Fsc Math First Year Mcqs CH#08 MATHEMATICAL INDUCTION AND BINOMIAL THEOREM

MATHEMATICAL INDUCTION AND BINOMIAL THEOREM MCQs Ch:08 Fsc First Year consist of 150+ Multiple Choice Questions. Prepare these mcqs for ECAT and examination. These mcqs are very helpful for preparing NTS and PPSC exams.

Q.1 In the Expression ( a + b) ⁷, the 2nd term is

(a) a⁷

(b) 7a⁶b

(d) None

( Gujranwala board,2004)

(b) 7a⁶b

Q.2 The inequality n! > $2^n$ -1 is valid if

(a) n = 3

(b) n $\leq$ 3

(d) n $\geq$ 4

( Lahore board,2006)

(d) n $\geq$ 4

Q.3 The coefficient of the last term (a -b)⁵ is

(a) 1

(b) -1

(d) None

-1

Q.4 The number of terms in the expression ( a + b)¹² is

(a) 13

(b) 12

(d) 10

Q.5 The middle term in the Expression (a + b) ¹² is

(a) 6th term

(b) 7th term

(d) 9th term

(b) 7th term

Q.6 Sum of exponents a and b in every term of expansion $\left ( a+b \right )^n$ is

(a) 1

(b) 0

(d) n

( Lahore board,2005)

(d) n

Q.7 General term of expansion $\left ( a+b \right )^n$ is

(a) $\frac{n!}{(n-r)!r!}a^{n-r}b^r$

(b) $\frac{n!}{(n-r)!}a^{n-r}b^r$

(d) $n!a^{n-r}b^r$

( Lahore board,2006)

(a) $\frac{n!}{(n-r)!r!}a^{n-r}b^r$

Q.8 Number of term in the expansion of $\left ( a+b \right )^n$ is

(a) n+1

(b) n-1

(d) n²+1

( Lahore board,2004)

(a) n+1

Q.9 If the exponent in the binomial expansion is 6, the middle term is

(a) 2th term

(b) 3th term

(d) 5th term

Q.10 If the exponent in the binomial expansion is 6, the number of terms is

(a) 12

(b) 8

(d) 6

Q.11 Sum of coefficients in the expansion $(1+x)^n$ is

(a) $n^2$

(b) $2n^{n-2}$

(d) $2^n$

( Gujranwala board,2004)

(d) $2^n$

Q.12 Sum of coefficients in the expansion $(1+x)^n$ is equal to the number of elements of the power set of a set with elemenets

(a) $n^2$

(b) $2n^{n-2}$

(d) n

( Lahore board,2006)

(d) n

Q.13 Sum of the odd coefficients in the expansion $(1+x)^n$ is

(a) $n^2$

(b) $2n^{n-2}$

(d) $2^n$

Q.14 Sum of the even coefficients in the expansion $(1+x)^n$ is

(a) $n^2$

(b) $2n^{n-2}$

(d) $2^n$

Q.15 Sum of the even coefficients and Sum of the odd coefficients in the expansion $(1+x)^n$ is

(a) Not same

(b) Same

(d) Natural Numbers

(b) Same

Q.16 Sum of coefficients in the expansion $(1+x)^4$ is

(a) 4

(b) 8

(d) 16

Q.17 Sum of odd coefficients in the expansion $(1+x)^4$ is

(a) 4

(b) 8

(d) 16

(b) 8

Q.18 Sum of even coefficients in the expansion $(1+x)^4$ is

(a) 4

(b) 8

(d) 16

(b) 8

Q.19 Sum of even coefficients in the expansion $(1+x)^5$ is

(a) 4

(b) 8

(d) 16

Q.20 Sum of odd coefficients in the expansion $(1+x)^5$ is

(a) 4

(b) 8

(d) 16

Q.21 Sum of odd coefficients in the expansion $(1+x)^3$ is

(a) 4

(b) 8

(d) 16

( Gujranwala board,2004)

(a) 4

Q.22 General term of expansion $\left ( a+b \right )^n$ is

(a) r th term

(b) (r-1)th term

(d) None of these

( Lahore board,2006)

