SSC CHSL Algebra Questions with solutions. Solved Algebra question answer with short tricks are very useful for upcoming SSC CGL, CHSL and other Competitive Exams.

### SSC CHSL ALGEBRA QUESTIONS

**Q.1:** If a + b = p, ab = q, then (a^{4} + b^{4} ) is equal to:

(A) p^{4} – 4p^{2}q + q^{2}

(B) p^{4} – 4p^{2}q^{2} + 2q^{2}

(C) p^{4} – 2p^{2}q^{2} + q^{2}

(D) p^{4} – 4p^{2}q + 2q^{2}

###### Show Answer

^{4}– 4p

^{2}q + 2q

^{2}

a + b = p , ab = q

(a + b)

^{2}= p

^{2}

a

^{2}+ 2ab + b

^{2}= p

^{2}

a

^{2}+ b

^{2}= p

^{2}– 2q

(a

^{2}+ b

^{2})

^{2}= (p

^{2}– 2q)

^{2}

a

^{4}+ b

^{4}+ 2a

^{2}b

^{2}= p

^{4}– 4p

^{2}q + 4q

^{2}[ab = q, a

^{2}b

^{2}= q

^{2}]

a

^{4}+ b

^{4}= p

^{4}– 4p

^{2}q + 2q

^{2}

**Q.2:** If , then what is the value of ? Given the x is real.

(A) 9

(B) 25

(C) 7

(D) 11

###### Show Answer

**Q.3:** If , then what will be the value of ?

(A) 18

(B) 8

(C) 12

(D) 20

###### Show Answer

**Q.4:** If , then the value of will be:

(A) 2712

(B) 2502

(C) 2270

(D) 2702

###### Show Answer

**Q.5:** If x^{2} + 1 – 2x = 0, x > 0 , then x^{2}(x^{2 }– 2) =_______.

(A) 0

(B) -1

(C) 1

(D)

###### Show Answer

x

^{2}+ 1 – 2x = 0

x > 0

x = 1, so 1 + 1 – 2 = 0

Put x = 1 in x

^{2}(x

^{2 }– 2)

1 (1 – 2)

= -1

**Q.6:** If , then what is the value of ?

(A)

(B)

(C)

(D)

###### Show Answer

**Q.7:** If x – y = 4 and xy = 3 , then what is the value of x^{3} – y^{3} ?

(A) 88

(B) 100

(C) 64

(D) 28

###### Show Answer

x – y = 4

(x – y)

^{3}= 4

^{3}

x

^{3}– y

^{3}– 3xy (x – y) = 64 [Put xy = 3, x – y =4]

x

^{3}– y

^{3}– 3 x 3 x 4 = 64

x

^{3}– y

^{3}= 64 + 36 = 100

**Q.8:** If , then what will be the value of ?

(A)

(B)

(C)

(D)

###### Show Answer

**Q.9:** If x + 2y = 19 and x^{3} + 8y^{3} = 361 , then xy is equal to:

(A) 58

(B) 56

(C) 55

(D) 57

###### Show Answer

x + 2y = 19

(x + 2y)

^{3}= (19)

^{3}

x

^{3}+ 8y

^{3}+ 6xy (x + 2y) = 6859

x

^{3}+ 8y

^{3}+ 6xy x 19 = 6859

6xy x 19 = 6859 – 361 = 6498

xy =

xy = 57

**Q.10:** If , then what is the value of ?

(A) 4

(B)

(C)

(D) 7

###### Show Answer

** SSC CHSL Algebra Questions with solutions for Competitive Exams**

**Q.11:** If x + y = 27 and x^{2} + y^{2} = 425 , then the value of (x – y)^{2} will be:

(A) 121

(B) 225

(C) 169

(D) 144

###### Show Answer

x + y = 27

x

^{2}+ y

^{2}= 425

(x + y)

^{2}= (27)

^{2}

x

^{2}+ y

^{2}+ 2xy = 729

2xy = 729 – 425

2xy = 304

(x – y)

^{2}= x

^{2}+ y

^{2}– 2xy

= 425 – 304

(x – y)

^{2}= 121

**Q.12:** If 3x + y = 12 and xy = 9 , then the value of (3x – y) is:

(A) 6

(B) 5

(C) 3

(D) 4

###### Show Answer

3x + y = 12

xy = 9

put x = 3, y = 3 Both Equation

So its satify

3x – y = 3 x 3 – 3

= 9 – 3 = 6

**Q.13:** If a^{2} + b^{2} + c^{2} = 576 and (ab + bc + ca) = 50 , then what is the value of (a + b + c), if (a+b+c) < 0 ?

