List of practice Questions

The line 4x+6y+9=0 touches y²=4x at the point

The circles x² + y² - 4x - 6y - 12 = 0 and x² + y² + 6x - 8y + 21 = 0

ABCD is a square A = (1,2), B = (3,-4). If line CD passes through (3,8) then midpoint of CD is

The eccentricity of a circle e is

\(\frac{1}{2.5}+\frac{1}{5.8}+\frac{1}{8.11}+...+\frac{1}{(3n-1)(3n+2)}\) is equal to

How many positive integers n can be formed using the digits 3,4,4,5,5,6,7, if n has to exceed 50,00,000?

Let \(f:R\rightarrow R\) be defined by \(f(x) = \begin{cases} k-2x,x\le-1\\ 2x+3,x\gt-1   \end{cases}\). If f(x) has a local minimum at x=- 1, then a possible value of k is

\(lt_{x\rightarrow\infin}(\frac{x^2+5x+3}{x^2+x+3})^{\frac{1}{3}}\) is

Find \(Lt_{x\rightarrow\infin}(\frac{x}{2+x})^{2x}\)

A missile fired from ground level rises x metres vertically upwards in 't' seconds and x = t( 100-12.5t). Then the maximum height reached by the missile is

If \(f(x) = \begin{cases}  1 + x & \text{if } 0 \leq x \leq 2 \\ 3 - x & \text{if } 2 < x \leq 3  \end{cases}\) , then \(f[f(x)]\) is

The points representing the complex numbers Z for which |Z + 4|² - |Z - 4|² = 8 lie on

If \(i=\sqrt{-1}\), then \(4+5(\frac{-1}{2}+\frac{i\sqrt3}{2})^{334}+3(\frac{-1}{2}+\frac{i\sqrt3}{2})^{265}\) is equal to

Number of integral values of x satisfying x² - 4x - 21 > 0 and x² - 9x + 8 < 0 is

If A is a non-singular matrix such that AA^T = A^TA and B = A^-1A^T , then matrix B is

If A+B=\(\begin{pmatrix} 2&-4 \\4&0 \end{pmatrix}\) and 3B=\(\begin{pmatrix}  -9&6 \\3&12 \end{pmatrix}\) then A+4B is

If I is the unit matrix of order n, where K≠0 is a constant, then adj(KI) =

If \(\Delta_1=\begin{vmatrix} x&b&b \\a&x&b\\a&a&x\end{vmatrix}\) and \(\Delta_2=\begin{vmatrix} x&b \\a&x\end{vmatrix}\), then \(\frac{d}{dx}(\Delta_1)\) is equal to

Which product is formed, when acetonitrile is hydrolysed partially with cold concentrated HCl

Which among the following cannot react with nitrous acid?

Which of the following statements about addition polymers is correct?

Each unit of DNA has

The values of is

If two sides of a triangle are the roots of the equation \(4x^2 - (2\sqrt{6})x + 1 = 0\) and the included angle is 60⁰ , then the third side is

The green flame of organic compound in Beilstein's test indicates presence of