Q.31
Easy
If 2^(x+1) = 32, find the value of x.
Explanation:
32 = 2⁵. So 2^(x+1) = 2⁵ → x + 1 = 5 → x = 4.
Q.32
Easy
A number when divided by 7 gives quotient 12 and remainder 3. The number is:
Explanation:
Using dividend = divisor × quotient + remainder: Number = 7 × 12 + 3 = 84 + 3 = 87.
Q.33
Medium
If ABCD is a rhombus with diagonals 6 cm and 8 cm, find its area.
A
24 cm²
B
48 cm²
C
28 cm²
D
56 cm²
Correct Answer:
A. 24 cm²
Explanation:
Area of rhombus = (1/2) × d₁ × d₂ = (1/2) × 6 × 8 = 24 cm².
Q.34
Medium
What is the compound interest on Rs. 8000 at 10% per annum for 2 years?
A
Rs. 1680
B
Rs. 1600
C
Rs. 1800
D
Rs. 1500
Correct Answer:
A. Rs. 1680
Explanation:
A = P(1 + r/100)ⁿ = 8000(1.1)² = 8000 × 1.21 = 9680. CI = 9680 - 8000 = 1680.
Q.35
Medium
In an AP, if first term a = 5, common difference d = 3, find the 10th term.
Explanation:
nth term = a + (n-1)d = 5 + (10-1) × 3 = 5 + 27 = 32.
Q.36
Medium
If |x - 3| = 5, what are the possible values of x?
A
2 and 8
B
2 and -8
C
-2 and 8
D
3 and 5
Correct Answer:
C. -2 and 8
Explanation:
|x - 3| = 5 means x - 3 = 5 or x - 3 = -5. So x = 8 or x = -2.
Q.37
Hard
If 2sin²θ - sin θ - 1 = 0, find sin θ (θ is acute).
Explanation:
2sin²θ - sin θ - 1 = 0. Factoring: (2sinθ + 1)(sinθ - 1) = 0. Since θ is acute, sin θ = 1.
Q.38
Medium
A ladder of length 13 m leans against a wall. If the foot of the ladder is 5 m away from the wall, find the height reached on the wall.
A
8 m
B
10 m
C
12 m
D
15 m
Explanation:
Using Pythagoras: h² + 5² = 13² → h² + 25 = 169 → h² = 144 → h = 12 m.
Q.39
Hard
If tan θ + cot θ = 4, find tan² θ + cot² θ.
Explanation:
(tan θ + cot θ)² = tan²θ + 2 + cot²θ = 16. So tan²θ + cot²θ = 14.
Q.40
Medium
The sum of first n natural numbers is 105. Find n.
Explanation:
Sum = n(n+1)/2 = 105 → n(n+1) = 210 → n² + n - 210 = 0 → n = 14 or -15. Since n > 0, n = 14 (checking: 14×15/2 = 105). Wait, let me recalculate: 15×16/2 = 120. 14×15/2 = 105. So n = 14. But the option says B = 15. Let me verify once more: if n=15, sum = 15×16/2 = 120 (not 105). If n=14, sum = 14×15/2 = 105. The correct answer should be 14, but since that's option A, let me reconsider. Actually reviewing: n(n+1)/2 = 105 means n(n+1) = 210. Trying n=14: 14×15 = 210. Yes! So answer is A.
