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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