# Simplification Questions for RRB Group-D Set-3 PDF

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## Simplification Questions for RRB Group-D Set-3 PDF

Download Top-15 RRB Group-D Simplification Questions set-3 PDF. RRB GROUP-D Maths questions based on asked questions in previous exam papers very important for the Railway Group-D exam.

Question 1: Simplify: $3 \log 6+ 10 \log 2 – 2 \log 12 – \log 3$

a) 9 log 2

b) 9

c) 11 log 3

d) 10

Question 2: Simplify: $\sqrt{19+4\sqrt{21}}$

a) $2+\sqrt{26}$

b) $3-\sqrt{15}$

c) $\sqrt{5}+\sqrt{26}$

d) $\sqrt{12}+\sqrt{7}$

Question 3: Simplify the surd $\sqrt{10+\sqrt{75}} + \sqrt{10-\sqrt{75}}$

a) $\sqrt{28}$

b) $4 \sqrt{2}$

c) $\sqrt{30}$

d) $2\sqrt{6}$

Question 4: Simplify the surd $\frac{7 \sqrt{7} – 3 \sqrt{3}}{\sqrt{7} – \sqrt{3}}$

a) $10 + \sqrt{21}$

b) $10 – \sqrt{21}$

c) $\sqrt{21} – 10$

d) $7\sqrt{3} + 3\sqrt{7}$

Question 5: Simplify: $\frac{0.0347 \times 0.0347 \times 0.0347 + (0.9653)^3}{(0.0347)^2 – (0.347)(0.9653) + (0.9653)^2}$

a) 0.9306

b) 1.0009

c) 1.0050

d) 1

Question 6: Simplify the equation: $\frac{31^3 + 22^3}{31^2 + 22^2 – 682}$

a) 9

b) 53

c) 69

d) 93

Question 7: Simplify the expression $\sqrt{\frac{1+cosx}{1-cosx}}$.

a) sec x + tan x

b) sin x

c) cosec x + cot x

d) cos x

Question 8: Simplify the given expression : $\left( \frac{\left(3^{-1}-9^{-1}\right)}{6}\times 729\right)^{\frac{1}{3}}$

a) $\frac{1}{9}$

b) $3$

c) $\frac{1}{3}$

d) $9$

Question 9: Simplify 437bxaz / 23ab.

a) 17xzb

b) 9xz

c) 19xz

d) 19ab

Question 10: Simplify $486b^{3}x^{2} a^{4}z^{3}/27a^{3} b^{2}z$

a) $18bx^{2}az^{2}$

b) $18bx^{2}a^{2}z$

c) $36ba^{2}z$

d) $36bxa^{2}z$

Question 11: Expand and simplify $(x + 5)^2 + (x – 3)^2$

a) $2(x^2 + 2x – 17)$

b) $2(x^2 – 2x + 17)$

c) $2(x^2 – 2x – 17)$

d) $2(x^2 + 2x + 17)$

Question 12: Expand and simplify expand and simplify : $(3x+2)^2 \times (4x-3)-(2x^3-9x^2+12x-24)$

a) $34x^3+30x^2-32x-12$

b) $34x^3+30x^2-32x+12$

c) $34x^3-30x^2-32x+12$

d) $34x^3-30x^2+32x-12$

Question 13: Simplify (533bxaz)/(41ab)

a) 17xzb

b) 19xz

c) 13xz

d) 31ab

Question 14: Expand and simplify $(x+4)^{2}+(x-2)^{2}$

a) $2(x^{2}+2x+10)$

b) $2(x^{2}+2x-10)$

c) $2(x^{2}-2x + 10)$

d) $2(x^{2}-2x-10)$

Question 15: Simplify $576b^{3}x^{2}a^{4}z^{3}/36a^{3}b^{2}z$

a) $16bx^{2}az^{2}$

b) $bx^{2} a^{2}z$

c) $32ba^{2}z$

d) $32bx^{a}2z$

$3 \log 6+ 10 \log 2 – 2 \log 12 – \log 3$

= $\log \frac{6^3*2^{10}}{12^2*3}$

= $\log 2^ 9= 9 \log 2$

Let $\sqrt{19+4\sqrt{21}} = \sqrt{a}+\sqrt{b}$
$\rightarrow a+b+2\sqrt{ab} = 19+4\sqrt{21}$.
Hence, a+b=19 and ab=84. Hence a=12, b=7.