(A) -24

(B)

(C)

(D) -26

###### Show Answer

(a + b + c)

^{2}= a

^{2}+ b

^{2}+c

^{2}+ 2 (ab + bc + ca)

576 + 2 x 50

(a + b + c)

^{2}= 676

a + b + c =

a + b + c < 0

so a+b+c = -26

**Q.14:** If , then the value of will be:

(A) 3024

(B) 3420

(C) 3042

(D) 3240

###### Show Answer

[ Multiply by 3]

=3240

**Q.15:**If 3x + 5y = 14 and xy = 6 , then what is the value of 9x^{2} + 25y^{2} ?

(A) 182

(B) 16

(C) 14

(D) 20

###### Show Answer

(3x + 5y)

^{2}= (14)

^{2}

9x

^{2}+ 25y

^{2}+ 30xy = 196

9x

^{2}+ 25y

^{2}+ 30 x 6 = 196

9x

^{2}+ 25y

^{2}= 196 – 180

9x

^{2}+ 25y

^{2}= 16

**Q.16:** If a – b = 7 and a^{2} + b^{2} = 169 where a,b >0 , then the value of 3 a+b is:

(A) 41

(B) 46

(C) 38

(D) 44

###### Show Answer

a – b = 7

(a – b)

^{2}= 7

^{2}

a

^{2}+ b

^{2}– 2ab = 49

169 – 2ab = 49

2ab = 169 – 49

2ab = 120

ab = 60 [12 x 5]

a = 12, b = 5

3a + b

= 3 x 12 + 5

= 41

**Q.17:** If a + 5b = 25 and ab = 20 , then one of the values of (a-5 b) is:

(A) 16

(B) 15

(C) 13

(D) 14

###### Show Answer

a + 5b = 25, ab = 20

Put a = 20

b = 1

so a – 5b

= 20 – 5 x 1 = 15

**Q.18:** If , then what will be the value of ?

(A) 10406

(B) 10402

(C) 9602

(D) 9606

###### Show Answer

= 9604 – 2

**Q.19:** If (7x – 10y) = 8 and xy = 5 , then what is the value of 49x^{2} + 100y^{2} ?

(A) 632

(B) 623

(C) 746

(D) 764

###### Show Answer

7x – 10y = 8

(7x – 10y)

^{2}= (8)

^{2}

49x

^{2}+ 100y

^{2}– 140xy = 64

49x

^{2}+ 100y

^{2}= 64 + 140xy

= 64 + 140xy

= 64 + 140 x 5

= 764

**Q.20:** If , then what is the value of ?

(A)

(B)

(C)

(D)

###### Show Answer

Both side

square Both side

** SSC CHSL Algebra Questions with solutions for Competitive Exams**

**Q.21:** If , x > 0 , then the value of is:

(A) 675

(B) 756

(C) 746

(D) 576

###### Show Answer

= 756

**Q.22:** If , then one of the values of is:

(A) 36

(B) 32

(C)

(D)

###### Show Answer

= 36

**Q.23:** The coefficient of x^{3} y in (x – 2y) x (5x + y)^{3} is:

(A) -150

(B) 75

(C) -175

(D) 250

###### Show Answer

(x – 2y) x (5x + y)

^{3}

(x – 2y) x [ 125x

^{3}+ y

^{3}+ 15xy (5x + y)

(x – 2y) x [ 125x

^{3}+ y

^{3}+ 75x

^{2}y + 15xy

^{2}]

coefficient of x

^{3}y

= 75x

^{3}– 250x

^{3}y

= -175x

^{3}y

so coefficient of x

^{3}y

= -175

**Q.24:** If 9x^{2} – 6x + 1 = 0 , then the value of 27x^{3} + (27x^{3})^{-1} will be:

(A) 1

(B) 4

(C) 2

(D) 8

###### Show Answer

9x

^{2}– 6x + 1 = 0

27x

^{3}+ (27x

^{3})

^{-1}

9x

^{2}– 6x + 1 = 0

(3x – 1)

^{2}= 0

3x – 1 = 0

3x = 1

put

= 1 + 1 = 2

**Q.25:** What is the coefficient of y^{2} in the expansion of ?

(A)

(B)

(C)

(D)

###### Show Answer

(a – b)

^{3}= a

^{3}– b

^{3}– 3ab(a – b)

