Q. 126. From a point 25 m from a tower’s base, the elevation angle to the top is . What is the tower’s height?
(A) m
(B) m
(C) m
(D) 40 m
Answer:
(B) m
Explanation:
Using trigonometry, . Thus, meters.
Q. 127. Two fair dice are thrown. What is the probability of getting a sum of 3?
(A)
(B)
(C)
(D)
Answer:
(B)
Explanation:
The only combinations summing to 3 are (1,2) and (2,1). There are 36 possible outcomes, so the probability is .
Q. 128. Find the amount on ₹5 000 at 20 % p.a. for 18 months, compounded half-yearly.
(A) ₹6 000
(B) ₹6 644
(C) ₹6 655
(D) ₹6 666
Answer:
(C) ₹6 655
Explanation:
For half-yearly compounding, the rate is 10% per half-year, and 18 months = 3 periods. Amount = $5000 \times (1 + 0.10)^3 = 5000 \times 1.331 = ₹6,655$.
Q. 129. Which statement about diagonals is incorrect?
(A) Diagonals of a rectangle are equal
(B) Diagonals of a rhombus are equal
(C) Diagonals of a rhombus bisect at right angles
(D) Diagonals of a square bisect at right angles
Answer:
(B) Diagonals of a rhombus are equal
Explanation:
The diagonals of a rhombus bisect each other at right angles but are not necessarily equal in length unless the rhombus is also a square.
Q. 130. The sum of a father’s and son’s ages is 44. In 6 years, the father will be three times as old as the son. What are their present ages (father, son)?
(A) 35 yr & 9 yr
(B) 36 yr & 8 yr
(C) 37 yr & 7 yr
(D) 38 yr & 6 yr
Answer:
(B) 36 yr & 8 yr
Explanation:
Let father’s age be F and son’s be S. $F + S = 44$. In 6 years, . Substituting gives , so . .
