List of practice Questions

If $\frac{1}{\sqrt{\alpha}}$ and $\frac{1}{\sqrt{\beta}}$ are the roots of the equation, $ax^{2} + bx +1 = 0 \left(a ^{ }\ne 0, a, b \in R\right)$, then the equation, $x\left(x + b^{3}\right) + \left(a^{3} ? 3abx\right)$ = 0 has roots :
If $ 1 + x^4 + x^5 = \sum\limits^{5}_{i =0} a_i$ $(1 + x)^i$ , for all $x$ in $R$, then $a_2$ is:
If a line intercepted between the coordinate axes is trisected at a point $A(4, 3)$, which is nearer to $x$-axis, then its equation is :
If $\lambda_{0}$ and $\lambda$ be the threshold wavelength and wavelength of incident light, the velocity of photoelectron ejected from the metal surface is :
If \[ \begin{vmatrix} p & q - y & r - z \\ p - x & q & r - z \\ p - x & q - y & r \end{vmatrix} = 0, \] then the value of \(\dfrac{p}{x} + \dfrac{q}{y} + \dfrac{r}{z}\) is
Let \( f:\mathbb{R} \to \mathbb{R} \) be a function defined by \( f(x) = \dfrac{x - m}{x - n} \), where \( m \neq n \). Then
If \(\begin{bmatrix} \alpha & \beta \\ \gamma & -\alpha \end{bmatrix}\) is a square root of identity matrix of order 2, then
Let \[ f(x)= \begin{cases} (x-1)\sin\!\left(\dfrac{1}{x-1}\right), & x \neq 1 \\ 0, & x = 1 \end{cases} \] Then which one of the following is true?
The coefficient of \(x^4\) in the expansion of \((1 + x + x^2 + x^3)^{11}\) is:
If the \((2p)^{\text{th}}\) term of a H.P. is \(q\) and the \((2q)^{\text{th}}\) term is \(p\), then the \(2(p+q)^{\text{th}}\) term is:
\(\displaystyle \lim_{x \to 0} \left(\csc x\right)^{\frac{1}{\log x}}\) is equal to:
Let \( R = \{(3,3), (6,6), (9,9), (12,12), (6,12), (3,9), (3,12), (3,6)\} \) be a relation on the set \( A = \{3,6,9,12\} \). Then, the relation is:
In a face centered cubic lattice atoms $A$ are at the corner points and atoms $B$ at the face centered points. If atom $B$ is missing from one of the face centered points, the formula of the ionic compound is :
In a large building, there are 15 bulbs of 40\, W, 5 bulbs of 100 W, 5 fans of $80\, W$ and 1 heater of $1\, kW$. The voltage of the electric mains is $220 \,V$. The minimum capacity of the main fuse of the building will be :
In a monoclinic unit cell, the relation of sides and angles are respectively :
In materials like aluminium and copper, the correct order of magnitude of various elastic modulii is :
In S$_N$2 reactions, the correct order of reactivity for the following compounds $CH_3Cl,CH_3CH_2Cl, (CH_3 )_2CHCl$ and (CH$_3 )_3CCl$ is
In the circuit shown, current (in A) through the 50 V and 30 V batteries are, respectively :
In the presence of peroxide, $HCl$ and $HI$ do not give anti-Markownikoff' s addition to alkenes because :
In the Victor-Meyer's test, the colour given by $1^{\circ}$, $2^{\circ}$and $3^{\circ}$ alcohols are respectively :
Let $f\left(n\right) = \left[\frac{1}{3} + \frac{3n}{100}\right]{n},$ where $\left[n\right]$ denotes the greatest integer less than or equal to n. Then $\sum\limits^{56}_{n = 1} \Delta_{r} f\left(n\right)$ is equal to :
Let $z\ne-i$ be any complex number such that $\frac{z-i}{z+i}$ is a purely imaginary number. Then $z+\frac{1}{z}$ is :
The conjugate base of hydrazoic acid is :
The correct order of bond dissociation energy among $N_2, O_2, O_2^-$ is shown in which of the following arrangements ?
The integral $\int x \,cos^{-1}\left(\frac{1-x^{2}}{1+x^{2}}\right) \,dx\, \left(x > 0\right)$ is equal to :