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

(a)

\([2,\infty]\)

(b)

\((2,\infty )\)

(c)

\((-\infty,2)\)

(d)

\((-2,\infty )\)

The solution 5x-1<24 and 5x+1 > -24 is

(a)

(4,5)

(b)

(-5,-4)

(c)

(-5,5)

(d)

(-5,4)

The solution set of the following inequality |x-1| \(\ge\) |x-3| is

(a)

[0, 2]

(b)

\([2,\infty)\)

(c)

(0, 2)

(d)

\((-\infty,2)\)

The value of \({ log }_{ \sqrt { 2 } }512\) is

(a)

16

(b)

18

(c)

9

(d)

12

The value of \({ log }_{ 3 }\frac { 1 }{ 81 } \) is

(a)

-2

(b)

-8

(c)

-4

(d)

-9

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

(a)

0

(b)

2

(c)

3

(d)

4

Are there two distinct irrational numbers such that their difference is a rational number? Justify.

Find two irrational numbers such that their sum is a rational number. Can you find two irrational numbers whose product is a rational number

A quadratic polynomial has one of its zeros as \(1+\sqrt { 5 } \) and it satisfies p(1) = 2. Find the quadratic polynomial.

Find the condition that one of the roots of ax²+ bx + c may be negative of the other.

Determine the region in the Plane determined by the inequalities \(y\ge 2x,\ -2x+3y\le 6\)

Given log₂¹⁶ = 4. Find log₁₆²

If a³+ b³= ab(8 - 3a - 3b), show that log \(\left( \frac { a+b }{ 2 } \right) =\frac { 1 }{ 3 } \)  (log a + log b)

If a and b are both rational numbers, find the values of a and b if \(\frac { 3+\sqrt { 7 } }{ 3-\sqrt { 7 } } =a+b\sqrt { 7 } \)

Simplify the rational expression : \(\frac { { y }^{ 2 }-15y-34 }{ { 3y }^{ 2 }-12 } \)

Simplify \((-1000)^{ \frac { -2 }{ 3 } }\)

Simplify \(\left( 3^{ -6 } \right) ^{ \frac { 1 }{ 3 } }\)

Simplify \(\frac { 1 }{ 3-\sqrt { 8 } } -\frac { 1 }{ \sqrt { 8 } -\sqrt { 7 } } +\frac { 1 }{ \sqrt { 7 } -\sqrt { 6 } } -\frac { 1 }{ \sqrt { 6 } -\sqrt { 5 } } +\frac { 1 }{ \sqrt { 5 } -2 } \)

If x=\(\sqrt { 2 } +\sqrt { 3 } \)  find \(\frac { { x }^{ 2 }+1 }{ { x }^{ 2 }-2 } \)

Solve : \({{2x+5}\over{x-1}}>5\)

The largest side of a triangle is 3 times the shortest side and the third side is 2 cm shorter than the longest side. If the perimeter of the triangle is atleast 61 cm, find the minimum length of the shortest side?