Simplification Questions for RRB JE PDF

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Simplification Questions for RRB JE PDF
Simplification Questions for RRB JE PDF

Simplification Questions for RRB JE PDF

Download Top 20 RRB JE Simplification Questions and Answers PDF. RRB JE Maths questions based on asked questions in previous exam papers very important for the Railway JE exam

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Question 1: If the roots of the equation 2x29x+7=0 are p and q then the equation with roots as p+1 and q+1 is ?

a) 2x213x+18=0

b) 2x211x+16=0

c) 2x2+11x16=0

d) 2x2+13x18=0

Question 2: If b1b=7, then what is the value of b+1b

a) 51

b) 52

c) 50

d) 53

Question 3: If a+1a=4, then what is the value of a1a

a) 11

b) 12

c) 10

d) 13

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Question 4: If a3+b3+c3=3abc, then find the value of (a+b)2c2.

a) -1

b) 1

c) 0

d) 2

Question 5: If x2+y2+x2+y2 = 4 then what is the value of x4+y4 ?

a) 0

b) -1

c) 2

d) 4

Question 6: If x2+1=2x, then find x3+1x3.

a) 4

b) 3

c) 2

d) 0

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Question 7: Find the value of x from the given equations.
7x + 3y + 5z = 27
6x + 6y + 10z = 14

a) 4

b) 11

c) 5

d) 9

Question 8: Find the value of 1+11+11+11+17.

a) 3821

b) 3823

c) 3623

d) 3920

Question 9: If x+1x=3,x6+1x6=?

a) 314

b) 322

c) 328

d) 316

Question 10: Find the value of x from the given equations.
7x + 3y + 5z = 27
6x + 6y + 10z = 14

a) 4

b) 11

c) 5

d) 9

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Question 11: Find the value of 1+11+11+11+17.

a) 3821

b) 3823

c) 3623

d) 3920

Question 12: If x+1x=3,x6+1x6=?

a) 314

b) 322

c) 328

d) 316

Question 13: Find the value of 1+11+11+11+14.

a) 2115

b) 2314

c) 2413

d) 2311

Question 14: Find the value of 1+11+11+11+27.

a) 3725

b) 4122

c) 4125

d) 3519

Question 15: If x4+(1x)4=34 then what is the value of x1/x

a) 2

b) 6

c) 8

d) 4

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Question 16: If x4+(1x)4=727 then what is the value of x3(1x)3

a) 140

b) 138

c) 134

d) 136

Question 17: If x4+(1x)4=119 then what is the value of x3(1x)3

a) 36

b) 24

c) 42

d) 30

Question 18: If p+1p=3, then find the value of p6+1p6.

a) 322

b) 348

c) 329

d) 342

Question 19: If px3+qx219x30=0 is completely divided by x2+5x+6, find the value of (p,q).

a) (1,0)

b) (2,1)

c) (1,0)

d) (4,1)

Question 20: If l3+m3 = -218 and lm=35 , then what is the value of l+m?

a) -6

b) -2

c) -4

d) -5

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Answers & Solutions:

1) Answer (A)

Given 2x29x+7=0
2x22x7x+7=0
2x(x1)7(x1)=0
(2x7)(x1)=0
p=3.5 and q=1
Roots of the new equation are p+1 an q+1 i.e 4.5 and 2
(x4.5)(x2)=0
2x213x+18=0

2) Answer (D)

b1b=7
Squaring on both sides we have
b22(b)(1/b)+(1b)2=49
b2+(1b)2=49+2 = 51
Adding 2 on both sides
b2+2+(1b)2=51+2
(b+1b)2=53
b+1b=53

3) Answer (B)

a+1a=4
Squaring on both sides we have
a2+2(a)(1/a)+(1a)2=16
a2+(1a)2=14
Subtracting 2 on both sides
a22+(1a)2=14-2
(a1a)2=12
a1a=12

4) Answer (C)

If a3+b3+c3=3abc, then a+b+c=0.
(a+b)2c2=(a+b+c)(a+bc)=0

5) Answer (C)

x2+y2+x2+y2=4
(x2+1x22)+(y2+1y22)=0
(x1x)2+(y1y)2=0
Sum of two squares is zero when both the numbers are zero.
x1x = 0 and y1y=0
x=1or 1 and y=1 or 1
In all the cases, x4+y4=2
Hence, option C is the correct answer.

