﻿ Engineering Entrance Exam Question and Answers | Principle of Mathematical Induction - Zigya

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# Principle of Mathematical Induction

#### Multiple Choice Questions

1.

If the number of terms in the expansion of  is 28, then the sum of the coefficients of all the terms in this expansion is

• 64

• 2187

• 243

• 243

392 Views

2.

Statement − 1: For every natural number n ≥ 2

Statement −2: For every natural number n ≥ 2,

• Statement −1 is false, Statement −2 is true

• Statement −1 is true, Statement −2 is true, Statement −2 is a correct explanation for Statement −1

• Statement −1 is true, Statement −2 is true; Statement −2 is not a correct explanation for Statement −1.

• Statement −1 is true, Statement −2 is true; Statement −2 is not a correct explanation for Statement −1.

125 Views

3.

If A =  and I =  , then which one of the following holds for all n ≥ 1, by the principle of mathematical induction

• An = nA – (n – 1)I

• An = 2n-1A – (n – 1)I

• An = nA + (n – 1)I

• An = nA + (n – 1)I

131 Views

4.

Let S(K) = 1 +3+5+..... (2K-1) = 3+K2. Then which of the following is true?

• S(1) is correct

• Principle of mathematical induction can be used to prove the formula

• S(K) ≠S(K+1)

• S(K) ≠S(K+1)

158 Views

5.

Maximum sum of coefficient in the expansion of (1 – x sinθ + x2 )n is

• 1

• 2n

• 3n

• 3n

126 Views

6.

For positive integer n, n3 + 2n is always divisible by

• 3

• 7

• 5

• 6

7.

The acceleration of a particle starting from rest moving in a straight line with uniform acceleration is 8 m/s2. The time taken by the particle to move the second metre is

• (√2-1)/2 S

• (√2+1)/2 S

• (1 + √2)S

• (√2-1)S

8.

Prove by induction that for n $\in$ N, n2 + n is an even integer (n $\ge$ 1)

#### Multiple Choice Questions

9.

A particle is moving in a straight line. At time t, the distance between the particle from its starting point is given by x = t - 6t2 + t3. Its acceleration will be zero at

• t = 1 unit time

• t = 2 unit time

• t = 3 unit time

• t = 4 unit time

10.

For each n $\in$ N, 23n - 1is divisible by

• 7

• 8

• 6

• 16