List of practice Questions

If the ratio of the absolute temperature of the sink and source of a Carnot engine is changed from 2:3 to 3:4, the efficiency of the engine changes by:

The focus of the parabola \(y^2 + 4y - 8x + 20 = 0\) is at the point:

Compound ‘X’ (C\(_6\)H\(_6\)O) reacts with aqueous NaOH to give compound ‘Y’. ‘Y’ reacts with CO\(_2\) followed by acidification to give compound ‘Z’. The compounds X, Y and Z are respectively

If three numbers are randomly selected from the set \( \{1,2,3,\dots,50\} \), then the probability that they are in arithmetic progression is: 

An ink mark is made on a piece of paper and a glass slab of thickness $t$ and refractive index $\mu$ is placed on it. If the image of the ink mark appears to be at a distance of $x$ from the top surface of the slab, then the value of $x$ is
The symmetric equation of the straight line passing through the points \( (-1, 4, 2) \) and \( (-3, 0, 5) \) is
A rectangular tank of depth 4 m is full of water of refractive index \(\frac 43\). When viewed from the top, the bottom of the tank is seen at a depth of
If \(v_1\) and \(v_2\) are the speeds of light in the two media of refractive indices \(n_1\) and \(n_2\) respectively, then
The pair of linear equations \(a_1x+b_1y+c_1=0\) and \(a_2x+b_2y+c_2=0\) has a unique solution, then
If a body is taken above the surface of the Earth, it loses its weight by 20% at a height of \( h = \frac{\sqrt{5}}{2} R \), where \( R \) is the radius of the Earth, then:
In the following OP-AMP circuit, 𝑣𝑖𝑛 and 𝑣𝑜𝑢𝑡 represent the input and output signals, respectively.
OP-AMP circuit
Choose the correct statement(s):
When two spheres of radii $r$ and $\frac{r}{2}$ are brought in contact, the gravitational force of attraction between them is proportional to
In the measurement of length 6 $\mu$m is equal to $x$ pm. Then the value of $x$ is
If m and M denote the mean deviations about mean and about median respectively of the data 20, 5, 15, 2, 7, 3, 11, then the mean deviation about the mean of m and M is:
A string of length \( L \) is fixed at both ends and vibrates in its fundamental mode. If the speed of waves on the string is \( v \), then the angular wave number of the standing wave is:
The maximum velocity of a fluid in a tube for which the flow remains streamlined is called its:

The general solution of the differential equation: \[ (6x^2 - 2xy - 18x + 3y) dx - (x^2 - 3x) dy = 0 \] 

A circle \( S \) passes through the points of intersection of the circles \( x^2 + y^2 - 2x - 3 = 0 \) and \( x^2 + y^2 - 2y = 0 \). If \( x + y + 1 = 0 \) is a tangent to the circle \( S \), then the equation of \( S \) is:
Let \( [P] \) denote the greatest integer \( \leq P \). If \( 0 \leq a \leq 2 \), then the number of integral values of \( a \) such that \( \lim_{x \to a} [x^2] - [x]^2 \) does not exist is:
When two objects are moving along a straight line in the same direction, the distance between them increases by 6 m in one second. If the objects move with their constant speed towards each other, the distance decreases by 8 m in one second. Then the speed of the objects are:
For the curve \[ y = \alpha x^2 + \cos y + \beta, \] the value of \( \frac{dy}{dx} \) at \( (1,0) \) is 2. Then the value of \( \alpha \beta \) is equal to
The total energy of a gas mixture of one mole of oxygen and 3 moles of argon at a temperature \( T \) by neglecting vibrational modes is:
The perimeter of two squares are 40 cm and 32 cm. The perimeter of a third square whose area is equal to the difference of the areas of the two squares is :
If the temperature of a gas is increased from \( 27^\circ C \) to \( 159^\circ C \), the increase in the rms speed of the gas molecules is:

A dealer sold three-fourth of his articles at a gain of 20% and the remaining at cost price. What is the gain earned by him in the whole transaction?