# Some Expected Questions in CGL Tier-2 2017 Which You Must Solve

Q1. If a circle has a square and a hexagon and the vertices of both touch the circle’s circumference then what is the ratio of the area of the two?
Solution: Ratio of Square and Hexagon = b2/6 × √3/4 a2
= (4/6√3)b2/a2
= 4/6√3 (√2r/r2)2
= 4 × 2 × r2/6 × √3× r2
= 4/3√3
= 4: 3√3

Q2. Area of which of the following is maximum when perimeter is equal?
circle, square, triangle
Solution: Circle’s area is maximum for a given fixed value of perimeter.

Q3. Sum of the squares of three numbers is 323. If the sum of squares of two numbers is twice of the third number, find the product of three numbers.
Sol: Let the numbers be x, y and z
Given,
x2 + y2 + z2 = 323       — (1)
x2 + y2 = 2z                 — (2)
Put 2 into 1 and solve it.

Q4. Find Compound Interest on 4000 rupees for 4 year at 10%rate of interest, compounded annually.
Solution: CI = P(1 + r/100)n – P, where P is principal amount; r is the rate of interest; and n is number of years.
Put the values and solve.

Q5. Find the value of (1+sec20° +cot70°)(1-cosec20° + tan70°)
Solution: (1 + 1/cos20° + cos70°/sin70°)(1 – 1/sin20° + sin70°/cos70°)
We know that sin(90 – θ) = cosθ
Hence, the expression will become:
(1 + 1/cos20° + sin20°/cos20°)(1 – 1/sin20° + cos20°/sin20°)
(cos20° + 1 + sin20°)(sin20° – 1 + cos20°)/sin20°cos20°
= [sin220 + cos220 + 2sin20.cos20 – 1]/sin20°cos20°
We know that, sin2θ + cos2θ = 1
[1 + 2sin20.cos20 – 1]/sin20°cos20°
2sin20.cos20/sin20°cos20°
= 2

Q6. Difference in compound interest is INR 723 at 20% for a yearly or half yearly basis. Find the Sum.
Sol: Since, the yearly interest rate is 20%, the half yearly interest rate will be 10%
Given,
P[1 + 10/100]2 – P[1 + 20/100]1 = 723

Solve it and get the value of P.