List of practice Questions

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

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

The value of \(\int\frac{xe^x dx}{(1+x)^2}\) is equal to

Which one of the following is correct for all elements from Sc to Cu ?

The value of \(\int\frac{x^2dx}{\sqrt{x^6+a^6}}\) is equal to

\(\int\frac{x^3\sin(\tan^{-1}(x^4))}{1+x^8}dx\) is equal to

The maximum slope of the curve y = -x³ + 3x² + 2x -27 is

The function f(x) = x² - 2x is strictly decreasing in the interval