List of practice Questions

The base of the hexadecimal number system is:
If \( f(x) \) is continuous and \( \int_0^9 f(x) \, dx = 4 \), then the value of the integral \( \int_0^3 x \cdot f(x^2) \, dx \) is: (a) 2
A source program is written in which language?
The two’s complement of a binary number is obtained by adding what to its one’s complement?
The radius of the base of a cone is increasing at the rate of 3 cm/minute and the altitude is decreasing at the rate of 4 cm/minute. The rate of change of lateral surface when the radius is 7 cm and altitude is 24 cm is:
Two objects A and B are placed at 15 cm and 25 cm from the pole in front of a concave mirror having radius of curvature 40 cm. The distance between images formed by the mirror is:

The descending order of magnitude of the eccentricities of the following hyperbolas is: 
A. A hyperbola whose distance between foci is three times the distance between its directrices. 
B. Hyperbola in which the transverse axis is twice the conjugate axis. 
C. Hyperbola with asymptotes \( x + y + 1 = 0, x - y + 3 = 0 \).

Let \( z \neq 1 \) be a complex number and let \( \omega = x + iy, y \neq 0 \). If \[ \frac{\omega -\overline{\omega}z}{1 -z} \] is purely real, then \( |z| \) is equal to
The wavelength (in cm) of the second line in the Lyman series of the hydrogen atomic spectrum is (Rydberg constant \( R \, \text{cm}^{-1})\).
Let the vectors \( \overrightarrow{AB} = 2\hat{i} + 2\hat{j} + \hat{k} \) and \( \overrightarrow{AC} = 2\hat{i} + 4\hat{j} + 4\hat{k} \) be two sides of a triangle ABC. If \( G \) is the centroid of \( \triangle ABC \), then \( \frac{22}{7} |\overrightarrow{AG}|^2 + 5 = \): (a) 25
If the relation between the direction ratios of two lines in \(\mathbb{R}^3\) are given by \(l + m + n = 0\), \(2lm + 2mn - ln = 0\), then the angle between the lines is:
The bond order of \( O_2 \) molecule and its magnetic property are respectively:

Let \( S \) denote the set of all subsets of integers containing more than two numbers. A relation \( R \) on \( S \) is defined by:

\[ R = \{ (A, B) : \text{the sets } A \text{ and } B \text{ have at least two numbers in common} \}. \]

Then the relation \( R \) is:

If the line with direction ratios \[ (1, a, \beta) \] is perpendicular to the line with direction ratios \[ (-1,2,1) \] and parallel to the line with direction ratios \[ (\alpha,1,\beta), \] then \( (\alpha, \beta) \) is:
The program that analyses and executes the source code line-by-line is called:
The decimal equivalent of \( 10010_{(2)} \) is:

Query language comes under ___________ generation programming languages.

Which of the following Operating System reads and reacts in actual time?

The centre of the hyperbola \(16x^2 - 4y^2 + 64x - 24y - 36 = 0\) is at the point:

If a freely falling body covers 80 m in the first 4 seconds, then in the next 4 seconds it covers a distance of:
Normally a capacitor is connected across the output terminals of a rectifier to
Water of mass \( m \) at \( 30^\circ C \) is mixed with \( 5 \) g of ice at \( -20^\circ C \). If the resultant temperature of the mixture is \( 6^\circ C \), then the value of \( m \) is: (Given: Specific heat capacity of ice = \( 0.5 \) cal \( g^{-1} \) \( ^\circ C^{-1} \), Specific heat capacity of water = \( 1 \) cal \( g^{-1} \) \( ^\circ C^{-1} \), Latent heat of fusion of ice = \( 80 \) cal \( g^{-1} \))
A body floats with \(\frac{1}{n}\) of its volume keeping outside of water. If the body has been taken to height \(h\) inside water and released, it will come to the surface after time \(t\). Then:
An alternating current having peak value 14.14 A is used to heat a metal wire. The value of the direct current \(i\) required to produce the same heating effect in the same wire is
Enthalpy of combustion of ethylene gas at constant pressure of 1 atm and at 300 K is -1410 kJ mol\(^{-1}\). The enthalpy change for the reaction at constant volume and at the same temperature is about (R = 8.3 J K\(^{-1}\) mol\(^{-1}\)):