List of practice Questions

If the extremities of the base of an isosceles triangle are the points $(2a, 0)$ and $(0, a)$ and the equation of one of the sides is $x = 2a$, then the area of the triangle, in square units, is :

If the integral $\int \frac{cos 8x+1}{cot 2x-tan 2x} dx=A cos 8x+k,$ where $k$ is an arbitrary constant, then $A$ is equal to:

If the surface area of a sphere of radius $r$ is increasing uniformly at the rate $8\, cm^2/s$, then the rate of change of its volume is :

If the three lines $x - 3y = p, \,ax + 2y = q$ and $ax + y = r$ form a right-angled triangle then :

If the time period $t$ of the oscillation of a drop of liquid of density $d$, radius $r$, vibrating under surface tension $s$ is given by the formula $t=\sqrt{r^{2b}s^{c}d^{a/2}}.$ It is observed that the time period is directly proportional to $\sqrt{\frac{d}{s}}.$ The value of $b$ should therefore be :

If the x-intercept of some line $L$ is double as that of the line, $3x+4y = 12$ and the $y$-intercept of $L$, is half as that of the same line, then the slope of $L$ is:

If $\vec{a}$ and $\vec{b}$ are non-collinear vectors, then the value of a for which the vectors $\vec{u}=\left(\alpha-2\right)\vec{a}+\vec{b}$ and $\vec{v}=\left(2+3\alpha\right)\vec{a}-3\vec{b}$ are collinear is :

In a face centred cubic lattice, atoms of $A$ form the comer points and atoms of $B$ form the face centred points. If two atoms of $A$ are missing from the comer points, the formula of the ionic compound is :

In a hydrogen like atom electron makes transition from an energy level with quantum number $n$ to another with quantum number $(n - 1). If n > > 1$, the frequency of radiation emitted is proportional to

In a metre bridge experiment null point is obtained at $40\, cm$ from one end of the wire when resistance $X$ is balanced against another resistance $Y$. If $X < Y$, then the new position of the null point from the same end, if one decides to balance a resistance of $3X$ against $Y$, will be close to:

In an experiment, a small steel ball falls through a liquid at a constant speed of $10\, cm/s$. If the steel ball is pulled upward with a force equal to twice its effective weight, how fast will it move upward ?

In Goldschmidt aluminothermic process which of the following reducing agents is used:

In nucleophilic substitution reaction, order of halogens as incoming (attacking) nucleophile is: $I^- > \, Br^{-} > \, Cl^-$ The order of halogens as departing nucleophile should be:

In reaction $A + 2B {\rightleftharpoons} 2C + D$, initial concentration of $B$ was $1.5$ times of $[A]$, but at equilibrium the concentrations of $A$ and $B$ became equal. The equilibrium constant for the reaction is :

Let $a_1, a_2, a_3,...$ be an $A.P$, such that $\frac{a_{1}+a_{2}+\ldots+a_{p}}{a_{1}+a_{2}+a_{3}+\ldots+a_{q}} = \frac{p^{3}}{q^{3}} ; p\ne q$ Then $\frac{a_{6}}{a_{21}}$ is equal to:

Let $A (-3,2)$ and $B (-2,1)$ be the vertices of a triangle $ABC$. If the centroid of this triangle lies on the line $3x + 4y+2 = 0$, then the vertex $C$ lies on the line :

Let $a=Im\left(\frac{1+z^{2}}{2iz}\right),$ where $z$ is any non-zero complex number. The set $A=\left\{a:\left|z\right|=1\,and\,z\ne\pm1\right\}$ is equal to:

Let $R=\left\{ \left(3,3\right) \left(5,5\right), \left(9,9\right), \left(12,12\right), \left(5,12\right), \left(3,9\right), \left(3,12\right), \left(3,5\right)\right\}$ be a relation on the set $A=\left\{3,5,9,12\right\}$. Then, $R$ is:

Let $x \in \left(0,1\right).$ The set of all x such that $sin^{-1} x >\, cos^{-1} x, $ is the interval:

Light is incident from a medium into air at two possible angles of incidence $(A) 20^{\circ}$ and $(B) 40^{\circ}$. In the medium light travels $3.0 \,cm$ in $0.2\, ns$. The ray will :

Rate of dehydration of alcohols follows the order:

Solid $Ba(NO_3)_2$ is gradually dissolved in a $1.0 \times 10^{-4}$ M $Na_2CO_3$ solution. At which concentration of $Ba^{2+}$, precipitate of $BaCO_3$ begins to form ? ($K_{sp}$ for $BaCO_3 = 5.1 \times 10^{-9}$)

Stability of the species $ Li_2 , Li_2^- , \, \, and \, \, Li_2^+ $ increases in the order of

The equation $x log x = 2 - x$ is satisfied by at least one value of $x$ lying between $1$ and $2$. The function $f(x) = x log x$ is an increasing function in $[1,2]$ and $g (x)=2-x$ is a decreasing function in $[1, 2]$ and the graphs represented by these functions intersect at a point in $[1,2]$