6) Answer (C)

Given, x2+1=2x
Dividing with x on both sides
x+1x=2
Cubing on both sides
(x+1x)3=23
x3+1x3+3×x×1x(x+1x)=8

x3+1x3+3×2=8
x3+1x3=86=2

7) Answer (C)

7x + 3y + 5z = 27 → (1)
6x + 6y + 10z = 14 → (2)
Multiplying equation (1) by 2 and subtracting (2) from (1) we get
8x = 40
⇒ x = 5
Hence, option C is the correct answer.

8) Answer (B)

1+11+11+11+17=1+11+11+187

=1+11+11+78

=1+11+1158

=1+11+815

=1+12315

=1+1523

=3823

9) Answer (B)

Given, x+1x=3
Squaring on both sides
(x+1x)2=32
x2+1x2+2×x×1x=9

x2+1x2+2=9

x2+1x2=7
Cubing above equation on both sides
(x2+1x2)3=73

Extra close brace or missing open brace

x6+1x6+3×7=343

x6+1x6+21=343

x6+1x6=34321=322

10) Answer (C)

7x + 3y + 5z = 27 → (1)
6x + 6y + 10z = 14 → (2)
Multiplying equation (1) by 2 and subtracting (2) from (1) we get
8x = 40
⇒ x = 5
Hence, option C is the correct answer.

11) Answer (B)

1+11+11+11+17=1+11+11+187

=1+11+11+78

=1+11+1158

=1+11+815

=1+12315

=1+1523

=3823

12) Answer (B)

Given, x+1x=3
Squaring on both sides
(x+1x)2=32
x2+1x2+2×x×1x=9

x2+1x2+2=9

x2+1x2=7
Cubing above equation on both sides
(x2+1x2)3=73

Extra close brace or missing open brace

x6+1x6+3×7=343

x6+1x6+21=343

x6+1x6=34321=322

13) Answer (B)

1+11+11+11+14=1+11+11+154

=1+11+11+45

=1+11+195

=1+11+59

=1+1149

=1+914

=2314

14) Answer (C)

1+11+11+11+27=1+11+11+197

=1+11+11+79

=1+11+1169

=1+11+916

=1+12516

=1+1625

=4125

15) Answer (A)

x4+(1x)4=34
Add 2 on both sides
x4+2+(1x)4=34+2
(x2+1x2)2=36
x2+(1x)2=6
Subtracting 2 on both sides
x2+(1x)22=4

(x1x)2=4
x1/x=2

16) Answer (A)

x4+(1x)4=727
Add 2 on both sides
x4+2+(1x)4=727+2
(x2+1x2)2=729
x2+(1x)2=27
Subtracting 2 on both sides
x2+(1x)22=27-2
x-1/x=5
Cubing on both sides we have
x3(1x)315=125
x3(1x)3=125+15=140

17) Answer (A)

x4+(1x)4=119
Add 2 on both sides
x4+2+(1x)4=119+2

(x2+1x2)2=121

x2+(1x)2=11
Subtracting 2 on both sides
x2+(1x)22=11-2
x-1/x=3
Cubing on both sides we have
x3(1x)39=27

x3(1x)3=36

18) Answer (A)

Given,
p+1p = 3

Squaring both sides,

p2 + 1p2 + 2×p×1p = 9

p2+1p2 = 7

Cubing on both sides,

p6+1p6 +3×p2×1p2(p2+1p2) =343

p6+1p6 +3(p2+1p2) =343

p6+1p6 +3(7)= 343

p6+1p6  = 34321

p6+1p6  = 322

19) Answer (C)

Given, px3+qx219x30=0 is divisible by x2+5x+6

x2+5x+6 can be factorized as (x+2)(x+3)

x = -2 and x = -3 should satisfy px3+qx219x30=0.

Substituting the values,

When, x=2

8p+4q+8=0 or 2pq2=0

When, x=3

27p+9q+27=0 or 3pq3=0

Subtracting both, p=1

Substituting the value of p=1, we get q=0

Hence, (p,q)(1,0).

20) Answer (B)

Given, l3+m3 = -218 and lm=35

(l+m)3=l3+m3+3lm(l+m)

(l+m)3=218+3(35)(l+m)

(l+m)3=218105(l+m)

we need to solve 3rd degree equation

so,without solving, by verification, we get l+m=2,

so the answer is option B.

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