Q.23 Sum of coefficients in the expansion $(1+x)^3$ is

(a) 1

(b) 2

(d) 8

Q.24 If n is not a natural number , then expansion of $(1+x)^n$ is valid for

(a) -1 < x < 1

(b) $-1\leq x \leq 1$

(d) $-2\leq x \leq 2$

(a) -1 < x < 1

Q.25 If a statement P(n) is true for n=1 and the truth of P(n) for n=k implies the truth of P(n) for n=k+1, then P(n) is true for all

(a) Positive real numbers n

(b) Real numbers n

(d) Positive integers n

Q.26 The number of terms in the expansion ( a + b) ⁷ is

(a) 4

(b) 6

(d) 8

Q.27 The number of terms in the expansion $(x^{2}-\frac{1}{x^{2}})^{7}$ is

(a) 2

(b) 7

(d) 12

(d) 8

Q.28 The number of terms in the expansion $(x^{2}-\frac{1}{x^{2}})^{6}$ is

(a) 2

(b) 7

(d) 12

(b) 7

Q.29 If the middle term in the expression $(a+b)^{n}$ is $\frac{n}{2}+1$ then n is

(a) odd

(b) even

(d) None of these

(b) even

Q.30 If n is even then middle term in the expansion of $(a+b)^{n}$ is

(a) $\frac{n}{2}+1$

(b) $\frac{n+1}{2}$

(d) None of these

(a) \frac{n}{2}+1

Q.31 If n is even then the expansion of $(a+b)^{n}$ has

(a) 2 middle terms

(b) 3 middle terms

(d) None of these

(a) 2 middle terms

Q.32 The middle term of the expansion $(1+2x)^{6}$ is

(a) 3rd

(b) 4th

(d) None of these

(a) 3rd

Q.33 $(1+x)^{n}=1+nx+\frac{n(n-1)}{2!}x^{2}+\frac{n(n-1)(n-2)}{3!}x^{3}+...$ is

(a) Binomial Series

(b) Binomial Theorem

(d) Taylor Theorem

(a) Binomial Series

Q.34 The expansion of $(1+\frac{x}{2})^{\frac{3}{2}}$ is

(a) Binomial Series

(b) Binomial Theorem

(d) None of these

(a) Binomial Series

Q.35 The expansion of $(1+\frac{x}{2})^{\frac{3}{2}}$ up to two terms is

(a) $32x^5+80x^3$

(b) $32x^5-80x^3$

(d) $32x^3+80x^5$

(b) $32x^5-80x^3$

Q.36 The expansion of $(3a-\frac{x}{3a})^{4}$ up to two terms is

(a) $27a^3-36a^2x$

(b) $27a^3+36a^2x$

(d) $81a^4-36a^2x$

Q.37 If $\mid x \mid <1$ , then the expansion of $(1-x)^\frac{1}{2}$ up to terms is

(a) $1+\frac{1}{2}x$

(b) $1-\frac{1}{2}x$

(d) 1+x

(b) $1-\frac{1}{2}x$

Q.38 The expansion of $(1+{2}x)^{-1}$ is valid if

(a) |x|< 1/2

(b) |x|< 1

(d) |x|< 3

(a) |x|< 1/2

Q.39 The expansion of $(1-3x)^{\frac{2}{3}}$ is valid if

(a) |x|< 1/3

(b) |x|< 1/2

(d) |x|< 1

(a) |x|< 1/3

Q.40 Second term in the expansion of $(1-2x)^{\frac{1}{3}}$ is

(a) x/2

(b) x/3

(d) - 2x/3

Q.41 The expansion of $(8-2x)^{-1}$ is valid if

(a) |x|> 4

(b) |x|< 4

(d) |x|= 4

(b) |x|< 4

Q.42 If n is a positive integer, then $4^n > 3^n +4$ is true for all

(a) n>2

(b) $n \geq 2$

(d) $n \leq 2$

(b) $n \geq 2$

Q.43 Sum of even coefficients in the expansion $(1+x)^4$ is

(a) 4

(b) 8

(d) 16

(b) 8

Q.44 Sum of even coefficients in the expansion $(1+x)^5$ is

(a) 4

(b) 8

(d) 16

Q.45 Sum of odd coefficients in the expansion $(1+x)^5$ is

(a) 4

(b) 8

(d) 16

Fsc Math First Year Mcqs CH#08 MATHEMATICAL INDUCTION AND BINOMIAL THEOREM

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