer - Term 1

 Class - X

Mathematics

Sample Question Paper - Term 1

1) The ratio of LCM and HCF of the least composite and the least prime numbers is _____

Solution

Least composite number = 4

Least prime number = 2

LCM of the least composite and the least prime numbers  

that is, LCM of 4 and 2 is 4

HCF of 4 and 2 is 2

ration of LCM and HCF = 4:2 = 2:1

Hence the answer is 2:1

2) The value of k for which the lines 5x+7y=3 and 15x+21y = k coincide is _______

Solution

consider the first equation 5x+7y=3

 observe the second equation, if we multiply the first equation by 3 then we will get the left-hand side of the second equation

that is, (5x+7y=3) * 3 

gives,  15x + 21y = 9

now let's compare the above equation with the second equation, 

we got k = 9

Hence the value of k is 9

Note: When two lines are coinciding with each other, then there could be no intercept difference between them. For example, 5x+7y=3 and 15x+21y = 9  are coinciding lines.

3) A girl walks 200m towards the East and then 150m towards the North. The distance of the girl from the starting point is _____

Solution 

Hence the distance of the girl from the starting point is 250m

4) The lengths of the diagonals of a rhombus are 24cm and 32cm, then the length of the altitude of the rhombus is _____

Solution

In Rhombus, all the sides are equal

Diagonals of the Rhombus are Perpendicular bisectors of each other.

AC is perpendicular to BD

so, OB = BD/2 = 32/2 = 16

      OA = AC/2 = 24/2 = 12

Now, in Right angle Triangle OAB , 

By Pythagorus theorem 

AB^2 = OA^2 + OB^2

          =  12^2 + 16^2

          = 144 + 256

AB^2 = 400

AB ( Base ) = 20

Area of Rhombus = 1/2 * diagonal 1 * diagonal 2

                              = 1/2 * 24 * 32  = 12 * 32

                              =  384 cm^2

Area using base and height :

 

Area of Rhombus = Base * Height

           384             =  20 * Height

height = 384/20 = 19.2Cm

Hence the altitude of the Rhombus = 19.2cm

5) Two fair coins are tossed. What is the probability of getting at the most one head?

Solution

Possible outcomes (Sample space S) = { HT , TT, HH , TH }

Number of possible outcomes [ n(S) = 4 ]

Favourable Outcome = Getting at the most one head = Outcomes with NO head + Outcome with 1 head

= { HT , TT , TH }

Number of favourable outcomes = 3

Probability = Number of favourable outcomes / Total number of outcomes

Probability of getting at the most one head = 3 / 4 or 3:4

Hence the answer is 3/4

6) ΔABC~ΔPQR. If AM and PN are altitudes of ΔABC and ΔPQR respectively and AB^2 : PQ^2 = 4 : 9, then AM:PN =

Solution

Given,  

               AB^2 : PQ^2 = 4 : 9

implies     AB^2 / PQ^2 = 4 / 9

               (AB/PQ)^2 = 2^2/3^2

                AB/PQ = 2/3

Also given, Triangle ABC and Triangle PQR are similar triangles then

Ratio of their altitudes = ratio of their sides

 AM : PN = AB : PQ

that is , AM : PN = 2 : 3

Hence the answer is 2 : 3

          

Trigonometry Ratios of 0°,30°,45°,60°,90°

 

Trigonometric Ratios of 45°

In Triangle ABC, right-angled at B

 if one of the angles is 45°, then the other angle is also 45° 

(The sum of the angles in a triangle is 180°. One angle is 90°, another angle is 45°, then the third angle is 45°.)

so, Angle B = 90°

      Angle A = Angle C = 45°

Trigonometry Ratio Table 

        

Grade 1,Grade 2 : SOF International Mathematics Olympiad (IMO) - Sample Question Paper with answer

Grade 1 , Grade 2 : Mathematics Olympiad - Sample Question Paper with Answer

Logical Reasoning

1) Select the odd one out.

A. CAT 

B. Rabbit

C. Turtle

D. Dog

Answer : C

2) Which of the following is the heaviest?

