List of practice Questions

Statements about heavy water are given below A. Heavy water is used in exchange reactions for the study of reaction mechanisms B. Heavy water is prepared by exhaustive electrolysis of water C. Heavy water has higher boiling point than ordinary water D. Viscosity of $H _{2} O$ is greater than $D _{2} O$

Calgon is used for water treatment. Which of the following statement is $NOT$ true about Calgon?

Given below are two statements : Two photons having equal linear momenta have equal wavelengths. If the wavelength of photon is decreased, then the momentum and energy of a photon will also decrease. In the light of the above statements, choose the correct answer from the options given below.

In Freundlich adsorption isotherm, slope of AB line is :

In the given figure, a mass \(M\) is attached to a horizontal spring which is fixed on one side to a rigid support. The spring constant of the spring is \(k\). The mass oscillates on a frictionless surface with the time period \(T\) and amplitude \(A\). When the mass is in an equilibrium position, as shown in the figure, another mass \(m\) is gently fixed upon it. The new amplitude of oscillation will be : 

The correct order of bond dissociation enthalpy of halogens is :

Which of the following are isostructural pairs? A. $SO _{4}^{2-}$ and $CrO _{4}^{2-}$ B. $SiCl _{4}$ and $TiCl _{4}$ C. $NH _{3}$ and $NO _{3}^{-}$ D. $BCl _{3}$ and $BrCl _{3}$ $BCl _{3}$ and $BrCl _{3}$

Two wires of same length and radius are joined end to end and loaded. The Young's moduli of the materials of the two wires are $Y_1$ and $Y_2$. The combination behaves as a single wire then its Young's modulus is :

The negative of the statement $\sim p \wedge( p \vee q )$ is

What is the major product formed by $HI$ on reaction with

According to molecular theory, the species among the following that does not exist is:

If the velocity-time graph has the shape AMB, what would be the shape of the corresponding acceleration-time graph ?

A possible value of $\tan \left(\frac{1}{4} \sin ^{-1} \frac{\sqrt{63}}{8}\right)$ is :

The vector equation of the plane passing through the intersection of the planes $\vec{ r } .(\hat{ i }+\hat{ j }+\hat{ k })=1$ and $\vec{ r } .(\hat{ i }-2 \hat{ j })=-2,$ and the point (1,0,2) is :

The angle of elevation of a jet plane from a point A on the ground is $60^{\circ}$. After a flight of 20 seconds at the speed of $432 km /$ hour, the angle of elevation changes to $30^{\circ} .$ If the jet plane is flying at a constant height, then its height is :

Let $f: R \rightarrow R$ be defined as, $f(x) = \begin{cases} -55x, & \text{if } x < -5 \\ 2x^3 -3x^2 -120x, & \text{if } 5 \le x \le 4 \\ 2x^3 -3x^2-36x-336& \text{if } x > 4, \end{cases} $ Let $A=\{ x \in R : f$ is increasing $\} .$ Then $A$ is equal to

Let $R =\{( P , Q ) | P$ and $Q$ are at the same distance from the origin $\}$ be a relation, then the equivalence class of (1,-1) is the set:

The period of oscillation of a simple pendulum is $T =2 \pi \sqrt{\frac{ L }{ g }}$. Measured value of 'L' is $1.0 m$ from meter scale having a minimum division of $1 mm$ and time of one complete oscillation is 1.95 s measured from stopwatch of $0.01 s$ resolution. The percentage error in the determination of 'g' will be :

The pitch of the screw gauge is $1 mm$ and there are $100$ divisions on the circular scale. When nothing is put in between the jaws, the zero of the circular scale lies $ 8$ divisions below the reference line. When a wire is placed between the jaws, the first linear scale division is clearly visible while $72^{\text {nd }}$ division on circular scale coincides with the reference line. The radius of the wire is

The value of $-{ }^{15} C _{1}+2 .{ }^{15} C _{2}-3 .{ }^{15} C _{3}+\ldots $ $-15 .{ }^{15} C _{15}+{ }^{14} C _{1}+{ }^{14} C _{3}+{ }^{14} C _{5}+\ldots .+{ }^{14} C _{11}$ is

If $P$ is a point on the parabola $y=x^{2}+4$ which is closest to the straight line $y =4 x -1$, then the co-ordinates of $P$ are

If $n \geq 2$ is a positive integer, then the sum of the series ${ }^{n+1} C_{2}+2\left({ }^{2} C_{2}+{ }^{3} C_{2}+{ }^{4} C_{2}+\ldots .+{ }^{n} C_{2}\right)$ is:

Let $f$ be a twice differentiable function defined on $R$ such that $f (0)=1, f'(0)=2$ and $f'(x)\neq 0$ for all $x \in R$. If $\left|\begin{array}{cc}f(x) & f'(x) \\ f'(x) & f''(x)\end{array}\right|=0,$ for all $x \in R,$ then the value of $f (1)$ lies in the interval:

The value of the integral, \[ \int_{1}^{3} \left[ x^{2} - 2x - 2 \right] \, dx, \] where \( [x] \) denotes the greatest integer less than or equal to \( x \), is:

If the curve $y=a x^{2}+b x+c, x \in R,$ passes through the point (1,2) and the tangent line to this curve at origin is $y = x ,$ then the possible values of $a , b , c$ are :