केवल y

^{2}का गुणांक लेने पर

y

^{2}का गुणांक

**Q.26:** If a + b + c = 2 and ab + bc + ca = -1 , then the value of a^{3} + b^{3} + c^{3} – 3abc is:

(A) 5

(B) 10

(C) 2

(D) 14

###### Show Answer

a + b + c = 2

(a + b + c)

^{2}= ( 2 )

^{2}

a

^{2}+b

^{2}+c

^{2}+ 2(ab + bc + ca) = 4

a

^{2}+b

^{2}+c

^{2}+ 2 x(-1) = 4

a

^{2}+b

^{2}+c

^{2}= 6

a

^{3}+b

^{3}+c

^{3}– 3abc = (a+b+c) [(a

^{2}+b

^{2}+c

^{2}) – (ab+bc+ca)]

= 2[6 – (-1)]

= 2 x 7 = 14

**Q.27:** If , then the value of will be:

(A) 237.6

(B) 273.6

(C) 367.2

(D) 376.2

###### Show Answer

9 से गुणा Both side

**Q.28:** If a+b+c = 11 and ab+bc+ca = 15 , then what is the value of a^{3}+b^{3}+c^{3} – 3abc ?

(A) 386

(B) 836

(C) 368

(D) 638

###### Show Answer

a+b+c = 11

(a+b+c)

^{2}= 11

^{2}

a

^{2}+b

^{2}+c

^{2}+ 2 (ab+bc+ca) = 121

a

^{2}+b

^{2}+c

^{2}+ 2 x 15 = 121

a

^{2}+b

^{2}+c

^{2}= 121 – 30

a

^{2}+b

^{2}+c

^{2}= 91

a

^{3}+b

^{3}+c

^{3}-3abc =(a+b+c) [(a

^{2}+b

^{2}+c

^{2})-(ab+bc+ca)]

= 11[91 – 15]

= 11 x 76

a

^{3}+b

^{3}+c

^{3}-3abc = 836

**Q.29:** If a+b+c = 5, a^{2}+b^{2}+c^{2} = 27, and a^{3}+b^{3}+c^{3} = 125 , then the value of is:

(A) -5

(B) -1

(C) 5

(D) 1

###### Show Answer

a+b+c = 5

(a+b+c)

^{2}= (5)

^{2}

a

^{2}+b

^{2}+c

^{2}+2(ab+bc+ca) = 25

27 + 2(ab+bc+ca) = 25

ab+bc+ca = -1

a

^{3}+b

^{3}+c

^{3}-3abc = (a+b+c) [(a

^{2}+b

^{2}+c

^{2}-(ab+bc+ca)

125 – 3abc = 5 [27 – (-1)

= 5 x 28

125 – 3abc = 140

3abc = -15

abc = -5

**Q.30:** If x^{4} + x^{-4} = 47, x>0 , then the value of (2x – 3)^{2} is:

(A) 9

(B) 5

(C) 3

(D) 7

###### Show Answer

x

^{2}+ 1 = 3x

4x

^{2}– 12x = -4

(2x – 3)

^{2}

= 4x

^{2}+ 9 – 12x

4x

^{2}– 12x + 9

-4 + 9 = 5

** SSC CHSL Algebra Questions with solutions for Competitive Exams**

**Q.31:** If , where a > 0, then the value of is:

(A) 45

(B) 60

(C) 65

(D) 56

###### Show Answer

Put x = 8 its satisfy this equation

So

64 + 1 = 65

**Q.32:** If x = 555, y = 556 and z = 557 , then find the value of x^{3}+y^{3}+z^{3} – 3xyz.

(A) 5002

(B) 5008

(C) 5006

(D) 5004

###### Show Answer

x

^{3}+y

^{3}+z

^{3}– 3xyz = (x+y+z)[(x – y)

^{2}+(y – z)

^{2}+(z – x)

^{2}]

= 3 x 1668

= 5004

**Q.33:** If 3x-2y+3=0 , then what will be the value of 27x^{3}+54xy+30-8y^{3} ?

(A) 57

(B) -57

(C) -27

(D) 3

###### Show Answer

3x-2y+3=0

3x-2y=-3

(3x-2y)

^{3}= (-3)

^{3}

27x

^{3}– 8y

^{3}+54xy =-27

27x

^{3}– 8y

^{3}=-27 – 54xy

27x

^{3}+54xy+30 -8y

^{3}

-27-54xy+54xy+30

= 30-27 = 3

Thanks for Study the SSC CHSL Algebra Questions with solutions

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