List of practice Questions

If 3 g of glucose (Molar mass = 180) is dissolved in 60 g of water at 15 degree, the osmotic pressure of the solution will be
The rise in boiling point of a solution containing 1.8 g of glucose in 100 g of solvent is 0.1 degree C. The molal elevation constant of the liquid is
Consider the linear programming problem:
Maximize   z=10x+5y
subject to the constraints
2x+3y≤120
2x + y ≤ 60
x,y≥0.
Then the coordinates of the corner points of the feasible region are
The integrating factor of the differential equation 4xdy-e-2y dy + dx = 0 is
The general solution of the differential equation \((x^2y^2+y)dx-(x-2x^3y)dy=0\) is
A particular solution of the differential equation \(\frac{dy}{dx}=xy^2\) with y(0)=1 is
The value of \(\displaystyle\int^{\frac{\pi}{16}}_{0}\cos6x\cos2xdx\) is equal to
If \(f(x) = \begin{cases}     \cos x       & for\ x\geq0 \\       2x      &for\ x\lt0  \end{cases}\), then the value of \(\displaystyle\int^{\frac{\pi}{2}}_{-2}dx\) is equal to
The value of \(\displaystyle\int^{10}_{-10}\frac{x^{10}\sin x}{\sqrt{1+x^{10}}}dx\) is equal to
The value of \(\int^{2}_{-1}(x-2)|x|)dx\) is equal to
The area bounded by the curve y = x(2-x) and the line y=x is
The value of \(\displaystyle\int^{\frac{\pi}{2}}_{\frac{\pi}{6}}\frac{\cot x}{\sin x}dx \) is equal to
\(\int\frac{dx}{x^2-x}=\)
\(\int\sin^3xdx+\int\cos^2x\sin xdx=\)
\(\int(\tan^2(2x)-\cot^2(2x))dx=\)
\(\int\frac{1}{x^3}\sqrt{1-\frac{1}{x^2}}dx=\)
The feasible region for a L.P.P. is shown in the figure below. Let z = 50x+15y be the objective function, then the maximum value of z is
The feasible region for a L.P.P. is shown in the figure below
\(\int\frac{sin^{25}x}{cos^{27}x}dx\) is equal to
\(\int\frac{e^{\frac{1}{\sqrt t}}}{t\sqrt t}dt=\)
Let f(x)=cosx for \(0\leq x \leq\frac{\pi}{3}\). Then the value of c which satisfies the conclusion of the Mean Value Theorem for the function f on \([0,\frac{\pi}{3}]\) is equal to
If x+13y=40 is normal to the curve y=5x2+ax+β at the point (1, 3), then the value of αß is equal to
The function f(x)=x5e-x is increasing in the interval
The normal to the curve y=√x at the point (25, 5) intersects the y-axis at
If x and y are both non-negative and if x+y=π, then the maximum value of 5sinxsiny is equal to
The equation of tangent to the circle (x-5)2+y2 = 25 at (2, 4) is