Algebra · SSC CGL previous year questions

If (a + b + c) = 16, and (a2 + b2 + c2) = 90, find the value of (ab + bc + ca).

1. A.84
2. B.83
3. C.82
4. D.81

What is the value of 64x3 + 38x2y + 20xy2 + y3, when x = 3 and y = - 4?

1. A.1236
2. B.488
3. C.536
4. D.1256

What is the value of a3 + b3 + c3 if (a + b + c) = 0?

1. A.a2 + b2 + c2 - 3 abc
2. B.0
3. C.3 abc
4. D.a2 + b2 + c2 - ab - bc - ca days days days days

Find the simplified value of the given expression. $4\frac{4}{5}÷\frac{3}{5}$ of $5+\frac{4}{5}\times \frac{3}{10}-\frac{1}{5}$

1. A.Option 1
2. B.Option 2
3. C.Option 3
4. D.Option 4

If $x+\frac{1}{x}=7$, then the value of $x^6+\frac{1}{x^6}$ is:

1. A.113682
2. B.103682
3. C.103882
4. D.103862

If x > 0, and , what is the value of ?

1. A.717√2
2. B.723√2
3. C.720√2
4. D.726√2

If Δ XYZ ≅ Δ LMR, then m + x + p = ____________.

1. A.7
2. B.6
3. C.9
4. D.13

If a = 17,b = 13, then find the value of the expression (a3 - b3 - 3a2b + 3ab2).

1. A.-64
2. B.-27000
3. C.27000
4. D.64

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

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

If $x+\frac{1}{x}=6$, then find the value of $\frac{3x}{2x^2-5x+2}$.

1. A.Option 1
2. B.Option 2
3. C.Option 3
4. D.Option 4

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

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

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

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

If $\sec \theta +\frac{1}{\cos \theta }=2$, find the value of ${\sec }^{55}\theta +\frac{1}{{\sec }^{55}\theta }$.

1. A.2
2. B.0
3. C.1
4. D.55

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

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

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

Which of the following statement is correct? I. The value of $100^2-99^2+98^2-97^2+96^2-95^2+94^2-93^2+\dots +22^2-21^2$ is 4840. II. The value of $\left(k^2+\frac{1}{k^2}\right)\left(k-\frac{1}{k}\right)\left(k^4+\frac{1}{k^4}\right)\left(k+\frac{1}{k}\right)\left(k^4-\frac{1}{k^4}\right)$ 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

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

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°

If x = 2 - + , then find the value of x3 - 6x2 + 18x.

1. A.40
2. B.33
3. C.45
4. D.22

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

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