Algebra · SSC CGL previous year questions

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2022 129 questions

Q542022 · 7 Dec 2022 · Shift 4
If $x + \frac{1}{x} = 7$ , find the value of $x^{3} + \frac{1}{x ^{3}}$ .
1. A.343
2. B.322
3. C.340
4. D.332
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Answer: B
Q562022 · 7 Dec 2022 · Shift 4
If (a + 1)2 + (a + 2)2 = 16 then what is the value of 40 + 12a + 4a2?
1. A.56
2. B.62
3. C.74
4. D.52
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Answer: B
Q622022 · 7 Dec 2022 · Shift 4
Which of the following statement is correct? I. If $K + \frac{1}{K} = 12$ , $K^{2} + \frac{1}{K ^{2}} = 142$ . II. The value of $(k^{2} + \frac{1}{k ^{2}}) (k - \frac{1}{k}) (k^{4} + \frac{1}{k ^{4}}) (k + \frac{1}{k})$ is $k^{16} - \frac{1}{k ^{16}}$ .
1. A.Only I
2. B.Neither I nor II
3. C.Both I and II
4. D.Only II
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Answer: A
Q512022 · 6 Dec 2022 · Shift 1
The value of 97 × 103 is ______.
1. A.7999
2. B.9991
3. C.8991
4. D.9981
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Answer: B
Q552022 · 6 Dec 2022 · Shift 1
If $x + \frac{1}{x} = 1$ , then the value of $x^{12} + x^{9} + x^{6} + x^{3} + 1$ is:
1. A.1
2. B.-1
3. C.0
4. D.-2
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Answer: A
Q562022 · 6 Dec 2022 · Shift 1
The mid points of AB and AC of a △ ABC are X and Y, respectively. If BC + XY = 24 units, then the value of BC - XY is:
1. A.5 cm
2. B.4 cm
3. C.6 cm
4. D.8 cm
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Answer: D
Q612022 · 6 Dec 2022 · Shift 2
If $\frac{a}{b} + \frac{b}{a} = 1$ and a + b = 2, then the value of $a^{3} + b^{3}$ is:
1. A.0
2. B.3
3. C.1
4. D.2
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Answer: A
Q652022 · 6 Dec 2022 · Shift 2
If 4x2 + y2 = 40 and xy = 6, find the positive value of 2x + y.
1. A.8
2. B.6
3. C.5
4. D.4
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Answer: A
Q692022 · 6 Dec 2022 · Shift 2
What is the value of $\frac{c o s 3 7 ^{\circ}}{s i n 5 3 ^{\circ}}$ ?
1. A.Option 1
2. B.Option 2
3. C.Option 3
4. D.Option 4
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Answer: D
Q732022 · 6 Dec 2022 · Shift 2
If $p = 7 + 43$ , then what is the value of $\frac{p ^{6} + p ^{4} + p ^{2} + 1}{p ^{3}}$ ?
1. A.2617
2. B.2167
3. C.2716
4. D.2176
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Answer: C
Q652022 · 6 Dec 2022 · Shift 3
If 2a + 3b = 10 and ab = 3, then find the value of 4a2 + 9b2.
1. A.60
2. B.62
3. C.64
4. D.66
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Answer: C
Q672022 · 6 Dec 2022 · Shift 3
If (4x - 7y) = 11 and xy = 8, what is the value of 16x2 + 49y2, given that x and y are positive numbers?
1. A.596
2. B.484
3. C.569
4. D.448
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Answer: C
Q732022 · 6 Dec 2022 · Shift 3
What is the value of $(k - \frac{1}{k}) (k^{2} + \frac{1}{k ^{2}}) (k^{4} + \frac{1}{k ^{4}}) (k^{8} + \frac{1}{k ^{8}}) (k^{16} + \frac{1}{k ^{16}}) (k^{32} + \frac{1}{k ^{32}})$ ?
