List of practice Questions

Three randomly chosen nonnegative integers $x, y$ and $z$ are found to satisfy the equation $x+y+z=10$. Then the probability that $z$ is even, is

If $8\sqrt{x}\left(\sqrt{9+\sqrt{x}}\right)dy = \left(\sqrt{4+\sqrt{9+\sqrt{x}}}\right)^{-1}\,\,dx, \,\,\,\,x > 0$ and $

Let $O$ be the origin and let $P Q R$ be an arbitrary triangle. The point $S$ is such that $\overrightarrow{O P} \cdot \overrightarrow{O Q}+\overrightarrow{O R} \cdot \overrightarrow{O S}=\overrightarrow{O R} \cdot \overrightarrow{O P}+\overrightarrow{O Q} \cdot \overrightarrow{O S}=\overrightarrow{O Q} \cdot \overrightarrow{O R}+\overrightarrow{O P} \cdot \overrightarrow{O S}$ Then the triangle $P Q R$ has $S$ as its

The equation of the plane passing through the point $(1, 1, 1)$ and perpendicular to the planes $2

In a bimolecular reaction, the steric factor $P$ was experimentally determined to be $4.5.$ The correct option(s) among the following is(are)

How many bridging carbonyl $ (s) $ is/are present in the compound $ Fe_3(CO)_{12} $ compound?

Consider an expanding sphere of instantaneous radius

Addition of excess aqueous ammonia to a pink coloured aqueous solution of $MCl _{2} \cdot 6 H _{2} O (X)$ and $NH _{4} Cl$ gives an octahedral complex $Y$ in the presence of air. In aqueous solution, complex $Y$ behaves as $1: 3$ electrolyte. The reaction of $X$ with excess $HCl$ at room temperature results in the formation of a blue colured complex $Z$. The calculated spin only magnetic moment of $X$ and $Z$ is $3.87\, B.M$., whereas it is zero for complex $Y$. Among the following options, which statement(s) is(are) correct ?

The correct statement(s) for the following addition reactions is(are)

The correct statement(s) about the oxoacids, $HClO_4$ and $HClO$, is(are)

Allene $ (C_3H_4) $ contains

A flat plate is moving normal to its plane through a gas under the action of a constant force $F$. The gas is kept at a very low pressure. The speed of the plate $v$ is much less than the average speed $u$ of the gas molecules. Which of the following options is/are true?

A converging lens has a focal length of $ 0.12\, m $ . To get an image of unit magnification the object should be placed at what distance from the converging lens?

Which of the following pairs of organic compounds give positive Tollens? test?

$ IF_7 $ is known to exist while $ BrF_7 $ does not exist. The reason is

The geometry and type of hybrid orbital present around the central atom in $ BF_3 $ is

Which of the following elements involves gradual filling of $ 4f $ -levels?

A bird flies at an angle of $ 60^{\circ} $ to the horizontal. Its horizontal component of velocity is $ 10\, m\, s ^{-1} $ . Find the vertical component of velocity in $ m s ^{-1} $ .

A very long conductor carries a current of $ 1 A $ . The magnetic field at a point whose distance is $ 0.1\, m $ from one end of the conductor is (in $ T $ )

A body of mass $ 5 \,kg $ acquires an angular acceleration of $ 10\, rad\, s^{-2} $ by an applied torque of $ 2 \,N m $ . Find its radius of gyration.

A projectile is fired at an angle of $ 45^{\circ} $ and reaches the highest point in its path after $ 2\sqrt2\,s $ . Find the velocity of projectile in $ m s ^{-1} $ ,

The motion of a particle is represented by the equation $ S = 8t^3 - 2t^2+ 6t + 7 $ . Find the velocity of the particle at the end of $ 2 $ seconds in $ m s^{-1} $

In a Young?s double slit experiment, the two slits which are separated by $ 1.2\, mm $ are illuminated with a monochromatic light of wavelength $ 6000 $ angstorm. The interference pattern is observed on a screen placed at a distance of $ 1m $ from the slits. Find the number of bright fringes formed over $ 1 \,cm $ width on the screen.

What will be the distance of $ (1, 0, 2) $ from the point of intersection of plane $ x - y + z = 16 $ and the line $ \left(\frac{x-2}{3}\right) = \left(\frac{y+1}{4}\right) = \left(\frac{z-2}{12}\right) $ ?

$ P $ speaks truth in $ 70\% $ cases and $ Q $ speaks in $ 80\% $ of the cases. In what percentage of cases are they likely to contradict each other in stating the same fact?