List of practice Questions

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
If the parabola y = αx2 - 6x + β passes through the point (0, 2) and has its tangent at x = \(\frac{3}{2}\) parellel to x axis, then
A particle starts form rest and its angular displacement (in radians) is given by \(\theta=\frac{t^2}{20}+\frac{t}{5}\). If the angular velocity at the end of t = 4 is k, then the value of 5k is
If y = (x - 1)2 (x - 2)3 (x - 3)5 then \(\frac{dy}{dx}\) at x = 4 is equal to
If the parametric equation of curve is given by x = cosθ + log tan \(\frac{θ}{2}\) and y = sinθ, then the points for which \(\frac{dy}{dx}=0\) are given by
Which of the following does not represent property stated against it ?
Consider the following statements :
Statement 1 : If y = log10x + logex then \(\frac{dy}{dx}=\frac{\log_{10}e}{x}+\frac{1}{x}\)
Statement 2 : \(\frac{d}{dx}(\log_{10}x)=\frac{\log x}{\log 10}\ \text{and}\ \frac{d}{dx}(\log_ex)=\frac{\log x}{\log e}\)
A colourless, neutral, paramagnetic oxide of Nitrogen ‘P’ on oxidation gives reddish brown gas Q. Q on cooling gives colourless gas R. R on reaction with P gives blue solid S. Identify P, Q, R, S respectively
XeF6 on partial hydrolysis gives a compound X, which has square pyramidal geometry ‘X’ is
The correct order of boiling point in the following compounds is
Which of the following property is true for the given sequence NH3 > PH3 > AsH3 > SbH3 > BiH3 ?
Which of the following compound on heating gives N2O ?
For constant a, \(\frac{d}{dx}\)(xx + xa+ ax + aa) is