1. A.Option 1
2. B.Option 2
3. C.Option 3
4. D.Option 4
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Answer: A
Q552022 · 6 Dec 2022 · Shift 4
If $x + \frac{1}{x} = 2$ , then the value of $x^{57} + \frac{1}{x ^{57}}$ is:
1. A.1
2. B.-2
3. C.0
4. D.2
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Answer: D
Q602022 · 6 Dec 2022 · Shift 4
If $m x^{m} - n x^{n} = 0$ , then what is the value of $\frac{1}{x ^{m} + x ^{n}} + \frac{1}{x ^{m} - x ^{n}}$ terms of $x^{n}$ is: Where x, m, n are > 0
1. A.2mn/(xn(n2 + m2)
2. B.2mn/(xn(m2 - n2)
3. C.2mn/(xn(m2 + n2)
4. D.2mn/(xn(n2 - m2)
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Answer: D
Q642022 · 6 Dec 2022 · Shift 4
If, for a non-zero x, $5 x^{2} + 7 x + 5 = 0$ , then the value of $x^{3} + \frac{1}{x ^{3}}$ is:
1. A.Option 1
2. B.Option 2
3. C.Option 3
4. D.Option 4
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Answer: D
Q562022 · 5 Dec 2022 · Shift 1
If $x + \frac{1}{x} = - 14$ , and x < -1, what will be the value of $x^{2} - \frac{1}{x ^{2}}$ ?
1. A.Option 1
2. B.Option 2
3. C.Option 3
4. D.Option 4
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Answer: B
Q632022 · 5 Dec 2022 · Shift 1
If $k^{4} + \frac{1}{k ^{4}} = 47$ , then what is the value of $k^{3} + \frac{1}{k ^{3}}$ ?
1. A.4.5
2. B.54
3. C.18
4. D.9
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Answer: C
Q552022 · 5 Dec 2022 · Shift 2
If a - b = 2 and a 3 - b 3 = 80, then what will be the value of ab?
1. A.12
2. B.-24
3. C.24
4. D.-12
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Answer: A
Q562022 · 5 Dec 2022 · Shift 2
If , then the value of x is :
1. A.Option 1
2. B.Option 2
3. C.Option 3
4. D.Option 4
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Answer: D
Q692022 · 5 Dec 2022 · Shift 2
Which of the following statement is correct? I. The value of $10 0^{2} - 9 9^{2} + 9 8^{2} - 9 7^{2} + 9 6^{2} - 9 5^{2} + 9 4^{2} - 9 3^{2} + \dots + 2 2^{2} - 2 1^{2}$ is 4840. II. The value of $(k^{2} + \frac{1}{k ^{2}}) (k - \frac{1}{k}) (k^{4} + \frac{1}{k ^{4}}) (k + \frac{1}{k}) (k^{4} - \frac{1}{k ^{4}})$ is $k^{16} - \frac{1}{k ^{16}}$ .
1. A.Neither I nor II
2. B.Only II
3. C.Only I
4. D.Both I and II
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Answer: C
Q632022 · 5 Dec 2022 · Shift 3
Select the correct algebraic expression.
1. A.ab – a – b + 1 = (a – 1) (b – 1)
2. B.ab + a – b + 1 = (1 – a) (1 – b) (1 – a) (1 + b)
3. C.ab – a – b + 1 = (1 – a) (b – 1)
4. D.ab – a – b + 1 = (a – 1) (1 – b)
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Answer: A
Q642022 · 5 Dec 2022 · Shift 3
What is the value of 100 2- 99 2+ 98 2- 97 2+ 96 2- 95 2+ 94 2- 93 2+ ................ 12 2- 11 2
1. A.5050
2. B.4985
3. C.4995
4. D.4950
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Answer: C
Q522022 · 5 Dec 2022 · Shift 4
If x 2+ y 2+ z 2= xy + yz + zx and x = 1, then find the value of
1. A.2
2. B.0
3. C.-1
4. D.1
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Answer: D
Q552022 · 5 Dec 2022 · Shift 4
If $x + \frac{1}{2 x} = 3$ , then evaluate $8 x^{3} + \frac{1}{x ^{3}}$ .
1. A.212
2. B.216
3. C.180
4. D.196
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Answer: C