Algebra · SSC CGL previous year questions

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2022 129 questions

Q592022 · 12 Dec 2022 · Shift 1
If $m + \frac{1}{m - 2} = 4$ , then find the value of $(m - 2)^{2} + \frac{1}{( m - 2 ) ^{2}}$ .
1. A.−2
2. B.4
3. C.0
4. D.2
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Answer: D
Q632022 · 12 Dec 2022 · Shift 1
In ∆ ABC, D and E are points on sides AB and AC, such that DE ΙΙ BC. If AD = x + 3, DB = 2x − 3, AE = x + 1 and EC = 2x − 2, 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: C
Q662022 · 12 Dec 2022 · Shift 1
If a = 26 and b = 22, then the value of $\frac{a ^{3} - b ^{3}}{a ^{2} - b ^{2}} - \frac{3 ab}{a + b}$ is ______.
1. A.Option 1
2. B.Option 2
3. C.Option 3
4. D.Option 4
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Answer: C
Q582022 · 12 Dec 2022 · Shift 2
If $a + \frac{1}{a} = 5$ , then what is the value of $a^{3} + \frac{1}{a ^{3}}$ ?
1. A.110
2. B.15
3. C.105
4. D.–10
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Answer: A
Q632022 · 12 Dec 2022 · Shift 2
What is the value of a2 + b2 + c2 - 2ab - 2bc + 2ca ?
1. A.(2a + b + c)2
2. B.(a – b + c)2
3. C.(a – b – 2c)2
4. D.(a + 2b – c)2
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Answer: B
Q702022 · 12 Dec 2022 · Shift 2
If , then the value of x3 is :
1. A.-256
2. B.-512
3. C.256
4. D.512
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Answer: B
Q562022 · 12 Dec 2022 · Shift 3
If the seven-digit number 52A6B7C is divisible by 33, and A, B, C are primes, then the maximum value of 2A + 3B + C is:
1. A.32
2. B.23
3. C.27
4. D.34
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Answer: B
Q672022 · 12 Dec 2022 · Shift 3
If p = 8.15, q = 9.06 and r = -17.21, then the value of p3 + q3 + r3 - 3pqr is:
1. A.-3.81
2. B.-5.62
3. C.4.75
4. D.0
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Answer: D
Q712022 · 12 Dec 2022 · Shift 3
The value of $\frac{1.6 \times 1.6 \times 1.6 - 0.6 \times 0.6 \times 0.6}{1.6 \times 1.6 + 1.6 \times 0.6 + 0.6 \times 0.6}$ is:
1. A.0
2. B.1
3. C.-1
4. D.2
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Answer: B
Q742022 · 12 Dec 2022 · Shift 3
If $x^{4} + \frac{16}{x ^{4}} = 15617$ , x > 0, then find the value of $x + \frac{2}{x}$ .
1. A.Option 1
2. B.Option 2
3. C.Option 3
4. D.Option 4
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Answer: B
Q562022 · 12 Dec 2022 · Shift 4
If x = 222, y = 223 and z = 224, then find the value of .
1. A.2007
2. B.2004
3. C.2006
4. D.2005
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Answer: A
Q602022 · 12 Dec 2022 · Shift 4
If $α, β$ are the roots of $6 x^{2} + 13 x + 7 = 0$ , then the equation whose roots are $α^{2}, β^{2}$ is:
1. A.Option 1
2. B.Option 2
3. C.Option 3
4. D.Option 4
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Answer: B
Q632022 · 12 Dec 2022 · Shift 4
If $cos θ + cos^{2} θ = 1$ , find the value of $sin^{4} θ + cos^{2} θ$ .
1. A.Option 1
2. B.Option 2
3. C.Option 3
4. D.Option 4
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Answer: A
Q712022 · 12 Dec 2022 · Shift 4
If x + y + z = 0 and x2 + y2 + z2 = 40, then what is the value of xy + yz + zx?
1. A.-20
2. B.5
3. C.-5
4. D.-10
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Answer: A
Q522022 · 9 Dec 2022 · Shift 1
If x + y + z = 0, then the value of $\frac{x ^{2}}{y z} + \frac{y ^{2}}{z x} + \frac{z ^{2}}{x y}$ is:
1. A.3
2. B.1
3. C.0
4. D.2
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Answer: A
Q662022 · 9 Dec 2022 · Shift 1
The value of , where p ≠ q ≠ r, is equal to:
1. A.Option 1
2. B.Option 2
3. C.Option 3
4. D.Option 4
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Answer: C
Q702022 · 9 Dec 2022 · Shift 1
What is the value of $(a + b)^{3} - a^{3} + b^{3}$ ?
1. A.-3ab (a - b) + 2
2. B.3ab(a + b) + 2b3
3. C.3ab(a-b)
4. D.-3ab(a + b) +
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Answer: B
Q542022 · 9 Dec 2022 · Shift 2
If $X^{2} + \frac{1}{X ^{2}} = 66$ , the value of $X - \frac{1}{X}$ is ______.
1. A.10
2. B.8
3. C.9
4. D.6
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Answer: B
Q572022 · 9 Dec 2022 · Shift 2
If $\frac{s i n θ + c o s θ}{s i n θ - c o s θ} = \frac{3}{2}$ , then the value of $sin^{4} θ - cos^{4} θ$ is:
1. A.Option 1
2. B.Option 2
3. C.Option 3
4. D.Option 4
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Answer: B
Q602022 · 9 Dec 2022 · Shift 2
If $k + \frac{1}{k} = 4$ , then what is the value of $k^{4} + \frac{1}{k ^{4}}$ ?
1. A.410
2. B.192
3. C.212
4. D.194
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Answer: D
Q682022 · 9 Dec 2022 · Shift 2
If 36 : 81 :: X : 63, what is the value of X?
1. A.30
2. B.31
3. C.28
4. D.29
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Answer: C
Q752022 · 9 Dec 2022 · Shift 2
If p + q = 6 and pq = 4, then what is the value of ?
1. A.512
2. B.144
3. C.288
4. D.432
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Answer: D
Q572022 · 9 Dec 2022 · Shift 3
If $p - \frac{1}{p} = 6$ , then what is the value of $p^{4} + \frac{1}{p ^{4}}$ ?
1. A.1562
2. B.1432
3. C.1442
4. D.1444
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Answer: C
Q582022 · 9 Dec 2022 · Shift 3
In a 7-digit number 89476*2, what is the smallest possible value of * such that the number is divisible by 8?
1. A.2
2. B.1
3. C.4
4. D.3
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Answer: D
Q602022 · 9 Dec 2022 · Shift 3
Simplify x4 - 15x3 + 15x2 - 15x + 40; given x = 14.
1. A.0
2. B.40
3. C.14
4. D.26
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Answer: D