List of practice Questions

$ \int\left[sin \left(log\,x\right)+cos\left(log\,x\right)\right]dx $ is equal to

Two identical light waves, propagating in the same direction, have a phase difference $\delta$. After they superpose the intensity of the resulting wave will be proportional to

The half-life of a radioactive element is 10 hours. How much will be left after 4 hours in 1 g atom sample?

Which one of the following types of organisms occupy more than one trophic level in a pond ecosystem ?

Which one of the following is monoecious?

Which one of the following is considered important in the development of seed habit?

A fruit developed from hypanthodium inflorescence is called

Which one of the following is a vascular cryptogam ?

Which one of the following has haplontic life cycle?

The sum of the series $ \left( 1+\frac{{{({{\log }_{e}}\,n)}^{2}}}{2!}+\frac{{{({{\log }_{e}}n)}^{4}}}{4!}+... \right) $ is

If $ {{\tan }^{-1}}\,2 $ and $ {{\tan }^{-1}}\,3 $ are two angles of a triangle, then the third angle is

The image of the point $ (6,3,9) $ in the straight line $ x-2=\frac{1-y}{2}=\frac{z}{2} $ is

The term independent of $x$ in the expansion of $ {{\left( \sqrt{\frac{x}{3}}+\frac{3}{2{{x}^{2}}} \right)}^{10}} $ is

The number of ways in which $5$ boys and $5$ girls can be seated for a photograph so that no two girls sit next to each other is

If $ {{x}_{1}},{{x}_{2}},......{{x}_{18}} $ are observations such, that $ \sum\limits_{j=1}^{18}{({{x}_{j}}-8)=9} $ and $ \sum\limits_{j=1}^{18}{{{({{x}_{j}}-8)}^{2}}=45,} $ then the standard deviation of these observations is

$ \frac{^{8}{{C}_{0}}}{6}{{-}^{8}}{{C}_{1}}{{+}^{8}}{{C}_{2}}\cdot 6{{-}^{8}}{{C}_{3}}{{.6}^{2}}+....{{+}^{8}}{{C}_{8}}{{\cdot 6}^{7}} $ is equal to

The number of solutions of the equation $ \sin \,x\,\,\cos \,\,3x=\sin \,3x\,\,\cos \,5x $ in $ \left[ 0,\frac{\pi }{2} \right] $ is

The point on the x-axis equidistant from the points $ (4,3,1) $ and $ (-2,\,-6,\,-2) $ is

In $ \Delta \,\,ABC $ if $ si{{n}^{2}}A+si{{n}^{2}}B+si{{n}^{2}}C=2, $ then the triangle is

The value of $ {{\cos }^{-1}}\,\left( \sin \,\frac{7\pi }{6} \right) $ is equal to

Find the function $ f(x_1, x_2, x_3) $ satisfying $ f(x_1, x_2, x_3) = 1 $ at $ x_1 = 1, x_2 = x_3 = 0 $ .

Joint equation of pair of lines through $ (3, - 2) $ and parallel to $ x^2 - 4xy + 3y^2 = 0 $ is

If $\alpha$ and $\beta$ are roots of the quadratic equation $ {{x}^{2}}+4x+3=0, $ then the equation whose roots are $ 2\alpha \,\text{+}\,\beta $ and $ \alpha \,\text{+2}\,\beta $ is

If the third term of a $G.P.$ is $3$, then the product of its first $5$ terms is

The number of diagonals of a polygon of $20$ sides is