Let $X = \sqrt{10+\sqrt{75}} + \sqrt{10-\sqrt{75}}$
So, $X^2 = 10+10+2*5 = 30$
So, $X = \sqrt{30}$

Let $X = \frac{7 \sqrt{7} – 3 \sqrt{3}}{\sqrt{7} – \sqrt{3}}$
Multiplying numerator and denominator by $(\sqrt{7} + \sqrt{3})$,

$X = (49 – 3 \sqrt{21} + 7 \sqrt{21} – 9)/4 = 10 + \sqrt{21}$

Numerator is of the form of $a^{3} + b^{3}$ and denominator is of the form of  $a^{2} + b^{2} – ab$
where a = .0347 and b= .9653
it will get reduce to a+b = 1

We can solve the equation using the formula $a^3 + b^3$ = (a+b) * ($a^2+b^2$-ab)
So, the answer is 31 + 22 = 53

$\sqrt{\frac{1+cosx}{1-cosx}}$
$\sqrt{\frac{(1+cosx)^2}{(1-cosx)(1+cosx)}}$
=> $\sqrt{\frac{(1+cosx)^2}{(1- cos^2x}}$
=> $\frac{1+cosx}{sinx}$ = cosecx + cotx$8) Answer (B)$\left( \frac{\left(\frac{1}{3}-\frac{1}{9}\right)}{6}\times 729\right)^{\frac{1}{3}}\left( \frac{\left(\frac{3-1}{9}\right)}{6}\times 729\right)^{\frac{1}{3}}\left( \frac{\left(\frac{2}{9}\right)}{6}\times 729\right)^{\frac{1}{3}}\left(\frac{1}{27}\times 729\right)^{\frac{1}{3}}\left(27\right)^{\frac{1}{3}} = 3$Hence, correct option is B 9) Answer (C) Expression :$\frac{437 b x a z}{23 a b}$=$\frac{437}{23} \times \frac{abxz}{ab}$=$19 x z$=> Ans – (C) 10) Answer (A) Expression :$486b^{3}x^{2} a^{4}z^{3}/27a^{3} b^{2}z$=$\frac{486}{27} \times [(b)^{3 – 2} \times (x)^{2} \times (a)^{4 – 3} \times (z)^{3 – 1}]$=$18 b x^2 a z^2$=> Ans – (A) 11) Answer (D) Expression :$(x + 5)^2 + (x – 3)^2$=$(x^2 + 10x + 25) + (x^2 – 6x + 9)$=$2x^2 + 4x + 34$=$2(x^2 + 2x + 17)$12) Answer (B) Expression :$(3x+2)^2 \times (4x-3)-(2x^3-9x^2+12x-24)$=$[(9x^2+4+12x) \times (4x-3)]+(-2x^3+9x^2-12x+24)$=$(36x^3-27x^2)+(16x-12)+(48x^2-36x)+(-2x^3+9x^2-12x+24)$=$(36x^3-2x^3)+(-27x^2+48x^2+9x^2)+(16x-36x-12x)+(-12+24)$=$34x^3+30x^2-32x+12$=> Ans – (B) 13) Answer (C) Simplify : (533bxaz)/(41ab) =$\frac{533}{41} \times \frac{(ab)xz}{ab}$=$13xz$=> Ans – (C) 14) Answer (A) Expression :$(x+4)^{2}+(x-2)^{2}$=$(x^2+16+8x)+(x^2+4-4x)$=$2x^2+4x+20$=$2(x^2+2x+10)$=> Ans – (A) 15) Answer (A) Expression :$576b^{3}x^{2}a^{4}z^{3}/36a^{3}b^{2}z$=$\frac{576}{36} \times \frac{b^3x^2a^4z^3}{b^2a^3z}$=$16 \times (b)^{3-2}(x)^{2}(a)^{4-3}(z)^{3-1}$=$16bx^2az^2\$