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.
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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) $2\sqrt{6}$
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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
RRB Group D previous year papers
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) $2(x^2 + 2x + 17)$
RRB Group-D Important Questions (download PDF)
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) $32bx^{a}2z$
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Answers & Solutions:
1) Answer (A)
$3 \log 6+ 10 \log 2 – 2 \log 12 – \log 3$
= $\log \frac{6^3*2^{10}}{12^2*3}$
= $\log 2^ 9= 9 \log 2$
2) Answer (D)
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.
3) Answer (C)
Let $X = \sqrt{10+\sqrt{75}} + \sqrt{10-\sqrt{75}}$
So, $X^2 = 10+10+2*5 = 30$
So, $X = \sqrt{30}$
4) Answer (A)
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}$
5) Answer (D)
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
6) Answer (B)
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
7) Answer (C)
$\sqrt{\frac{1+cosx}{1-cosx}}$
Multiplying the numerator and denominator by 1+cosx, we get
$\sqrt{\frac{(1+cosx)^2}{(1-cosx)(1+cosx)}}$
=> $\sqrt{\frac{(1+cosx)^2}{(1- cos^2x}}$
=> $\frac{1+cosx}{sinx}$ = 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 : $576b^{3}x^{2}a^{4}z^{3}/36a^{3}b^{2}z$
= $\frac{576}{36} \times \frac{b^3x^2a^4z^3}{b^2a^3z}$
= $16 \times (b)^{3-2}(x)^{2}(a)^{4-3}(z)^{3-1}$
= $16bx^2az^2$
=> Ans – (A)
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