A. Mango

B. Orange

C. Apple

D. WaterMelon

Answer : D

3) Who is farthest from the pole?

A. Peppa

B. Jerry

C. Tom

D. Dora

Answer : A

4) There is a certain relationship between the pair of figures given on either side of : : . Identify the relationship of given pair and find the missing figure.

Answer : B

5) Which of the following options will complete the pattern in the given figure.

20 , 22 , __ , 26 , 28

A. 30

B. 23

C. 24

D. 27

Answer : C

6) Count the number of triangles in the given figure.

A. 4

B. 3

C. 5

D. 2

Answer : A

7) Jerry is standing between

A. Tom and Peppa

B. 2nd from right

C. Tom and peppa

D. 2nd from left

Answer : C

8. _______ is the shortest line

A. Green line

B. Black line

C. Blue line

D. Red line

Answer : B

9. 5pm is _____

A. Morning

B. Afternoon

C. Night

D. Evening

Answer : D

10. Find the missing number in the given pattern

35 , 40 , 45, ___, 55 , 60

A. 50

B. 65

C. 52

D. 51

Answer : A

Mathematical Reasoning

11. Which of the following shows the greatest number

A . 54 - 42

B. 35 - 21

C. 98 - 87

D. 86 - 73

Answer :  B 

54 - 42 = 12

35 - 21 = 14

98 - 87 = 11

86 - 73 = 13

12. Which of the following shows the greatest number?

A. 7 - 3 = 4

B. 7 - 4 = 3

C. 7 - 5 = 2

D. 7 - 2 = 5

Answer : B

total circles = 7, 4 circles gets canceled

7-4=3

13. Select the Incorrect match

A. 8tens 1 ones = 18

B. 4 ones 3 tens = 34

C. 7 tens 9 ones = 79

D. 5 ones 2 tens = 25

Answer : A

8tens 1 ones = 81 not 18.

14. Find the sum of the greatest and the least number from the following set of numbers

 20 , 25 , 15 , 45 , 80 , 70 , 75 , 15 , 35

A. 40

B. 85

C. 95

D. 70

Answer : C

 least number = 15 , greatest number = 80

Sum = 80+15 = 95

15.  ⃞ = 1 unit , then pole A is ____ units shorter than pole B

A. 1

B. 2

C. 3

D. 4

Answer : B

16.  I am a two-digit number smaller than 18 and greater than 12. Identify the number.

A. 20

B. 17

C. 10

D . 18

Answer : B

17. Arrange the numbers from greatest to the smallest.

P=16+3 

Q=20-5 

R = 23 + 1 

S = 50-25

A. Q , P , R , S

B. S , R , P , Q

C. R , S , P , Q

D. P , Q , R , S

Answer : B

18. Find the value of X + Y .

          34 + 2X = Y8

A. 16

B. 10

C. 18

D. 9

Answer: D

X = 4 , Y = 5

34 + 24 = 58 

X + Y = 4 + 5 = 9

19. The given number line shows _______

A. Counting by 2's

B. Counting by 3's

C. Counting by 4's

D. Counting by 1's

Answer: A

20. Which shapes make up this arrow? 

      

