modal question paper - class 7- pt3

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MODAL QUESTION PAPER - PT 3

SECTION A – OBJECTIVE TYPE

1. Multiple Choice Questions (4 × 1 = 4)

1. A number is multiplied by 2³ and then divided by 2⁵. The final result is the original number multiplied by
   a) 2²
   b) 2⁻²
   c) 2⁸
   d) 2⁻⁸

2. The sides of a right-angled triangle are consecutive integers. The perimeter of the triangle is 24 cm.
   The length of the hypotenuse is
   a) 9 cm
   b) 10 cm
   c) 11 cm
   d) 13 cm

3. A square and a rectangle have equal areas. The rectangle has length 12 cm and breadth 3 cm.
   The perimeter of the square is
   a) 24 cm
   b) 36 cm
   c) 48 cm
   d) 30 cm

4. If
   
   (3²) ̽ = 3¹⁰   then the value of (x) is
   a) 2
   b) 4
   c) 5
   d) 10

2. Fill in the Blanks (2 × 1 = 2)

5. If a right-angled triangle has sides 6 cm and 8 cm, then the length of the hypotenuse is ________ cm.

6. The value of  2⁵ × 5⁵ / 10³  is __________.

3. True or False (2 × 1 = 2)

7. If the area of a square is numerically equal to the perimeter of a rectangle, then the dimensions of the rectangle are uniquely determined.
   (True / False)

8. If (a ͫ  ÷  a ⁿ = a ͫ  ⁻ ⁿ ) then the rule is valid for all integers (m) and (n), where (a is not equal to 0 ).
   (True / False)

4. Assertion – Reason (2 × 1 = 2)

9. Assertion (A): A triangle with sides 5 cm, 12 cm and 13 cm is right-angled.
   Reason (R): (13² = 5² + 12² )

a) Both A and R are true and R is the correct explanation of A
b) Both A and R are true but R is not the correct explanation of A
c) A is true but R is false
d) A is false but R is true

10. Assertion (A): The perimeter of a square increases four times when its side is doubled.
    Reason (R): Perimeter of a square is directly proportional to its side.

a) Both A and R are true and R is the correct explanation of A
b) Both A and R are true but R is not the correct explanation of A
c) A is true but R is false
d) A is false but R is true

SECTION B – SHORT ANSWER

11. The perimeter of a rectangle is 72 cm. If its length is double its breadth, find the area of the rectangle.

12. A square and a rectangle have equal perimeters. The rectangle has dimensions 18 cm × 12 cm.
    Find the area of the square.

13. Simplify:  

    
    
    

14. The diagonal of a square is 14√2 cm. Find the area of the square.

15. In a right-angled triangle, the hypotenuse is 26 cm and one side is 10 cm. Find the length of the other side.

16. a) Which is greater, 3 ¹² or 6 ⁶?

     b) If 4^x =128, then find the value of x.
17. A ladder 13 m long reaches the top of a wall. The foot of the ladder is 5 m away from the wall. Find the height of the wall. 

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SECTION C – LONG ANSWER

18. A rectangular playground is 28 m long and 21 m wide.
    A path of uniform width runs along the boundary of the playground.
    If the area of the path is 420 m², find the width of the path.

19. The length and breadth of a rectangle are in the ratio 5 : 3.
    If its perimeter is 64 cm, find
    a) its dimensions
    b) its area

20. A triangle has sides 9 cm, 40 cm and 41 cm.
    a) Verify whether the triangle is right-angled.
    b) Identify the hypotenuse.

21. Find n if 

    
    
    

22. Construct a triangle ABC such that
    AB = 6 cm, AC = 5 cm and ∠A = 90°.
    Name the congruence rule used and justify it.