List of practice Questions

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