List of practice Questions

Calculate the current flowing through two long parallel wires carrying equal currents and separated by a distance of 1.35 cm, experiencing a force per unit length of $ 4.76 \times 10^{-2} \, \text{N/m} $.

The ratio of wavelengths of proton and deuteron accelerated by potential $V_p$ and $V_d$ is $1: \sqrt{2}$ Then, the ratio of $V_p$ to $V_d$ will be

From the figure of column chromatography given below, identify incorrect statements

A. Compound 'c' is more polar than 'a' and 'b'
B. Compound 'a' is least polar
C. Compound 'b' comes out of the column before 'c' and after 'a'
D. Compound 'a' spends more time in the column
Choose the correct answer from the options given below

Compound A from the following reaction sequence is

Br2 , C S 2 0 − 5 ° C 0 − 5 ° 𝐶 → 𝐵 𝑟 2 , 𝐶 𝑆 2 B. N a N O 2 / H C l

Match List I with List II

Choose the correct answer from the options given below:

Let a tangent to the curve $y^2=24 x$ meet the curve $x y=2$ at the points $A$ and $B$ Then the mid points of such line segments $A B$ lie on a parabola with the

If $\int\limits_0^1\left(x^{21}+x^{14}+x^7\right)\left(2 x^{14}+3 x^7+6\right)^{1 / 7} d x=\frac{1}{l}(11)^{m / n}$ where $l, m, n \in N , m$ and $n$ are coprime then $l+m+n$ is equal to ______

If $m$ and $n$ respectively are the numbers of positive and negative values of $\theta$ in the interval $[-\pi, \pi]$ that satisfy the equation $\cos 2 \theta \cos \frac{\theta}{2}=\cos 3 \theta \cos \frac{99}{2}$, then $m n$ is equal to__

Two billiard balls of mass $005\, kg$ each moving in opposite directions with $10 \, ms ^{-1}$ collide and rebound with the same speed If the time duration of contact is $t =0005 \, s$, then what is the force exerted on the ball due to each other?

Major product of the following reaction is

Let $f(x)=\begin{cases}x^2 \sin \left(\frac{1}{x}\right) & , x \neq 0 \\ 0 & , x=0\end{cases}$Then at $x=0$

Match the terms in Column-I with their description in Column-II and choose the correct option:

Column I (Chemical reactions)		Column II (Enzymes used)
(i)	Glucose → CO₂+ Ethanol	a	Pepsin
(ii)	Sucrose→Glucose + Fructose	b	Diastase
(iii)	Starch →Maltose	c	Zymase
(iv)	Protein→Amino acids	d	Invertase

If f(x) = [a+13 sinx] & x ε (0, $\pi$), then number of non-differentiable points of f(x) are [where 'a' is integer]

A solid sphere and a ring have equal masses and equal radius of gyration. If the sphere is rotating about its diameter and ring about an axis passing through and perpendicular to its plane, then the ratio of radius is $\sqrt{\frac{x}{2} }$ then find the value of x.

The number of solutions of cos4θ – 2cos2θ + 3sin6θ + 1 = 0 in [0,2π] is

$96\cos\frac{π}{33}\cos \frac{2π}{33}\cos\frac{4π}{33}\cos\frac{8π}{33}\cos\frac{16π}{33}$ is equal to

For a periodic motion represented by the equation y = sin ωt + cos ωt, the amplitude of the motion is

The standard reduction potential at 298 K for the following half cells are given below
NO − 3 3 − + 4H+ + 3e- → NO(g) +2H2O E0 = 0.97V
$V^{2+} (aq) + 2e^-→V$ E⁰ = -1.19V
$Fe^{3+}(aq) + 3e^- → Fe$ E⁰= -0.04V
$Ag^+ (aq) + e^- → Ag(s)$ E⁰ = 0.80V
$Au^{3+}(aq)+3e^-→Au(s)$ E⁰= 1.40V
The number of metal(s) which will be oxidized by $N0^-_3$ Oin aqueous solution is______.

A solid sphere is rolling on a horizontal plane without slipping. If the ratio of angular momentum about axis of rotation of the sphere to the total energy of moving sphere is π : 22 then, the value of its angular speed will be ______ rad/s.

Let $H$ be the hyperbola, whose foci are $(1 \pm \sqrt{2}, 0)$ and eccentricity is $\sqrt{2}$. Then the length of its latus rectum is _____

The wave function $(\Psi)$ of $2 s$ is given by $\Psi_{2 n }=\frac{1}{2 \sqrt{2 \pi}}\left(\frac{1}{a_0}\right)^{1 / 2}\left(2-\frac{r}{a_0}\right) e^{-\frac{r}{2 a_0}}$ At $r=r_0$, radial node is formed Thus, $r_0$ in terms of $a_0$

Consider the lines $L_1$ and $L_2$ given by
$L_1: \frac{x-1}{2}=\frac{y-3}{1}=\frac{z-2}{2} $
$L_2: \frac{x-2}{1}=\frac{y-2}{2}=\frac{z-3}{3} $
A line $L_3$ having direction ratios $1,-1,-2$, intersects $L_1$ and $L_2$ at the points $P$ and $Q$ respectively Then the length of line segment $P Q$ is