List of practice Questions

Evaluate the definite integral: \(∫^\frac{π}{2}_0 cos^2 x dx\)

Evaluate the definite integral: \(∫_0^1 \frac{dx}{√1-x^2}\)
Evaluate the definite integral: \(∫_0^\frac{π}{2}cos2xdx\)
Integrate the function: \(tan^{-1}x\)
Find the integrals of the function: \(tan^4x\)
Find the integrals of the function: \(tan^3 2x\, sec 2x\)
Find the integrals of the function: \(\frac{cos x - sin x}{1+sin 2x}\)
Find the integrals of the function: \(\frac{cos2 x-cos2 α}{cos x - cos α}\)
Which one of the following pairs is mismatched ?
Find the integrals of the function: \(\frac{sin2 x}{1+cos x}\)
Which one of the following pairs is mismatched ?
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: \(∫^1_0sin^{-1}x\,dx=\frac{π}{2}-1\)