List of practice Questions

\(1.5g\) of \(CdCl_2\) was found to contain \(0.9g\) of Cd. Calculate the atomic weight of Cd.

How many tripeptides can be prepared by linking the amino acids glycine, alanine and phenyl alanine?

A codon has a sequence of \(A\) and specifies a particular \(B\) that is to be incorporated into a \(C\). What are \(A\), \(B\), \(C\)?

Parkinson's disease is linked to abnormalities in the levels of dopamine in the body. The structure of dopamine is

The type of bonds present in sulphuric anhydride are -

\(\cos^{-1}\left(-\frac{1}{2}\right)-2\sin^{-1}\left(\frac{1}{2}\right)+3\cos^{-1}\left(-\frac{1}{\sqrt{2}}\right)-4\tan^{-1}(-1)\) equals

If \(f:\mathbb{R}\rightarrow \mathbb{R}\) is defined by
\[ f(x)= \begin{cases} \dfrac{2\sin x-\sin 2x}{2x\cos x}, & x\neq 0 \\ a, & x=0 \end{cases} \] then the value of \(a\) so that \(f\) is continuous at \(0\) is

The line \(x=\frac{\pi}{4}\) divides the area of the region bounded by \(y=\sin x\), \(y=\cos x\) and x-axis \((0\leq x\leq \frac{\pi}{2})\) into two regions of areas \(A_1\) and \(A_2\). Then \(A_1:A_2\) equals

The solution of the differential equation
\[ \frac{dy}{dx}=\sin(x+y)\tan(x+y)-1 \] is

If \(p\Rightarrow(\sim p\vee q)\) is false, then the truth value of \(p\) and \(q\) are respectively

If
\[ x=\cos^{-1}\left(\frac{1}{\sqrt{1+t^2}}\right), \quad y=\sin^{-1}\left(\frac{t}{\sqrt{1+t^2}}\right), \] then \(\frac{dy}{dx}\) is equal to

If
\[ \frac{d}{dx}\left[a\tan^{-1}x+b\log\left(\frac{x-1}{x+1}\right)\right]=\frac{1}{x^4-1} \] then \(a-2b\) is equal to

If
\[ y=e^{a\sin^{-1}x}=(1-x^2)y_{n+2}-(2n+1)xy_{n+1} \] is equal to

The function \(f(x)=x^3+ax^2+bx+c\), \(a^2\leq 3b\) has

If
\[ \int \left(\frac{2-\sin2x}{1-\cos2x}\right)e^x\,dx \] is equal to

If \(I_n=\int \sin^n x\,dx\), then \(I_n-nI_{n-2}\) equals

The number of normals drawn to the parabola \(y^2=4x\) from the point \((1,0)\) is

If the circle \(x^2+y^2=a^2\) intersects the hyperbola \(xy=c^2\) in four points \((x_1,y_1)\) for \(i=1,2,3,4\), then \(y_1+y_2+y_3+y_4\) equals

The mid point of the chord \(4x-3y=5\) of the hyperbola \(2x^2-3y^2=12\) is

The perimeter of the triangle with vertices at \((1,0,0),(0,1,0)\) and \((0,0,1)\) is

If a line in the space makes angles \(\alpha,\beta,\gamma\) with the coordinate axes, then
\[ \cos2\alpha+\cos2\beta+\cos2\gamma+\sin^2\alpha+\sin^2\beta+\sin^2\gamma \] equals

The radius of the sphere
\[ x^2+y^2+z^2=12x+4y+3z \] is

Evaluate
\[ \lim_{x\to 0}\left(\frac{x+5}{x+2}\right)^{x+3} \]

If \(X\) is a binomial variable with the range \(\{0,1,2,3,4,5,6\}\) and \(P(X=2)=4P(X=4)\), then the parameter \(p\) of \(X\) is

The area (in square unit) of the circle which touches the lines \(4x+3y=15\) and \(4x+3y=5\) is