If |x+2| \(\le\) 9, then x belongs to

(a)

\((-\infty ,-7)\)

(b)

[-11, 7]

(c)

\((-\infty ,-7)\cup (11,\infty)\)

(d)

(-11, 7)

If \(\frac { |x-2| }{ x-2 } \ge 0\), then x belongs to

(a)

\([2,\infty]\)

(b)

\((2,\infty )\)

(c)

\((-\infty,2)\)

(d)

\((-2,\infty )\)

If \({ log }_{ \sqrt { x } }\) 0.25 = 4, then the value of x is

(a)

0.5

(b)

2.5

(c)

1.5

(d)

1.25

The value of log_a b log_b c log_c a is

(a)

2

(b)

1

(c)

3

(d)

4

If 3 is the logarithm of 343, then the base is

(a)

5

(b)

7

(c)

6

(d)

9

Find a so that the sum and product of the roots of the equation 2x²+ (a - 3) x + 3a - 5 = 0 are equal is

(a)

1

(b)

2

(c)

0

(d)

4

If a and b are the roots of the equation x²- kx + 16 = 0 and a²+ b² = 32, then the value of k is

(a)

10

(b)

-8

(c)

-8, 8

(d)

6

The number of solution of x² + |x - 1| = 1 is

(a)

1

(b)

0

(c)

2

(d)

3

The equation whose roots are numerically equal but opposite in sign to the roots 3x²- 5x -7 = 0 is

(a)

3x²- 5x - 7 = 0

(b)

3x²+ 5x - 7 = 0

(c)

3x²- 5x + 7 = 0

(d)

3x² + x - 7

If 8 and 2 are the roots of x²+ ax + c = 0 and 3, 3 are the roots of x² + dx + b = 0; then the roots of the equation x²+ ax + b = 0 are

(a)

1, 2

(b)

-1, 1

(c)

9, 1

(d)

-1, 2

The number of roots of (x + 3)⁴+ (x + 5)⁴ = 16 is

(a)

4

(b)

2

(c)

3

(d)

0

If x < 7, then ___________

(a)

-x < -7

(b)

- x ≤ -7

(c)

-x > -7

(d)

-x ≥ -7

If - 3x + 17 < -13 then ___________

(a)

x ∈ (10, ∞)

(b)

x ∈ [10, ∞)

(c)

x ∈ (-∞, 10]

(d)

x ∈ [10, 10)

If x is a real number and |x| < 5 then ___________

(a)

x ≥ 5

(b)

-5 < x < 5

(c)

x ≤ -5

(d)

-5 ≤ x ≤ 5

If |x + 3| ≥ 10 then ___________

(a)

x ∊ (-13, 7]

(b)

x ∊ [-13, 7)

(c)

x ∊ (-∞, -13] \(\cup\) [7, ∞)

(d)

x ∊ (-∞, -13] \(\cup\) [7, ∞)

\(\sqrt [ 4 ]{ 11 } \) is equal to ___________

(a)

\(\sqrt [ 8 ]{ 11^{ 2 } } \)

(b)

\(\sqrt [ 8 ]{ 11^{ 4 } } \)

(c)

\(\sqrt [ 8 ]{ 11^{ 8 } } \)

(d)

\(\sqrt [ 8 ]{ 11^{ 6 } } \)

The rationalising factor of \(\frac { 5 }{ \sqrt [ 3 ]{ 3 } } \) is

(a)

\(\sqrt [ 3 ]{ 6 } \)

(b)

\(\sqrt [ 3 ]{ 3 } \)

(c)

\(\sqrt [ 3 ]{ 9 } \)

(d)

\(\sqrt [ 3 ]{ 27 } \)

\((\sqrt { 5 } -2)(\sqrt { 5 } +2)\) is equal to ___________

(a)

1

(b)

3

(c)

23

(d)

21

The number of real solution of |2x - x²- 3| = 1 is ___________

(a)

0

(b)

2

(c)

3

(d)

4

If x is real and k = \(\frac { { x }^{ 2 }-x+1 }{ { x }^{ 2 }+x+1 } \) then ___________

(a)

\(k\epsilon \left[ \frac { 1 }{ 3 } ,3 \right] \)

(b)

k ≥ 3

(c)

\(k\le \frac { 1 }{ 3 } \)

(d)

none of these

If the roots of x²-bx + c = 0 are two consecutive integer,then b²- 4c is ___________

(a)

0

(b)

1

(c)

2

(d)

none of these

The logarithmic form of 5² = 25 is ___________

(a)

\({ log }_{ 5 }^{ 2 }=25\)

(b)

\({ log }_{ 2 }^{ 5 }=25\)

(c)

\({ log }_{ 2 }^{ 25 }=2\)

(d)

\({ log }_{ 25 }^{ 5 }=2\)

The Value of \({ log }_{ 3/4 }^{ (4/3) }\) is ___________

(a)

-2

(b)

1

(c)

2

(d)

-1

The value of log₁₀⁸ + log₁₀⁵- log₁₀⁴ = ___________

(a)

\({ log }_{ 10 }^{ 9 }\)

(b)

\({ log }_{ 10 }^{ 36 }\)

(c)

1

(d)

-1

(x²-2x+2)(x²+2x+2) are the factors of the polynomial ___________

(a)

(x²-2x)²

(b)

x⁴-4

(c)

x⁴+4

(d)

(x²-2x+2)²