81.

Let m and n (m < n) be the roots of the equation x² – 16x + 39 = 0. If four terms p, q, r and s are inserted between m and n to form an AP, then what is the value of p + q + r + s ?

• 29

• 30

• 32

• 35

What is the number of diagonals of an octagon ?

• 48

• 40

• 28

• 20

A geometric progression (GP) consists of 200 terms. If the sum of odd terms of the GP is m, and the sum of even terms of the GP is n, then what is its common ratio ?

• m/n

• n/m

• m + (n/m)

• n + (m/n)

If $\left|{\mathrm{x}}^2 - 3\mathrm{x} + 2\right| > {\mathrm{x}}^2 - 3\mathrm{x} +\hspace{0.17em}2$, then which one of the following is correct ?

• $\mathrm{x} \le 1 \mathrm{or} \mathrm{x} \ge 2$

• $1 \le \mathrm{x} \le 2$

• $1 < \mathrm{x} < 2$

• x is any real value except 3 and 4

If the roots of the equation

a(b - c)x² + b (c – a)x + c(a - b) = 0

are equal, then which one of the following is correct ?

• a, b and c are in AP

• a, b and c are in GP

• a, b and c are in HP

• a, b and c do not follow any regular pattern

If the sum of first n terms of a series is (n + 12), then what is its third term ?

• 1

• 2

• 3

• 4

What is the value of 1 – 2 + 3 – 4 + 5 - ... + 101 ?

• 51

• 55

• 110

• 111

If the angle of a triangle ABC are in AP and b : c = $\sqrt{3} :\hspace{0.17em}\sqrt{2}$, then what is the measure of angle A ?

• $30°$

• $45°$

• $75°$

• $60°$

Arithmetic meanof 10 observation is 60 and sum of squares of deviations from 50 is 5000. What is the standard deviation of the observation ?

• 20

• 21

• 22, 36

• 24, 70

If (1 + 2x – x²)⁶ = a⁰ + a¹x + a²x² + ... + a¹²x¹², then what is a⁰ – a¹ + a² – a³ + a⁴ - ... + a¹² equal to ?

• 32

• 64

• 2048

• 4096