List of practice Questions

The straight lines l1 and l2 pass through the origin and trisect the line segment of the line L: 9x + 5y = 45 between the axes. If m1 and m2 are the slopes of the lines l1 and l2, then the point of intersection of the line y = (m1 + m2)x with L lies on

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?
problem figure
Slack time in PERT Analysis

Let $\vec{a}=\hat{i}+2 \hat{j}+\lambda \hat{k}, \vec{b}=3 \hat{i}-5 \hat{j}-\lambda \hat{k}, \vec{a} \cdot \vec{c}=7,2 \vec{b} \cdot \vec{c}+43=0, \vec{a} \times \vec{c}=\vec{b} \times \vec{c}$. Then $|\vec{a} \cdot \vec{b}|$ is equal to

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 entityList-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 :
Let \(a \in R\) and let \(\alpha, \beta\) be the roots of the equation \(x^2+60^{\frac{1}{4}} x+a=0\). If \(\alpha^4+\beta^4=-30\), then the product of all possible values of \(a\) is_____
For a real number \(x\) , if \(\frac{1}{2},\frac{log_3(2^x-9)}{log_34}\), and \(\frac{log_5\bigg(2^x+\frac{17}{2}\bigg)}{log_54}\) are in an arithmetic progression, then the common difference is

7 boys and 5 girls are to be seated around a circular table such that no two girls sit together is?

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?
Shaded region of the figure
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
If \(\vec{a}+2\vec{b}+3\vec{c}=\vec{0}\) and
\((\vec{a}\times\vec{b})+(\vec{b}\times\vec{c})+(\vec{c}\times\vec{a})=\lambda(\vec{b}\times\vec{c})\)
then the value of λ is equal to
In the interval (0, π/2), area lying between the curves y = tan x and y = cot x and the X-axis is