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. <panel>

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) $4880$
  <btn type=“link” collapse=“a1”>See Answer</btn>

  (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) $21$
  <btn type=“link” collapse=“a2”>See Answer</btn>

  ©: $28$

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) $96$
  <btn type=“link” collapse=“a3”>See Answer</btn>

  (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) $\dfrac{n+2}{n-1}$
  <btn type=“link” collapse=“a4”>See Answer</btn>

  (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) $696$
  <btn type=“link” collapse=“a5”>See Answer</btn>

  (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) $4775$
  <btn type=“link” collapse=“a6”>See Answer</btn>

  (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) $81$
  <btn type=“link” collapse=“a7”>See Answer</btn>

  ©: $512$

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

• (a) $21$
• (b) $20$
• (c) $35$
• (d) $81$
  <btn type=“link” collapse=“a7”>See Answer</btn>

  (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) $1$
  <btn type=“link” collapse=“a7”>See Answer</btn>

  ©: 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) $P(A)-P(B)$
  <btn type=“link” collapse=“a7”>See Answer</btn>

  (d): $A \cap B=\phi$

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<btn type=“success”>Question 2 ></btn> 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