🔥 SET 3 (Higher Complexity)

TOPICS: A Tale of three intersecting lines, Arithmetic Expressions, Expressions using letter numbers.

SECTION – A

1. Which cannot be third side if two sides are 12 cm and 7 cm?
   (a) 18 cm
   (b) 5 cm
   (c) 10 cm
   (d) 17 cm
2. If p and q are twin primes and pq = 899, find p + q.
3. What must be subtracted from (7x² – 3x + 4) to get (2x² + x – 6)?
4. The cost of x pens is ₹(5x + 20). Write algebraic expression for cost of (x + 3) pens.
5. If a and b are consecutive primes greater than 3, then a + b is always:
   (a) even
   (b) odd
   (c) prime
   (d) multiple of 3
6. Assertion–Reason
   Assertion: If exterior angle of triangle is 120° and two opposite interior angles are equal, each is 60°.
   Reason: Exterior angle equals sum of opposite interior angles.

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SECTION – B

7. Simplify:

(i) 50 – 10 × 4 + 6 × 3 – 8

(ii) 5x – 3y(4 – 6) + (2x – y) – (3x + 2y)

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8. Contributions:

A: 4(2m + n – p) – 3(m – 2n + p)
B: 3(m + 2n – 3p) – 2(2m – n + p)
C: 5(m – n + 2p) – (3m + 2n – p)

a) Total
b) Compare with target (20m + 15n – 18p)

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9. Perimeter of triangle (3x + 1), (2x + 5), (x + 7) equals twice perimeter of square side (x + 2). Find x.

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10. In isosceles triangle, vertex angle is 5 times base angle. Find angles.

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11. Construct triangle using ASA:
    AB = 7 cm, ∠ BAC = 35°, ∠ ABC = 85°

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SECTION – C

12. Case Study

Rohan selects strips 4 cm, 6 cm, 11 cm.

(a) Can triangle form?
(b) State inequality property.
(c) Find all possible integer values of third side if other sides are 5 cm and 9 cm.