A. Rectangle , Square

B. Square , Triangle

C. Rectangle , Triangle

D. Square , Triangle

Answer: C

Everyday Mathematics

21. Who has the maximum number of balls?

A. Tom

B. Peppa

C. Dora

D. Jerry

Answer: C

Dora has 6 balls

22. Jerry has 32 candies. He buys 5 more candies. How many candies he have altogether?

A. 35

B. 38

C. 39

D. 37

Answer: D

32 + 5 = 37

23. Peppa has 80 marbles. She gave 25 marbles to Dora and 15 to Tom. How many marbles are left with Peppa?

A. 40

B. 30

C. 50

D. 20

Answer: A

25 + 15 = 40

marbles left = 80 - 40 = 40

24. A bag of toys weighs 3kg. How much do 4 such bags of toy weigh?

A. 8 kg

B. 12 kg

C. 10 kg

D. 15 Kg

Answer: B

3 * 4 = 12

26. Which activity can be done in 1 minute?

A. Sharpening a pencil

B. Painting a wall

C. Going to school

D. Playing Chess

Answer: A

27. Tom has Rs.25 with him. He gives Rs. 10 to Jerry and Rs 5 to Dora. How much money is left with Tom now?

A. 20

B. 15

C. 10

D. 5

Answer: C

amount he gives = 10 + 5 = 15

Money left = 25 - 15 = 10

28. A Rectangle has ____ number of curved lines.

A. 4

B. 3

C. 5

D. 0

Answer: D

Rectangle has only straight lines no curved lines

29. Jerry has Rs.60. Which of the following items can he buy, if he spends all his money?

Notebook = Rs. 30

Pencil = Rs 5

Eraser = Rs 5

Pen = Rs 10

A. 1 Notebook, 2Eraser

B. 2pens, 2 eraser, 1Notebook

C. 1 pen, 2Notebook

D. 3Eraser, 1pencil, 3 pens

Answer: B

2pens = 20 , 2eraser = 10 , 1notebook = 30

20 + 10 + 30 = 60

30. Peppa has 20 flowers. She puts them equally into baskets of 3 flowers each. How many flowers are left in the end?

A. 3

B. 0

C. 2

D. 1

Answer: C

20 divided by 3 , Remainder = 2

Achievers Section

31. Dora has different types of fruits. She has 3 more apples than oranges. She has 6 more oranges than bananas. If she has 4 bananas, then the total number of fruits she has is ____?

A. 40

B. 15

C. 27

D. 13

Answer:  C

number of bananas = 4

oranges = 6 + bananas = 6+4 = 10

Apple =  oranges + 3 = 10 + 3 = 13

Total number of fruits = 4 + 10 + 13 = 27

32. Replace P and Q with appropriate signs respectively.

           8 P 2 = 2 Q 4

A. +,+

B. -, -

C. + , -

D. - , +

Answer: D

8 - 2 = 2 + 4 = 6

33. If day before yesterday was Thursday, then day after tomorrow will be ________

A. Sunday

B. Monday

C. Friday

D. Saturday

Answer: B

Day before yesterday = Thursday

Yesterday = Friday

Today = Saturday

Tomorrow = Sunday

Day after tomorrow = Monday

34. One doll cost Rs 30. Find the maximum number of dolls Peppa can buy for Rs. 70

A. 1

B. 2

C. 3

D. 4

Answer: B

One doll = Rs 30 , 2 dolls = Rs 60 , 3dolls = Rs 90.She is having Rs 70.So she can buy 2dolls.

35. Select the odd one out.

A. 5+5

B. 3+7

C. 4+5

D. 8+2

Answer: C

5+5=10 , 3+7=10 , 4+5=9 , 8+2 = 10

Grade 1,Grade 2 : SOF International Mathematics Olympiad (IMO) - Sample Question Paper

 Grade 1 , Grade 2 : Mathematics Olympiad - Sample Question Paper 

 

For Answers click here

Logical Reasoning

1) Select the odd one out.

A. CAT 

B. Rabbit

C. Turtle

D. Dog

2) Which of the following is the heaviest?

A. Mango

B. Orange

C. Apple

D. WaterMelon

3) Who is farthest from the pole?

A. Peppa

B. Jerry

C. Tom

D. Dora

4) There is a certain relationship between the pair of figures given on either side of : : . Identify the relationship of given pair and find the missing figure.

5) Which of the following options will complete the pattern in the given figure.

20 , 22 , __ , 26 , 28

A. 30

B. 23

C. 24

D. 27

6) Count the number of triangles in the given figure.

