List of practice Questions

The probability that the same number appear on throwing three dice simultaneously, is

The solution of the differential equation $\frac{d y}{d x}+\frac{2 y x}{1+x^{2}}=\frac{1}{1+x^{22}}$ is

If a=\(\log _{2} 3, b=\log _{2} 5, c=\log _{7} 2,\) then \(\log _{140} 63\) in terms of a, b, c is

If $(\cos \theta+i \sin \theta)(\cos 2 \theta+i \sin 2 \theta) \ldots . .(\cos n \theta+i \sin n \theta)=1$, then the value of $\theta$ is, $m \in N$

The length of the common chord of the ellipse $\frac{(x+1)^{2}}{9}+\frac{(y-2)^{2}}{4}=1$ and the circle $x-1^{2}+y-2^{2}=1$ is

For the hyperbola $\frac{x^{2}}{\cos ^{2} \alpha}-\frac{y^{2}}{\sin ^{2} \alpha}=1$, which of the following remains constant when $\alpha$ varies

$(x -1) (x^2 - 5x + 7) < (x -,1),$ then $x$ belongs to

If $\sin^{-1} \, x + \sin^{-1} \, y = \frac{\pi}{2},$ then $\frac{dy}{dx} $ is equal to

In the below reaction $x$ is.

The relative humidity on a day when partial pressure of water vapour is $0.012 \times 10^{5} Pa$ at $12^{\circ} C$ is (Take vapour pressure of water at this temperature as $0.016 \times 10^{5}Pa)$

Alizarin belongs to the class of

There are two planets. The ratio of radius of the two planets is $k$ but ratio of acceleration due to gravity of both planets is g. What will be the ratio of their escape velocity?

In the absence of intermolecular forces of attraction, the observed pressure $P$ will be

A rod of a certain metal is $1.0\, m$ long and $0.6\, cm$ in diameter. Its resistance is $ 3.0 \times 10^3\, \Omega$ Another disc made of the same metal is $2.0\, cm$ in diameter and $1.0\, mm$ thick. What is the resistance between the round faces of the disc?

An electric line of force in the $xy$ plane is given by equation $x^2 + y^2 = 1$. A particle with unit positive charge, initially at rest at the point $x = 1, y = 0$ in the $xy$ plane

In the relation $P =\frac{a}{\beta} e ^{-\frac{a z}{ k \theta}}, p$ is the pressure, $z$ the distance, $k$ is Boltzmann constant and $\theta$ is the temperature, the dimensional formula of $\beta$ will be

The extension in a string obeying Hooke's law $v$ is $x$. The speed of sound in the stretched string is $v$. If the extension in the string is increased to $1.5\, x$, the speed of sound will be

Two springs have their force constant as $k_1$ and $k_2 (k_1 > k_2)$. when they are stretched by the same force

In the following sentence choose the erroneous segment.
A                   B                       C
\(\text{\underline{We took a taxi so we would be on time for the meeting}}\)

When radiation is incident on a photoelectron emitter, the stopping potential is found to be $9V$. If elm for the electron is $1.8 \times 10^{11} \, C \, kg^{-1}$, the maximum velocity of the ejected electron is

The transformation ratio in the step-up transformer is

The equation of progressive wave is $y=0.2 \sin 2 \pi\left[\frac{t}{0.01}-\frac{x}{0.3}\right]$, where $x$ and $y$ are in metre and t is second. The velocity of propagation of the wave is

A ball whose density is $0.4 \times 10^3 \, kg/m^3$ falls into water from a height of $9\,cm$. To what depth does the ball sink?

The table below shows the temperatures in degrees Fahrenheit in a city over one week. If m represents the median temperature, f represents the temperature that occurs most often, and a represents the average (arithmetic mean) of the seven temperatures, which of the following is the correct order of m, f, and a?

Noontime Temperature
Mon	Tue	Wed	Thu	Fri	Sat	Sun
66	78	75	69	78	77	70

Consider the following piecewise definition of the function f.
\(f(x) =   \begin{cases}   3-x,\,\,\,if & \quad x≤0\\     x^2 +2,\,if & \quad x≥0  \end{cases}\)
Evaluate f(-3).