List of practice Questions

The shortest distance between the lines \[ \frac{x - 3}{2} = \frac{y - 2}{3} = \frac{z - 1}{-1} \] and \[ \frac{x + 3}{2} = \frac{y - 6}{1} = \frac{z - 5}{3} \] is:

If $ P(B) = \frac{3}{5} $, $ P(A \mid B) = \frac{1}{2} $, and $ P(A \cup B) = \frac{4}{5} $, then the value of $ P(A \cup B)' + P(A' \cup B) $ is:

In a current carrying coil of inductance 60 mH,the current is changed from 2.5 A in one direction to 2.5 A in the opposite direction in 0.10 sec. The average induced EMF in the coil will be:

Arrange the following events relating to India in the correct time line sequence.
A. First 'Industrial Policy Resolution'
B. "Modern Bread", a bread manufacturing firm sold to private sector
C. First phase of green revolution
D. Setting up of planning commission
Choose the correct answer from the options given below:

If $ n(A) = 4 $ and $ n(B) = 7 $, then the difference between the maximum and minimum value of $ n(A \cup B) $ is:

The domain of the function \[ f(x) = \frac{1}{\sqrt{9 - x^2}} \] is:

Evaluate: \[ \cos^{-1} \frac{1}{2} + \sin^{-1} (1) + \tan^{-1} \frac{1}{\sqrt{3}} \]

The determinant of the matrix:

is:

The number of nonzero terms in the expansion of \[ (1 + 3\sqrt{2}x)^9 + (1 - 3\sqrt{2}x)^9 \] is:

The general solution of the differential equation given by: \[ \tan^{-1} x + \tan^{-1} y = c \]

If the function \[ f(x) = \begin{cases} 1, & x \leq 2 \\ ax + b, & 2 < x < 4 \\ 7, & x \geq 4 \end{cases} \] is continuous at $ x = 2 $ and $ x = 4 $, then the values of $ a $ and $ b $ are:

Consider a curve $ y = y(x) $ in the first quadrant as shown in the figure. Let the area $ A_1 $ be twice the area $ A_2 $. The normal to the curve perpendicular to the line \[ 2x - 12y = 15 \] does NOT pass through which point?

If \[ f(x) = \frac{x + |x|}{x} \] then the value of \[ \lim_{x \to 0} f(x) \] is:

In a certain coding system, if 2 = 5, 4=18, 6=39 then 10 = ?

At a certain depth "$d$" below surface of earth, value of acceleration due to gravity becomes four times that of its value at a height $3 R$ above earth surface Where $R$ is Radius of earth (Take $R =6400\, km$ ) The depth $d$ is equal to

Find the number which will replace the question mark in the following problem figure?

Slack time in PERT Analysis

One mole of an ideal gas at 350K is in a 2.0 L vessel of thermally conducting walls, which are in contact with the surroundings. It undergoes isothermal reversible expansion from 2.0L to 3.0L against a constant pressure of 4 atm. The change in entropy of the surroundings (ΔS) is JK (Nearest integer) Given: R = 8.314 J K^-1 Mol^-1.

Match List I with List II :

List-I Coordination entity		List-II Wavelength of light absorbed in nm
A.	$[CoCl(NH_3)_5]^{2+}$	I.	310
B.	$[Co(NH_3)_6]^{3+}$	II.	475
C.	$[Co(CN)_6]^{3−}$	III.	535
D.	$[Cu(H_2O)_4]^{2+}$	IV.	600

Choose the correct answer from the options given below :

A parallel plate capacitor consists of two square metal plates 5.0 cm of side and separated by 1 cm. A sulphur slab of thickness 5 mm is placed on the lower plate. What will be the capacitance of the capacitor? (Dielectric constant of sulphur = 4)

Which of the following is an empty set ?

Ten chairs are numbered as 1 to 10. Three women and two men wish to occupy one chair each. First the women choose the chairs marked 1 to 6, then the men choose the chairs from the remaining. The number of possible ways is

List-I Coordination entity		List-II Wavelength of light absorbed in nm
A.	\([CoCl(NH_3)_5]^{2+}\)	I.	310
B.	\([Co(NH_3)_6]^{3+}\)	II.	475
C.	\([Co(CN)_6]^{3−}\)	III.	535
D.	\([Cu(H_2O)_4]^{2+}\)	IV.	600