Algebra Questions for SSC CGL Set-3 PDF
Download SSC CGL Algebra Questions set-3 PDF. Top 10 SSC CGL questions based on asked questions in previous exam papers very important for the SSC exam.
Download Algebra Questions for SSC CGL Set-3 PDF
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Question 1: If xy = 56 and $x^{2} + y^{2} = 113$, then what will be the value of (x + y)?
a) 29
b) 21
c) 36
d) 15
Question 2: If a + b = 11 and $a^2 + b^2$ = 61, then value of ab is
a) 12
b) 96
c) 24
d) 30
Question 3: If 4(2x -4) – 2 > 3x – 1 ≥ 4x -7, then x can take which of the following values?
a) 7
b) 6
c) 2
d) 0
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Question 4: Factors of $48x^{3} – 8x^{2} – 93x – 45$ are
a) (4x + 3)(4x - 3)(3x - 5)
b) (4x – 3)(4x - 3)(3x - 5)
c) (4x + 3)(4x + 3)(3x - 5)
d) (4x - 3)(4x + 3)(3x + 5)
Question 5: Divide 32 into two parts such that the sum of the square of the parts is 674. What is the value of the parts?
a) 22, 10
b) 30, 2
c) 25, 7
d) 20, 12
Question 6: If (4x -5) = (3x -1), then the numerical value of $(x + 4)^{2}$ is
a) 16
b) 64
c) 32
d) 8
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Question 7: If 2(3x + 5) > 4x - 5 < 3x + 2; then x can take which of the following values?
a) -8
b) 6
c) 8
d) 10
Question 8: If 51.97 -(81.18 -x ) -59.39 = 5.268, then value of x will be
a) 24.912
b) 68.492
c) 93.868
d) 197.808
Question 9: What should be added to 3(x-2y) to obtain 2(3x + y) - 5(2x + 3)?
a) 8y -7x -15
b) 8y-7x + 15
c) 8y + 7x + 15
d) 8y + 7x -15
Question 10: If 1/6 of x – 7/2 of 3/7 equals – 7/4, then the value of x is
a) -1.5
b) 3
c) -2.5
d) 6
Answers & Solutions:
1) Answer (D)
Given : $(x^2 + y^2) = 113$ and $xy = 56$
Using $(x + y)^2 = x^2 + y^2 + 2xy$
=> $(x + y)^2 = 113 + (2 \times 56)$
=> $(x + y)^2 = 113 + 112 = 225$
=> $(x + y) = \sqrt{225} = 15$
=> Ans – (D)
2) Answer (D)
Given : $(a + b) = 11$ and $a^2 + b^2 = 61$
Using $(a + b)^2 = a^2 + b^2 + 2ab$
=> $(11)^2 = 61 + (2 \times ab)$
=> $2 ab = 121 – 61 = 60$
=> $ab = \frac{60}{2} = 30$
=> Ans – (D)
3) Answer (B)
Expression 1 : 4(2x -4) – 2 > 3x – 1
=> $8x-16-2$ > $3x-1$
=> $8x-3x$ > $-1+18$
=> $x$ > $\frac{17}{5}$ ————(i)
Expression 2 : 3x – 1 ≥ 4x -7
=> $4x-3x \leq -1+7$
=> $x \leq 6$ ———–(ii)
Combining inequalities (i) and (ii), we get : $\frac{17}{5}$ < $x \leq 6$
The only value that $x$ can take among the options = 6
=> Ans – (B)
4) Answer (C)
(A) : (4x + 3)(4x - 3)(3x - 5)
= $(16x^2 – 12x + 12x – 9)(3x – 5)$
= $(16x^2 – 9)(3x – 5)$
= $48x^3 – 80x^2 – 27x + 45$
(B) : (4x – 3)(4x - 3)(3x - 5)
= $(16x^2 – 24x + 9)(3x – 5)$
= $48x^3 – 80x^2 – 72x^2 + 120x + 27x – 45$
= $48x^3 – 152x^2 + 147x – 45$
(C) : (4x + 3)(4x + 3)(3x - 5)
= $(16x^2 + 24x + 9)(3x – 5)$
= $48x^3 – 80x^2 + 72x^2 – 120x + 27x – 45$
= $48x^3 – 8x^2 – 93x – 45$
=> Ans – (C)
5) Answer (C)
Let the first part = $x$ and second part = $(32 – x)$
According to ques, => $(x)^2 + (32 – x)^2 = 674$
=> $x^2 + (x^2 + 1024 – 64x) = 674$
=> $2x^2 – 64x + 1024 – 674 = 0$
=> $x^2 – 32x + 175 = 0$
=> $x^2 – 25x – 7x + 175 = 0$
=> $x(x-25) – 7(x-25) = 0$
=> $(x-25)(x-7) = 0$
=> $x = 25,7$
=> Ans – (C)
6) Answer (B)
Given : (4x - 5) = (3x -1)
=> $4x – 3x = 5 – 1$
=> $x = 4$
To find : $(x + 4)^2$
= $(4 + 4)^2 = 8^2 = 64$
=> Ans – (B)
7) Answer (B)
Expression 1 : 2(3x + 5) > 4x - 5
=> $6x+10$ > $4x-5$
=> $6x-4x$ > $-5-10$
=> $2x$ > $-15$
=> $x$ > $\frac{-15}{2}$ ——–(i)
Expression 2 : 4x - 5 < 3x + 2
=> $4x-3x$ < $2+5$
=> $x$ < $7$ ———(ii)
Combining inequalities (i) and (ii), we get : $\frac{-15}{2}$ < $x$ < $7$
The only value that $x$ can take = 6
=> Ans – (B)
8) Answer (C)
Expression : 51.97 -(81.18 -x ) -59.39 = 5.268
=> 51.97 – 81.18 + x = 5.268 + 59.39
=> -29.21 + x = 64.658
=> x = 64.658 + 29.21
=> x = 93.868
=> Ans – (C)
9) Answer (A)
Let $m$ should be added to 3(x-2y) to obtain 2(3x + y) - 5(2x + 3)
=> $(m) + [3(x-2y)] = 2(3x+y)-5(2x+3)$
=> $m + 3x-6y=6x+2y-10x-15$
=> $m = (2y+6y)+(-4x-3x)-15$
=> $m=8y-7x-15$
=> Ans – (A)
10) Answer (A)
According to ques,
=> $(\frac{1}{6} \times x) – (\frac{7}{2} \times \frac{3}{7}) = \frac{-7}{4}$
=> $\frac{x}{6} – \frac{3}{2} = \frac{-7}{4}$
=> $\frac{x}{6} = \frac{3}{2} – \frac{7}{4}$
=> $\frac{x}{6} = \frac{-1}{4}$
=> $x = \frac{-6}{4} = -1.5$
=> Ans – (A)
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