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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