Simplification Questions for RRB Group-D Set-3 PDF

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

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

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) $18b{x}^{2}a{z}^2$

b) $18b{x}^2{a}^{2}z$

c) $36b{a}^{2}z$

d) $36bx{a}^{2}z$

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) $2(x^2+2x+17)$

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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) $16b{x}^{2}a{z}^2$

b) $b{x}^2{a}^{2}z$

c) $32b{a}^{2}z$

d) $32b{x}^{a}2z$

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Answers & Solutions:

1) Answer (A)

$3\log 6+10\log 2–2\log 12–\log 3$

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

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

2) Answer (D)

Let $\sqrt{19+4\sqrt{21}}=\sqrt{a}+\sqrt{b}$
$\to a+b+2\sqrt{ab}=19+4\sqrt{21}$.
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, $X^2=10+10+2\ast 5=30$
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
$\sqrt{\frac{(1+cosx{)}^2}{(1-cosx)(1+cosx)}}$
=> $\sqrt{\frac{(1+cosx{)}^2}{(1-co{s}^{2}x}}$
=> $\frac{1+cosx}{sinx}$ = cosecx + cotx$

8) Answer (B)

${(\frac{(\frac{1}{3}-\frac{1}{9})}{6}\times 729)}^{\frac{1}{3}}$
${(\frac{\left(\frac{3-1}{9}\right)}{6}\times 729)}^{\frac{1}{3}}$
${(\frac{\left(\frac{2}{9}\right)}{6}\times 729)}^{\frac{1}{3}}$
${(\frac{1}{27}\times 729)}^{\frac{1}{3}}$
${\left(27\right)}^{\frac{1}{3}}=3$
Hence, correct option is B

9) Answer (C)

Expression : $\frac{437bxaz}{23ab}$

= $\frac{437}{23}\times \frac{abxz}{ab}$

= $19xz$

=> Ans – (C)

10) Answer (A)

Expression : $486b^3{x}^2{a}^4{z}^3/27a^3{b}^{2}z$

= $\frac{486}{27}\times [(b{)}^{3–2}\times (x{)}^2\times (a{)}^{4–3}\times (z{)}^{3–1}]$

= $18b{x}^{2}a{z}^2$

=> 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 : $576b^3{x}^2{a}^4{z}^3/36a^3{b}^{2}z$

= $\frac{576}{36}\times \frac{b^3{x}^2{a}^4{z}^3}{b^2{a}^{3}z}$

= $16\times (b{)}^{3-2}(x{)}^2(a{)}^{4-3}(z{)}^{3-1}$

= $16b{x}^{2}a{z}^2$

=> Ans – (A)

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We hope this Simplification Questions set-3 PDF for RRB Group-D Exam will be highly useful for your preparation.