List of practice Questions

Calculate the wavelength associated with an electron moving with a velocity of $10^{6} m / s$ (mass of $e^{-}=9.1 \times 10^{-31} kg,\, \left. h=6.6 \times 10^{-34} kg\, m ^{2} s ^{-1}\right)$
Which of the following pairs is not correctly matched?
Above the Boyle temperature, the compressibility factor of the real gases, $ Z $ is
The bond order of $N _{2}^{+}$on the basis of molecular orbital theory is [Atomic number of $N =7$ ]
A uniform rope of mass $ 0.1 \,kg $ and length $ 2.45 \,m $ hangs from a ceiling. The time taken by a transverse wave to travel the full length of the rope is
A thermodynamic state of a given sample of an ideal gas is completely described, if its
A steady current $I$ flows along an infinitely long hollow cylindrical conductor of radius $R$. This cylinder is placed coaxially inside an infinite solenoid of radius $2R$. The solenoid has $n$ turns per unit length and carries a steady current $I$. Consider a point $P$ at a distance $r$ from the common axis. The correct statement(s) is (are)
A rectangular sheet of fixed perimeter with sides having their lengths in the ratio $8 : 15$ is converted into an open rectangular box by folding after removing squares of equal area from all four corners. If the total area of removed squares is $100$, the resulting box has maximum volume. Then the lengths of the sides of the rectangular sheet are
A particle of mass $m$ is projected from the ground with an initial speed $u _{0}$ at an angle $\alpha$ with the horizontal. At the highest point of its trajectory, it makes a completely inelastic collision with another identical particle, which was thrown vertically upward from the ground with the same initial speed $u_{0}$. The angle that the composite system makes with the horizontal immediately after the collision is
A particle of mass $M$ and positive charge $Q$, moving with a constant velocity $u _{1}=4 \hat{i}ms ^{-1}$, enters a region of uniform static magnetic field normal to the $x$-y plane. The region of the magnetic field extends from $x =$ 0 to $x = L$ for all values of $y$. After passing through this region, the particle emerges on the other side after 10 milliseconds with a velocity $\vec{ u }_{2}=2(\sqrt{3} i +\hat{ j }) m / s ^{-1}$. The correct statement(s) is (are)
Let $\omega$ be a complex cube root of unity with $\omega \ne 0$ and $P = [P_{ii}] $ be an $n \times \, n$ matrix with $p_{ij} = \omega^{i+j}$ Then, $P^2 \ne 0$ when $n$ =
Two lines $L_1:x = 5\, \frac{y}{3-\alpha} = \frac{z}{-2}$ and $L_1:x = \alpha \, \frac{y}{-1} =\frac{z}{2-\alpha}$ are coplaner. Then, $\alpha$ can take value(s)
A line $l$ passing through the origin is perpendicular to the lines $ L_1 : (3+t) \widehat {i} +(1-2t) \widehat {j}+(4+2t)\widehat {k}, - \infty < t < \infty$ $ L_2 : (3+2s) \widehat {i} +(3+2s) \widehat {j}+(2+s)\widehat {k}, - \infty < s < \infty$ Then, the coordinate(s) of the point(s) on $l_2$ at a distance of $\sqrt 17$ from the point of intersection of l and $l_1$ is (are)
Four persons independently solve a certain problem correctly with probabilities $\frac{1}{2},\frac{3}{4},\frac{1}{4},\frac{1}{8}$ Then,the probability that the problem is solved correctly by at least one of them, is
A multiple choice examination has $5$ questions. Each question has three alternative answers of which exactly one is correct. The probability that a student will get $4$ or more correct answers just by guessing is
A microscope is focused on a coin lying at the bottom of a beaker. The microscope is now raised up by $1 cm$. To what depth should the water be poured into the beaker so that coin is again in focus? (Refractive index of water is $\frac{4}{3}$ )
A magnifying glass of focal length $ 5\,cm $ is used to view an object by a person whose smallest distance of distinct vision is $ 25\,cm $ . If he holds the glass close to eye, the magnification is
A glass plate of refractive index $1.5$ is coated with a thin layer of thickness t and refractive index $1.8$. Light of wavelength $648 \,nm$ travelling in air is incident normally on the layer. It is partly reflected at upper and lower surfaces of the layer and the two reflected rays interfere. The least value of $t$ for which the rays interfere constructively is
A cyclotron is operated at an oscillator frequency of $ 12\, MHz $ and has a dee radius $ R = 50\,cm $ . What is the magnitude of the magnetic field needed for a proton to be accelerated in the cyclotron ?
The expression for effective magnetic moment $ (\mu _{\text{eff}}) $ is
The known oxidation states for both $V$ and $CO$ are
The image of an object, formed by a plano-convex lens at a distance of $8\,m$ behind the lens, is real and is one-third the size of the object. The wavelength of light inside the lens is $\frac{2}{3}$ times the wavelength in free space. The radius of the curved surface of the lens is
A ray of light travelling in the direction $\frac{1}{2}(\hat{i}+\sqrt{3})$ is incident on a plane mirror. After reflection, it travels along the direction $\frac{1}{2}(\hat{i}-\sqrt{3} j)$. The angle of incidence is
Two non-reactive monoatomic ideal gases have their atomic masses in the ratio $2 : 3$. The ratio of their partial pressures, when enclosed in a vessel kept at a constant temperature, is $4 : 3$. The ratio of their densities is
In the Young's double slit experiment using a monochromatic light of wavelength $\lambda$ the path difference (in terms of an integer $n$) corresponding to any point having half the peak intensity is