List of practice Questions

A long conducting wire carrying a current $I$ is bent at $120^{\circ}$ (see figure). The magnetic field $B$ at a point $P$ on the right bisector of bending angle at a distance d from the bend is $\left(\mu_{0}\right.$ is the permeability of free space)

Let $S$ denote the sum of the infinite series $1+\frac{8}{2!}+\frac{21}{3!}+\frac{40}{4!}+\frac{65}{5!} ....... $. Then

The condition for the lines $l x+m y+n=0$ and $l_{1} x+m_{1} y+n_{1}=0$ to be conjugate with respect to the circle $x^{2}+y^{2}=r^{2}$, is

The fact that transverse property of a wave can be easily explained by

One mole of an ideal monoatomic gas is heated at a constant pressure from $0^{\circ} C$ to $100^{\circ} C$. Then the change in the internal energy of the gas is (Given $R=8.32 \,J\,mol ^{-1} \,K ^{-1}$ )

The compound that reacts the fastest with sodium methoxide is

In garden pea, round shape of seeds is dominant over wrinkled shape. A pea plant heterozygous for round shape of seed is selfed and 1600 seeds produced during the cross are subsequently germinated. How many seedlings would have the parental phenotype ?

The slopes of the focal chords of the parabola $y^{2}=32 x$, which are tangents to the circle $x^{2}+y^{2}=4$, are

A child is standing with folded hands at the centre of a platform rotating about its central axis. The kinetic energy of the system is $K$. The child now stretches his arms so that the moment of inertia of the system doubled. The kinetic energy of the system now is

$50\,cm^3$ of $0.04 \,M \,K_2 Cr_2 O_7$ in acidic medium oxidizes a sample of $H_2S$ gas to sulphur. Volume of $0.03\, M$ $KMnO_4$ required to oxidize the same amount of $H_2S$ gas to sulphur, in acidic medium is

The IUPAC name of the complex ion formed when gold dissolves in aquaregia is

Wires $ A $ and $ B $ have resistivities $ \rho_{A} $ and $ \rho_{B} $ , $ (\rho_{B}=2\rho_{A}) $ and have lengths $ l_{A} $ and $ l_{B} $ . If the diameter of the wire $ B $ is twice that of $ A $ and the two wires have same resistance, then $ \frac{l_{B}}{l_{4}} $ is

The point at which the circles $x^{2}+y^{2}-4 x-4 y+7=0 $ and $x^{2}+y^{2}-12 x -10 y+45=0$ touch each other, is

A system consists of three masses \(m_1\), \(m_2\) and \(m_3\) connected by a string passing over a pulley \(P\). The mass \(m_1\) hangs freely and \(m_2\) and \(m_3\) are on a rough horizontal table (the coefficient of friction = \(\mu\)). The pulley is frictionless and of negligible mass. The downward acceleration of mass \(m_1\) is (Assume \(m_1 = m_2 = m_3 = m\))

A car moves from $A$ to $B$ with a speed of $30 \,kmph$ and from $B$ to $A$ with a speed of $20\,kmph$. What is the average speed of the car ?

Coefficient of $ x^{11}$ in the expansion of $(1 + x^2)^4 (1 + x^3)^7 (1 + x^4)^{12} $

If $ x, y $ and $ z $ are all different and $ \begin{vmatrix}x&x^{2}&1+x^{3}\\ y&y^{2}&1+y^{3}\\ z&z^{2}&1+z^{3}\end{vmatrix}=0 $ then

Let the straight line $ x = b $ divide the area enclosed by $ y = (1 - x)^2 $ , $ y = 0 $ and $ x = 0 $ into two parts $ R_1(0 \le x \le b) $ and $ R_2(b \le x \le 1) $ such that $ R_1-R_2 = \frac {1}{4}. $ Then, $b$ equals

If \(\alpha, \beta\) are the roots of the quadratic equation \(x^2 + px + q = 0\), then the values of \(\alpha^{3}, \beta^{3}\) and \(\alpha^{4}+\alpha^{2}\beta^{3}+\beta^{4}\) are respectively

Which of these is an excitatory neurotransmitter in brain?

The component of bacteria that retains the crystal violet stain during Gram-staining is

Which of the following organs does not produce any digestive enzymes?

How many ATP are produced when one molecule of $FADH_2$ is oxidized to $FAD$ through Electron Transport System?

If $ \alpha,\beta $ are the roots of the equation $ ax^2+bx+c = 0 $ and $ S_n = \alpha^n + \beta^n, $ then a $ S_{n+1} + bS_{n} + cS_{n-1} $ is equal to