List of practice Questions

Two dice are thrown. If it is known that the sum of numbers on the dice was less than 6 the probability of getting a sum as 3 is

If A,B and C are three independent events such that P(A) = P(B) = P(C) = P then P(at least two of A, B, C occur) =

Given that A and B are two events such that P(B) = \(\frac{3}{5}\) P(A/B) = \(\frac{1}{2}\) and P(A ∪ B) = \(\frac{4}{5}\) then P(A) =

The shaded region is the solution set of the inequalities

The area of the quadrilateral ABCD, when A(0, 4, 1), B(2, 3, -1), C(4, 5, 0) and D(2, 6, 2) is equal to

If a plane meets the coordinate axes at A, B and C in such a way that the centroid of triangle ABC is at the point (1, 2, 3) then the equation of the plane is

The angle between the lines whose direction cosines are \((\frac{\sqrt3}{4},\frac{1}{4},\frac{\sqrt3}{2})\) and \((\frac{3}{4},\frac{1}{4},\frac{-\sqrt3}{2})\) is

The compound A (major product) is

The equation of the line joining the points (-3, 4, 11) and (1, -2, 7) is

If \(\vec{a}.\vec{b}=0\) and \(\vec{a}+\vec{b}\) makes an angle 60° with \(\vec{a}\) then

The correct order for wavelengths of light absorbed in the complex ions
[CoCl(NH₃)₅]²⁺, [Co(NH₃)₆]³⁺, [Co(CN)₆]^3- is

The diagonals of a parallelogram are the vectors \(3\hat{i}+6\hat{j}-2\hat{k}\) and \(-\hat{i}-2\hat{j}-8\hat{k}\) then the length of the shorter side of parallelogram is

Homoleptic complexes among the following are
(A) K₃[Al(C₂O₄)₃], (B) [CoCl₂(en)₂]⁺, (C) K₂[Zn(OH)₄]

The IUPAC name of [Co(NH₃)₅(CO₃)]Cl is

A vector \(\vec{a}\) makes equal acute angles on the coordinate axis.Then the projection of vector \(\vec{b}=5\hat{i}+7\hat{j}-\hat{k}\) on \(\vec{a}\) is

The number of solutions of \(\frac{dy}{dx}=\frac{y+1}{x-1}\) when y(1) = 2 is

Peroxide effect is observed with the addition of HBr but not with the addition of HI to unsymmetrical alkene because

Solution of Differential Equating xdy – ydx = 0 represents

For the crystal field splitting in octahedral complexes,

If the area of the Ellipse is \(\frac{x^2}{25}+\frac{y^2}{\lambda^2}=1\) is 20π square units, then λ is

The area of the region bounded by \(y=\sqrt{16-x^2}\) and x-axis is

The value of \(\int\limits_0^{4042}\frac{\sqrt{x}\ dx}{\sqrt{x}+\sqrt{4042-x}}\) is equal to

If \(I_n=^{\frac{\pi}{4}}_0\int\tan^n x\ dx\) where n is positive integer then I₁₀ + I₈ is equal to

The value of \(\int e^x[\frac{1+\sin x}{1+\cos x}]dx\) is equal to

When the absolute temperature of ideal gas is doubled and pressure is halved, the volume of gas