List of practice Questions

Find an anti derivative (or integral) of the following function by the method of inspection: (ax + b)2
Find an anti derivative (or integral) of the following function by the method of inspection: \(e^{2x}\)
Find an anti derivative (or integral) of the following function by the method of inspection:Cos 3x
Find an anti derivative (or integral) of the following function by the method of inspection: sin 2x
Choose the correct answer.
If \(a,b,c\),are in A.P.,then the determinant
\(\begin{vmatrix}x+2& x+3& x+2a\\ x+3& x+4& x+2b\\ x+4& x+5& x+2c\end{vmatrix}\) is:
Write Minors and Cofactors of the elements of following determinants:
I. \(\begin{vmatrix}1&0&0\\0&1&0\\0&0&1\end{vmatrix}\)II. \(\begin{vmatrix}1&0&4\\3&5&-1\\0&1&2\end{vmatrix}\)
Grey crescent is the area
Which one of the following is an inner orbital complex as well as diamagnetic in behaviour ?(Atomic no.: Zn=30,Cr=24 Co=27,Ni=28)
In a face-centered cubic lattice, a unit cell is shared equally by how many unit cells?
Which one of the following compounds is most acidic ?
The number of moles of KMnO4 reduced by one mole of KI in alkaline medium is:
Why is apple called a false fruit? Which part(s) of the flower forms the fruit?

<div>Which of the following undergoes nucleophilic substitution exclusively by SN1 mechanism ?</div>

Prove: \(∫^1_0sin^{-1}x\,dx=\frac{π}{2}-1\)
Prove: \(∫^{\frac{π}{4}}_0 2tan^3xdx=1-log2\)
Prove: \(∫^{\frac{π}{2}}_0 sin^3xdx=\frac{2}{3}\)
Prove: \(∫^1_{-1}x^{17}cos^{4}xdx\)
Ends of long bones are covered with
Ethyl alcohol is industrially prepared from ethylene by
Considering H2O as a weak field ligand, the number of unpaired electrons in [Mn(H2O6)]2+ will be – (At. no. of Mn = 25)
Prove: \(∫_0^1x.e^x\ dx=1\)
Prove: \(∫_1^3\frac {dx}{x^2(x+1)}=\frac 23+log\frac 23\)
Evaluate the definite integral: \(∫^π_0\frac{xtanx}{secx+tanx}dx\)
Evaluate the definite integral: \(∫_0^{\frac{π}{2}}sin2x\,tan^{-1}(sinx)dx\)

Examine the following functions for continuity.
(A) f(x) = x-5 
(B) f(x) =\(\frac {1}{x-5}\), x≠5 
(C) f(x) = \(\frac {x^2-25}{x+5}\), x≠-5 
(D) f(x) = |x-5|