List of practice Questions

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 \((\displaystyle\int_0^axdx)\le(a+4)\), then

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

Carbocation intermediate is involved in reactions,

The mechanism involved in the preparation of glycol from 1,2-dihaloethane using aqueous Na₂CO₃ is

The product formed in the reaction \(\text{C}_6\text{H}_5\text{-C}\equiv\text{C-CH}_3\frac{\text{HgSO}_4/\text{H}_2\text{SO}_4}{85^\circ\text{C}}\)