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

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

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

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

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

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

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

The value of log₃ 11.log₁₁ 13.log₁₃ 15.log₁₅ 27.log₂₇ 81 is

Given \(|\frac{3}{x-4}|<1\) then ___________

The condition that the equation ax² + bx + c = 0 may have one root is the double the other is ___________

Classify each element of \(\left\{ \sqrt { 7 } ,\frac { -1 }{ 4 } ,0,3.14,4,\frac { 22 }{ 7 } \right\} \) as a member of N, Q, R, -Q or Z.

Construct a quadratic equation with roots 7 and -3

If the difference of the roots of the equation \(2{ x }^{ 2 }-\left( a+1 \right) x+a-1=0\) is equal to their product, then prove that a = 2.

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

If x²+ x + 1 is a factor of the polynomial 3x³+ 8x²+ 8x + a, then find the value of a.

Determine the region in the plane determined by the inequalities.
\(2x+3y\le 6,\ x+4y\le 4,\ x\ge 0,\ y\ge 0.\)

Determine the region in the plane determined by the inequalities.
\(2x+y\ge 8,\ \ x+2y\ge 8,\ \ x+y\le 6\)

Solve 3|x - 2| + 7 = 19 for x.

Our monthly electricity bill contains a basic charge, that is independent of units consumed and a charge that depends on the units consumed. Let us say Electricity board charges Rs. 110 as basic charge and charges Rs. 4 for each unit we use. If a person wants to keep his electricity bill below Rs. 250, then what should be his electricity usage?

If \(\alpha\) and \(\beta\) are the roots of the equation x² - 2x + 3 = 0 from the equation where roots are
(a) \(\frac{1}{\alpha}\) and \(\frac{1}{\beta}\)
(b) \(\alpha^2\) and \(\beta^2\)
(c)  \(\frac{1}{\alpha^2}\) and \(\frac{1}{\beta^2}\)

Simplify \(\left( 125 \right) ^{ \frac { 2 }{ 3 } }\)

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

Simplify and hence find the value of n: \(3^{2 n} 9^{2} 3^{-n} / 3^{3 n}=27\)

Solve for x  \(\left| 3-x \right| <7\)

Prove that ap + q = 0 if f(x) = x³ - 3px + 2q is divisible by g(x) = x² + 2ax + a².

Represent the following inequalities in the interval notation:
\(x\ge -1\) and \(x<4\)

Let b > 0 and b ≠ 1. Express y = b^x in logarithmic form. Also state the domain and range of the logarithmic function.

Resolve the following rational expressions into partial fractions.
\({{1}\over{x^2-a^2}}\)

Resolve the following rational expressions into partial fractions.
\({{{(x-1)}^{2}}\over{x^3+x}}\)