List of practice Questions

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

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.	\([Cu(H_2​O)_4​]^{2+}\)	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

Given that a,b and x are real numbers and a< b, x < 0 then

The value of \(e^{\log_{10}\tan 1°+\log_{10}\tan 2°+\log_{10}\tan 3°+...+\log_{10}\tan89°}\) is

If f(x) = ax + b, where a and b are integers, f(-1) = -5 and f(3) = 3 then a and b are respectively

The shaded region in the figure given is the solution of which of the inequations?

A bag contains 2n + 1 coins. It is known that n of these coins have head on both sides whereas the other n + 1 coins are fair. One coin is selected at random and tossed. If the probability that toss results in heads is \(\frac{31}{42}\), then the value of n is

\(|\vec{a}\times\vec{b}|^2+|\vec{a}.\vec{b}|^2=144\) and \(|\vec{a}|=4\) then \(|\vec{b}|\) is equal to

If (2, 3, -1) is the foot of the perpendicular from (4, 2, 1) to a plane, then the equation of the plane is

The point of intersection of the line x + 1 = \(\frac{y+3}{3}=\frac{-z+2}{2}\) with the plane 3x + 4y + 5z = 10 is

The length of perpendicular drawn from the point (3, -1, 11) to the line \(\frac{x}{2}=\frac{y-2}{3}=\frac{z-3}{4}\) is

If a lines makes an angle of \(\frac{\pi}{3}\) with each X and Y axis then the acute angle made by Z-axis is

In the interval (0, π/2), area lying between the curves y = tan x and y = cot x and the X-axis is

The component of \(\hat{i}\) in the direction of the vector \(\hat{i}+\hat{j}+2\hat{k}\) is

If \(|\vec{a}+\vec{b}|=|\vec{a}-\vec{b}|\) then

The degree of the differential equation
\(1+(\frac{dy}{dx})^2+(\frac{d^2y}{dx^2})^2= \sqrt[3]{\frac{d^2y}{dx^2}+1}\) is

The area of the region bounded by the line y = x +1, and the lines x = 3 and x = 5 is