NTPC CBT- 2 MOST PROBABLE -SIMPLIFICATION QUIZ-16

Question 1:

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 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:

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

$2+8 \sqrt{3}$

$1-8 \sqrt{3}$

$1+5 \sqrt{3}$

$1+8 \sqrt{3}$

Question 4:

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 5:

Evaluate:-

$\left(3.2 x^{6} y^{3}\right) \times\left(2.1 x^{2} y^{2}\right)$ when $x=1$ and $y=0.5$

$0.24$

$0.36$

o.28

$0.21$

Question 6:

Simplify: $7 \frac{1}{2}-\left[2 \frac{1}{4} \div\left\{1 \frac{1}{4}-\frac{1}{2}\left(\frac{3}{2}-\overline{\frac{1}{3}-\frac{1}{6}}\right)\right\}\right]$

$3 \frac{9}{14}$

$5 \frac{9}{14}$

$3 \frac{7}{15}$

$3 \frac{8}{15}$

Question 7:

The value of $\frac{7-[4+3(2-2 \times 2+5)-8] \div 5}{2 \div 2 \text { of }(4+4 \div 4 \text { of } 4)}$ is:

$25 \frac{1}{2}$

24

26

$8 \frac{1}{2}$

Question 8:

The value of $\frac{(3.2)^{3}+(2.8)^{3}}{(32)^{2}-32 \times 28+ 784}$ is:

$0.03$

$0.05$

$0.06$

$0.02$

Question 9:

Simplify :- $\frac{\frac{1}{3}+\frac{1}{4}\left[\frac{2}{5}+\frac{1}{2}\right]}{1 \frac{1}{3} \text { of } \frac{3}{4}-\frac{3}{8} \times \frac{4}{5}}$

$\frac{53}{83}$

$\frac{67}{84}$

$\frac{58}{63}$

$ \frac{67}{81}$

Question 10:

Evaluate:-

$\sqrt{1024} \times 40+20^{2}+0.5 \%$ of $9600+469=?^{3}$

$23$

$13$

$17$

$19$