CDS MATHEMATICS SIMPLIFICATION QUIZ 15

Question 1:

If $\frac{7+\sqrt{5}}{7-\sqrt{5}}-\frac{7-\sqrt{5}}{7+\sqrt{5}}=a+7 \sqrt{5} b$ then find the value of a.

0

1

2

$-1$

Question 2:

If $m$ and $n$ be the two rational numbers such that $m^{n}=25$, then the value of $n^{m}$ is :

4

10

32

16

Question 3:

Simplify:-

$\sqrt{2} \cdot \sqrt[3]{3} \cdot \sqrt[4]{4}$

$2 \sqrt[3]{3}$

$5 \sqrt[3]{3}$

$3 \sqrt[3]{3}$

$2 \sqrt[4]{3}$

Question 4:

If a and b be two rational numbers, find the value of b.

$\frac{3+\sqrt{7}}{3-\sqrt{7}}=a+b \sqrt{7}$

4

3

2

1

Question 5:

If $\frac{4+2 \sqrt{5}}{4-3 \sqrt{5}}=a+b \sqrt{5}$, then find the value of a.

$\frac{-45}{29}$

$\frac{46}{27}$

$\frac{-43}{29}$

$\frac{-46}{29}$

Question 6:

Rationalize the denominator of the following :

$-2+\sqrt{3}$

$-\sqrt{2}-\sqrt{3}$

$2-\sqrt{3}$

$-2-\sqrt{3}$

Question 7:

Rationalize the denominator of the following

$\frac{\sqrt{5}-2}{\sqrt{5}+2}-\frac{\sqrt{5}+2}{\sqrt{5}-2}$

$-8 \sqrt{5}$

$6 \sqrt{5}$

$-4 \sqrt{5}$

$8 \sqrt{5}$

Question 8:

Simplify:-

$\sqrt[4]{36} \div \sqrt[3]{6}$

$\sqrt[6]{5}$

$\sqrt[6]{8}$

$\sqrt[5]{6}$

$\sqrt[6]{6}$

Question 9:

Simplify the following :

$\frac{\sqrt{7}-\sqrt{5}}{\sqrt{7}+\sqrt{5}}+\sqrt{35}$

8

6

4

12

Question 10:

IF $a=\frac{\sqrt{3}+1}{\sqrt{3}-1}$ and $b=\frac{\sqrt{3}-1}{\sqrt{3}+1}$, find the value of $\mathbf{a}^{2}+\mathbf{a b}-\mathbf{b}^{2}$.

$2+8 \sqrt{3}$

$1-8 \sqrt{3}$

$1+5 \sqrt{3}$

$1+8 \sqrt{3}$