Question 1 Review Exercise 7

Solutions of Question 1 of Review Exercise 7 of Unit 07: Permutation, Combination and Probablity. This is unit of A Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB or KPTBB) Peshawar, Pakistan. Chose the correct option.

i. In how many ways can we name the vertices of pentagon using any five of the letters $O, P, Q, R, S, T, U$ in any order?

  • (a) $2520$
  • (b) $9040$
  • (c) $5140$
  • (d) $4880$
    See Answer
    (a): $2520$

ii. How many two digits odd numbers can be formed form the digits $\{1,2,3,4,5,6,7\}$ if repeated digits are allowed?

  • (a) $14$
  • (b) $42$
  • (c) $28$
  • (d) $21$
    See Answer
    ©: $28$

iii. How many six digits number can be formed from the digits $\{1,2,3,4,6,7,8\}$ without repetition if the digits $3$ and $7$ must together?

  • (a) $120$
  • (b) $180$
  • (c) $144$
  • (d) $96$
    See Answer
    (a): $120$

iv. Evaluate $\dfrac{(n+2) !(n-2) !}{(n+1) !(n-1) !}$

  • (a) $(n-3)$
  • (b) $(\dot{n}-1)$
  • (c) $\dfrac{n+1}{n+2}$
  • (d) $\dfrac{n+2}{n-1}$
    See Answer
    (d): $\dfrac{n+2}{n-1}$

v. In how many different ways can $5$ couples be seated around a circular table if the couple must not be separated?

  • (a) $768$
  • (b) $724$
  • (c) $844$
  • (d) $696$
    See Answer
    (a): $768)$

vi. A committee of 4 people will be selected from 8 girls and 12 boys in a class. How many different selections are possible if at least one boy must be selected?

  • (a) $2865$
  • (b) $3755$
  • (c) $4225$
  • (d) $4775$
    See Answer
    (d): $4775$

vii. The number of all possible matrices of order $3 \times 3$ with each entry 0 and 1 is:

  • (a) $18$
  • (b) $27$
  • (c) $512$
  • (d) $81$
    See Answer
    ©: $512$

viii. How many diagonals can be drawn in plane figure of 8 sides?

  • (a) $21$
  • (b) $20$
  • (c) $35$
  • (d) $81$
    See Answer
    (b): $20$

ix. If $P(A)=\dfrac{1}{2}, P(B)=0$ then $P(A \mid B)$ is:

  • (a) $0$
  • (b) $\dfrac{1}{2}$
  • (c) not defined
  • (d) $1$
    See Answer
    ©: not defined

x. If $A$ and $B$ are events such that $P(A / B)=P(B / A)$ then

  • (a) $A \subset B$ but $A \neq B$
  • (b) $A=B$
  • (c) $A \cap B=\phi$
  • (d) $P(A)-P(B)$
    See Answer
    (d): $A \cap B=\phi$

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Question 2 > Q1 (i) What is the niddle term in the expansion of $(2 x+5 y)^4$ ? (a) $600 x^2 y^2$ (b) $120 x y^2$ © $5000 x y^3$ (d) $6 x^2 y^2$ (ii) What is the coefficient of the term $$ \left(x^3-2 y^2\right)^7 ? $$ (a) 84 (b) -280 © 560 (d) 448 (iii) The expansion of $\left(x+\sqrt{x^2-1}\right)^5+\left(x-\sqrt{x^2-1}\right)^5$ is a polynomial of degree (a) 5 (b) 6 © 7 (d) 8 (iv) Number of terms in expansion of $(\sqrt{x}+\sqrt{y})^{10}+(\sqrt{x}+\sqrt{y})^{10}$ is (a) 6 (b) 11 © 20 (d) 5 (v) $(\sqrt{2}+1)^5+(\sqrt{2}-1)^5=$ (a) 58 (b) $58 \sqrt{2}$ © -58 (d) $-58 \sqrt{2}$ (vi) $\left({ }^{\prime \prime}{ }_1{ }^1\right)+\left({ }^n{ }_2{ }^1\right)+\cdots+\left(\begin{array}{cc}n & 1 \\ n-1\end{array}\right)=\ldots \ldots$, $n>1$ (a) $2^n-1$ (b) $2^{n-2}$ © $2^n 1-1$ (d) $2^n$ (vii) Sum of the coefficients of last 15 terms in expansion of $(1+x)^{29}$ is (a) $2^{15}$ (b) $2^{30}$ © $2^{29}$ (d) $2^{28}$ (viii) ${ }^{10} C_1+{ }^{10} C_3+{ }^{10} C_5+\cdots+{ }^{10} C_9$ $=$ (a) 512 (b) 1024 © 2048 (d) 1023