A. 4

B. 3

C. 5

D. 2

7) Jerry is standing between

A. Tom and Peppa

B. 2nd from right

C. Tom and peppa

D. 2nd from left

8. _______ is the shortest line

A. Green line

B. Black line

C. Blue line

D. Red line

9. 5pm is _____

A. Morning

B. Afternoon

C. Night

D. Evening

10. Find the missing number in the given pattern

35 , 40 , 45, ___, 55 , 60

A. 50

B. 65

C. 52

D. 51

Mathematical Reasoning

11. Which of the following shows the greatest number

A . 54 - 42

B. 35 - 21

C. 98 - 87

D. 86 - 73

12. Which of the following shows the greatest number?

A. 7 - 3 = 4

B. 7 - 4 = 3

C. 7 - 5 = 2

D. 7 - 2 = 5

13. Select the Incorrect match

A. 8tens 1 ones = 18

B. 4 ones 3 tens = 34

C. 7 tens 9 ones = 79

D. 5 ones 2 tens = 25

14. Find the sum of the greatest and the least number from the following set of numbers

 20 , 25 , 15 , 45 , 80 , 70 , 75 , 15 , 35

A. 40

B. 35

C. 65

D. 70

15.  ⃞ = 1 unit , then pole A is ____ units shorter than pole B

A. 1

B. 2

C. 3

D. 4

16.  I am a two-digit number smaller than 18 and greater than 12. Identify the number.

A. 20

B. 17

C. 10

D . 18

17. Arrange the numbers from greatest to the smallest.

P=16+3 

Q=20-5 

R = 23 + 1 

S = 50-25

A. Q , P , R , S

B. S , R , P , Q

C. R , S , P , Q

D. P , Q , R , S

18. Find the value of X + Y .

          34 + 2X = Y8

A. 16

B. 10

C. 18

D. 9

19. The given number line shows _______

A. Counting by 2's

B. Counting by 3's

C. Counting by 4's

D. Counting by 1's

20. Which shapes make up this arrow? 

      

A. Rectangle , Square

B. Square , Triangle

C. Rectangle , Triangle

D. Square , Triangle

Everyday Mathematics

21. Who has the maximum number of balls?

A. Tom

B. Peppa

C. Dora

D. Jerry

22. Jerry has 32 candies. He buys 5 more candies. How many candies he have altogether?

A. 35

B. 38

C. 39

D. 37

23. Peppa has 80 marbles. She gave 25 marbles to Dora and 15 to Tom. How many marbles are left with Peppa?

A. 40

B. 30

C. 50

D. 20

24. A bag of toys weighs 3kg. How much do 4 such bags of toy weigh?

A. 8 kg

B. 12 kg

C. 10 kg

D. 15 Kg

26. Which activity can be done in 1 minute?

A. Sharpening a pencil

B. Painting a wall

C. Going to school

D. Playing Chess

27. Tom has Rs.25 with him. He gives Rs. 10 to Jerry and Rs 5 to Dora. How much money is left with Tom now?

A. 20

B. 15

C. 10

D. 5

28. A Rectangle has ____ number of curved lines.

A. 4

B. 3

C. 5

D. 0

29. Jerry has Rs.50. Which of the following items can he buy, if he spends all his money?

Notebook = Rs. 30

Pencil = Rs 5

Eraser = Rs 5

Pen = Rs 10

A. 1 Notebook, 2Eraser

B. 2pens, 2 eraser, 1Notebook

C. 1 pen, 2Notebook

D. 3Eraser, 1pencil, 3 pens

30. Peppa has 20 flowers. She puts them equally into baskets of 3 flowers each. How many flowers are left in the end?

A. 3

B. 0

C. 2

D. 1

Achievers Section

31. Dora has different types of fruits. She has 3 more apples than oranges. She has 6 more oranges than bananas. If she has 4 bananas, then the total number of fruits she has is ____?

A. 40

B. 15

C. 27

D. 13

32. Replace P and Q with appropriate signs respectively.

           8 P 2 = 2 Q 4

A. +,+

B. -, -

C. + , -

D. - , +

33. If day before yesterday was Thursday, then day after tomorrow will be ________

A. Sunday

B. Monday

C. Friday

D. Saturday

34. One doll cost Rs 30. Find the maximum number of dolls Peppa can buy for Rs. 70

A. 1

B. 2

C. 3

D. 4

35. Select the odd one out.

A. 5+5

B. 3+7

C. 4+5

D. 8+2