11th Class Math MCQS Chapter 8

For every positive integer n a_n where a₁,a₁ + d,a₁ + 2d ….. form an A.P.

nd

a₁ + nd

None of these

a₁ + (n – 1)d

We can use the principle of extended mathematical induction to prove that

n! > 2ⁿ – 1 for integral values of n > 4

n > 2^n-1 for integral values of n > 4

n! > 2^n-1 for integral values of n > 2

n! > 2ⁿ for integral values of n > 4

For every positive integer n 2 + 4 + 6+…..+2n=

n + 1

n(n – 1)

n² + 1

n(n + 1)

Second term in the expansion of (1 – 2x) 1/3 is:

-2x/3

2x/3

x/2

x/3

If n is positive integer than 3+6+9+……….+, +3n =

3n(n+1)/2

3n(n+1)

3n(n+1)/4

2n(n+1)/3

We can use the principle of extended mathematical induction to prove that

n! > n² integral values of n > 4

n! > n for integral values of n > 4

n! > n² for integral values of n > 4

n! > n² integral values of n > 2

An algebraic expression consisting of two terms such as a + x,x – 2y, 2x+b etc called a

Polynomial induction

Binomial expression

Binomial theorem

Binomial induction

In the expansion of (a+x)⁴ the exponent of a decreases from

Index 2

Index 3

Index 5

Index zero

Binomial theorem holds if

a or x is real

a and x is both real

All of above

a or x is complex

For every positive integer n 1+2+4+….+2^n-1=

2ⁿ – 2

2ⁿ⁺¹

2ⁿ – 1

2ⁿ