Algebra · SSC CGL previous year questions

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2022 129 questions

Q582022 · 13 Dec 2022 · Shift 1
Which of the following statement is correct? I. If x = 12, y = -2 and z = -10, then x3 + y3 + z3 = 360. II. If x + y = 48 and 4xy = 128, then 4x2 + 4y2 = 4480.
1. A.Neither I nor II
2. B.Only I
3. C.Both I and II
4. D.Only II
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Answer: A
Q622022 · 13 Dec 2022 · Shift 1
If $K + \frac{1}{K} + 2 = 0$ and K < 0, then what is the value of $K^{11} + \frac{1}{K ^{4}}$ ?
1. A.0
2. B.-2
3. C.-1
4. D.-17
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Answer: A
Q662022 · 13 Dec 2022 · Shift 1
If $x + \frac{1}{x} = 6$ , then find the value of $\frac{3 x}{2 x ^{2} - 5 x + 2}$ .
1. A.Option 1
2. B.Option 2
3. C.Option 3
4. D.Option 4
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Answer: B
Q512022 · 13 Dec 2022 · Shift 2
If a = 45° and b = 15°, what is the value of ?
1. A.2 - 2√2
2. B.3 - √6
3. C.3 - √2
4. D.2 - √3
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Answer: D
Q602022 · 13 Dec 2022 · Shift 2
If a - b = 8 and ab = 9, then the value of a + b is ________.
1. A.±9
2. B.±7
3. C.±8
4. D.±10
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Answer: D
Q672022 · 13 Dec 2022 · Shift 2
If 2p + q = 19 and 8p3 + q3 = 361, then find the value of pq.
1. A.56
2. B.59
3. C.58
4. D.57
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Answer: D
Q682022 · 13 Dec 2022 · Shift 2
Which of the following statement is correct? I. If x = 12, y = -2 and z = -10, then x3 + y3 + z3 = 720 II. If x + y = 48 and 4xy = 128, then s the value of 4x2 + 4y2 is 8960
1. A.Neither I nor II
2. B.Only I
3. C.Both I and II
4. D.Only II
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Answer: C
Q522022 · 13 Dec 2022 · Shift 3
If $sec θ + \frac{1}{c o s θ} = 2$ , find the value of $sec^{55} θ + \frac{1}{s e c ^{55} θ}$ .
1. A.2
2. B.0
3. C.1
4. D.55
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Answer: A
Q612022 · 13 Dec 2022 · Shift 3
If, $\frac{r}{13} + \frac{13}{r} = 1$ then the value of $r^{3}$ is:
1. A.-2157
2. B.2197
3. C.2157
4. D.-2197
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Answer: D
Q622022 · 13 Dec 2022 · Shift 3
If $\frac{a}{b} + \frac{b}{a} = - 1$ and a - b = 2, then the value of $a^{3} - b^{3}$ is:
1. A.Option 1
2. B.Option 2
3. C.Option 3
4. D.Option 4
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Answer: A
Q692022 · 13 Dec 2022 · Shift 3
If ΔABC ≅ ΔPQR and ∠ABC = (x + 60)°, ∠PQR = (85 - 4x)°, and ∠RPQ = (3x + 65)°, then the value of ∠ABC in degree is:
1. A.15
2. B.5
3. C.45
4. D.65
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Answer: D
Q752022 · 13 Dec 2022 · Shift 3
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.Both I and II
3. C.Only II
4. D.Only I
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Answer: D
Q562022 · 13 Dec 2022 · Shift 4
If the nine-digit number 3422213AB is divisible by 99, then what is the value of 2A + B?
1. A.11
2. B.12
3. C.10
4. D.13
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Answer: A
Q612022 · 13 Dec 2022 · Shift 4
In the given figure, ∠ABC = 81° and ∠ACB = 9°. What is the value of ∠BDC?
1. A.80°
2. B.90°
3. C.70°
4. D.60°
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Answer: B
Q622022 · 13 Dec 2022 · Shift 4
If x = 2 - + , then find the value of x3 - 6x2 + 18x.
1. A.40
2. B.33
3. C.45
4. D.22
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Answer: D
Q642022 · 13 Dec 2022 · Shift 4
If a + b + c = 5, a3+ b3 + c3 = 85 and abc = 25, then find the value of a2 + b2+ c2 - ab - bc - ca.
1. A.2
2. B.4
3. C.6
4. D.8
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Answer: A
Q672022 · 13 Dec 2022 · Shift 4
If a = -12, b = -6 and c = 18, then what is the value of (2abc)/9
1. A.554
2. B.288
3. C.-288
4. D.144
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Answer: B
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