Algebra Questions and Answers for SSC CGL with solutions

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SSC CGL Questions and Answers
SSC CGL Questions and Answers

Algebra and equations are important for the SSC CGL exam. We have provided some SSC CGL algebra questions and answers with solutions and detailed explanations. Practice questions on maths algebra.

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Question 1:

If 3.352 – (9.759 – x ) – 19.64 = 7.052, then what is the value of x?

a) -6.181
b) 13.581
c) 33.099
d) 39.803

Question 2:

If 7 + 3x ≥ 5 – x/2 and 2x + 3 ≤ 5 – 2x; then x can take which of the following values?

a) 0
b) 1
c) 2
d) -1

Question 3:

Coefficient of $x^2$ in (x + 3)(2 – 4x)(5x – 6)  is

a) 26
b) -74
c) 74
d) -26

Question 4:

If a + b = 10 and $a^2 + b^2$ = 58, then find ab

a) 21
b) 24
c) 25
d) 16

Question 5:

If 2x – 2(4 – x) < 2x – 3 < 3x + 3; then x can take which of the following values?

a) 2
b) 3
c) 4
d) 5

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Question 6:
Coefficient of x in (x + 9)(8 – 5x) is

a) 37
b) -53
c) -37
d) 53

 

Question 7:

If x – y = -9 and xy = -20, then find $x^{2} + y^{2}$

a) 61
b) 41
c) 85
d) 113

Question 8:
If 4x – 5(2x – 1) > 2x + 3 > 2 – 3x; then x can take which of the following values?

a) 1
b) 0
c) 2
d) -3

Question 9:

Which of the following is correct?

a) $(6x + y)(x – 6y) = 6x^2 + 35xy – 6y^2$
b) $(6x + y)(x – 6y) = 6x^2 – 35xy – 6y^2$
c) $(6x + y)(x – 6y) = 6x^2 – 37xy – 6y^2$
d) $(6x + y)(x – 6y) = 6x^2 + 37xy – 6y^2$

Question 10:

If a – b = -5 and $a^2 + b^2$ = 73, then find ab.

a) 35
b) 14
c) 50
d) 24

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Solutions: (1 to 10)

1) Answer (c)

Expression : 3.352 – (9.759 – x ) – 19.64 = 7.052

=> 3.352 – 9.759 + x = 7.052 + 19.64
=> x = 26.692 + 9.759 – 3.352
=> x = 36.451 – 3.352
=> x = 33.099
=> Ans – (C)

2) Answer (a)

Expression 1 : 7 + 3x ≥ 5 – x/2
=> $3x + \frac{x}{2} \geq 5 – 7$
=> $\frac{7x}{2} \geq -2$
=> $x \geq \frac{-4}{7}$ ———(i)
Expression 2 : 2x + 3 ≤ 5 – 2x
=> $2x + 2x \leq 5 – 3$
=> $4x \leq 2$
=> $x \leq \frac{2}{4} = \frac{1}{2}$ ———-(ii)
Combining inequalities (i) and (ii), we get : $\frac{-4}{7} \leq x \leq \frac{1}{2}$
Thus, the only possible value that $x$ can take among the given options = 0
=> Ans – (A)

3) Answer (d)

A coefficient is a numerical or constant quantity placed before and multiplying the variable in an algebraic expression. Eg : In $ax^2$, coefficient is $a$

Expression : $(x + 3)(2 – 4x)(5x – 6)$
= $(2x – 4x^2 + 6 – 12x)(5x – 6)$
= $(-4x^2 – 10x + 6)(5x – 6)$
= $5x(-4x^2 – 10x + 6) – 6(-4x^2 – 10x + 6)$
= $-20x^3 – 50x^2 + 30x + 24x^2 + 60x – 36$
= $-20x^3 – 26x^2 + 90x – 36$
$\therefore$ Coefficient of $x^2$ = -26
=> Ans – (D)

4) Answer (a)

Given : $(a + b) = 10$ and $a^2 + b^2 = 58$
Using $(a + b)^2 = a^2 + b^2 + 2ab$
=> $(10)^2 = 58 + (2 \times ab)$
=> $2 ab = 100 – 58 = 42$
=> $ab = \frac{42}{2} = 21$
=> Ans – (A)

5) Answer (a)

Expression 1 : $2x – 3 < 3x + 3$
=> $3x – 2x$ > $-3 – 3$
=> $x$ > $-6$ ———-(i)
Expression 2 : $2x – 2(4 – x) < 2x – 3$
=> $4x – 8$ < $2x – 3$
=> $4x – 2x$ < $8 – 3$
=> $x$ < $\frac{5}{2}$ ——(ii)
Combining inequalities (i) and (ii), we get : $-6$ < $x$ < $\frac{5}{2}$
Thus, only value that $x$ can take among the options = 2
=> Ans – (A)

6) Answer (c)

A coefficient is a numerical or constant quantity placed before and multiplying the variable in an algebraic expression. Eg : In $ax^2$, coefficient is $a$
Expression : $(x + 9)(8 – 5x)$
= $8x – 5x^2 + 72 – 45x$
= $-5x^2 – 37x + 72$
$\therefore$ Coefficient of $x$ = -37
=> Ans – (C)

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7) Answer (b)

Given : $(x – y) = -9$ and $xy = -20$
Using $(x – y)^2 = x^2 + y^2 – 2xy$
=> $(-9)^2 = (x^2 + y^2) – (2 \times -20)$
=> $(x^2 + y^2) = 81 – 40 = 41$
=> Ans – (B)

8) Answer (b)

Expression 1 : $2x + 3$ > $2 – 3x$
=> $2x + 3x$ > $2 – 3$
=> $x$ > $\frac{-1}{5}$ ———-(i)
Expression 2 : $4x – 5(2x – 1)$ > $2x + 3$
=> $-6x + 5$ > $2x + 3$
=> $2x + 6x$ < $5 – 3$
=> $x$ < $\frac{1}{4}$ ——(ii)
Combining inequalities (i) and (ii), we get : $\frac{-1}{5}$ < $x$ < $\frac{1}{4}$
Thus, only value that $x$ can take among the options = 0
=> Ans – (B)

9) Answer (b)

Expression : $(6x + y)(x – 6y)$
= $6x^2 – 36xy + xy – 6y^2$
= $6x^2 – 35xy – 6y^2$
=> Ans – (B)

10) Answer (b)

Given : $(a – b) = -5$ and $a^2 + b^2 = 73$
Using $(a – b)^2 = a^2 + b^2 – 2ab$
=> $(-5)^2 = 73 – (2 \times ab)$
=> $2 ab = 73 – 25 = 48$
=> $ab = \frac{48}{2} = 24$
=> Ans – (D)

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