List of practice Questions

Consider a glass slab which is silvered at one side and the other side is transparent, given the refractive index of the class slab to be 1.5 if a Ray of light is incident at an angle at 45 degree on the transparent side the deviation of the ray of life from its initial path when comes out of the slab is

When a compact disc (CD) is illuminated by small source of white light coloured band are observed. This is due to

\(\sqrt{2 + \sqrt{2 + \sqrt{2 + 2\cos(8\theta)}}}\)=

The value of \(\sin \frac{5\pi}{12} \sin \frac{\pi}{12}\) is

The domain of the function \(f(x) = \frac{1}{\log(1-x)} + \sqrt{x+2}\) is

Suppose that the number of elements in set A is p, the number of elements in set B is q and the number of elements in \(A \times B\) is 7 then \(p^2 + q^2 =\)

If A and B are two independent events such that \(P(\overline{A}) = 0.75\), \(P(A \cup B) = 0.65\) and \(P(B) = x\), then find the value of x:

A pandemic has been spreading all over the world. The probabilities are 0.7 that there will be a lockdown , 0.8 that the pandemic is controlled in one month if there is a lockdown and 0.3 that it is controlled in one month if there is no lockdown. the probability that the pandemic will be controlled in one month is

If A and B are the two events such that \(P(A) = \frac{1}{2}\), \(P(B) = \frac{1}{3}\) and \(P(A|B) = \frac{1}{4}\), then \(P(A' \cap B')\) is

Find the mean number of heads in three tosses of fair coin:

The distance of the point whose position vector is \(\mathbf{2\hat{i} + \hat{j} - \hat{k}}\) from the plane vector \(\vec{r} \cdot (\hat{i} - 2\hat{j} + 4\hat{k}) = 4\) is

A dietician has to develop a special diets using two foods X and Y. Each packet (containing 30g) of food. X contains 12 units of calcium, 4 units of iron, 6 units of cholesterol and 6 units of vitamin A. Each packet of the same quantity of food Y contains 3units of calcium , 20 unit of iron, 4 units of cholesterol and 3 units of vitamin A.The diet requires atleast 240 units of calcium, atleast 460 units of iron and atmost 300 units of cholesterol. The corner points of the feasible region are

The corner points of the feasible region of an LPP are (0,2), (3,0), (6,0), (6,8) and (0,5), then the minimum value of z = 4x + 6y occurs at

The angle between the pair of lines \(\frac{x+3}{3} = \frac{y-1}{5} = \frac{z+3}{4}\) and \(\frac{x+1}{1} = \frac{y-4}{4} = \frac{z-5}{2}\) is

The co-ordinates of the foot of the perpendicular drawn from the origin to the plane 2x - 3y + 4z = 29 are

The sum of the degree and order of differential equation \(\left(1 + y_1^2\right)^{\frac{2}{3}} = y_2\) is

If \(|\vec{a}\times\vec{b}|\) + \(|\vec{a}.\vec{b}|^2=36\) and \(|\vec{a}|=3\) then \(|\vec{b}|\) is equal to

If y(x) be the solution of the differential equation \(x \log(x) \frac{dy}{dx} + y = 2x \log(x), \quad y(e)\) is equal to

The solution of the differential equation \(\frac{dy}{dx} = (x+y)^2\) is

If \(\frac{dy}{dx} + \frac{y}{x} = x^2\) then \(2y (2) - y (1) =\)

\(\int\limits_{0}^{\frac{\pi}{2}}\frac{\cos x\sin x}{1+\sin x}\ dx\) is equal to