List of practice Questions

The directrix of the parabola y$^2$ + 4x + 3 = 0 is
The length of the parabola y$^2$ = 12x cut off by the latus-rectum is
The shortest distance between the straight lines through the points $A_1 = (6, 2, 2)$ and $A_2 = (-4, 0, -1)$, in the directions of $(1, -2, 2)$ and $(3, -2, -2)$ is
If $\left|\frac{z-25}{z-1}\right|=5$ , the value of |z|
Probability of getting positive integral roots of the equation x$^2$ - n = 0 for the integer n, 1 $\le$ n $\le$ 40 is
Solution of the differential equation $xdy - ydx - \sqrt{x^{2}+y^{2}}dx = 0$ is
The simplified expression of sin ($tan^{-1} x$), for any real number $x$ is given by
The center and radius of the sphere $x^2 + y^2 + z^2 + 3x - 4z + 1 = 0$ are
The value of $\int^{^a}_{0}\sqrt{\frac{a-x}{x}}dx$ is
The value of $f(0)$ so that $\frac{\left(-e^{x} +2^{x}\right)}{x}$may be continuous at $x = 0$ is
Which of the following is ketohexose ?
According to Cahn-Ingold-Prelog sequence rules, the correct order of priority for the given groups is
When same quantity of electricity is passed through aqueous $AgNO_3$ and $H_2SO_4$ solutions connected in series, $ 5.04 \times 10^{-2} \, g $ of $H_2$ is liberated. What is the mass of silver (in grams) deposited? (E wts. of hydrogen = $ 1.008,$ silver = $108$)
When electric current is passed through acidified water for $1930\, s,\, 1120\, mL$ of $H_2$ gas is collected (at STP) at the cathode. What is the current passed in amperes?
Starting from rest, the time taken by a body sliding down on a rough inclined plane at $45^{\circ}$ with the horizontal is, twice the time taken to travel on a smooth plane of same inclination and same distance. Then the coefficient of kinetic friction is
The orbit of geo-stationary satellite is circular, the time period of satellite depends on - (i) mass of the satellite (ii) mass of the earth (iii) radius of the orbit (iv) height of the satellite from the surface of earth Which of the following is correct?
The bond length of $HCl$ molecule is $1.275\,?$ and its dipole moment is $1.03\, D$. The ionic character of the molecule (in percent) (charge of the electron $= 4.8 \times 10^{-10}$ esu) is
When $25\, g$ of a non-volatile solute is dissolved in $100\,g$ of water, the vapour pressure is lowered by $2.25 \times 10^{-1}\, mm$. If the vapour pressure of water at $20^{\circ} C$ is $17.5\, mm$, what is the molecular weight of the solute?
What is the temperature at which the kinetic energy of $0.3$ moles of helium is equal to the kinetic energy of $0.4$ moles of argon -at $400\, K$ ?
A steel wire can withstand a load up to $2940\, N$. A load of $150\, kg$ is suspended from a rigid support. The maximum angle through which the wire can be displaced from the mean position, so that the wire does not break when the load passes through the position of equilibrium, is
A load of $1\, kg$ weight is a attached to one end of a steel wire of area of cross-section $ 3 \, mm^2$ and Young's modulus $10^{11} \, N/m^2$. The other end is suspended vertically from a hook on a wall, then the load is pulled horizontally and released. When the load passes through its lowest position the fractional change in length is $(g = 10 \, m/s^2)$
There is some change $W$ length when a $ 33000 \, N$ tensile force is applied on a steel rod of area of cross-section $10^{-3} \, m^2$. The change of temperature required to produce the same elongation, if the steel rod is heated, is (The modulus of elasticity is $3 \times 10^{11} N/m^2$ and the coefficient of linear expansion of steel is $ 1.1 \times 10^{-5} /^{\circ} C)$.
The surface tension of soap solution is $0.03\, N/m$. The work done in blowing to form a soap bubble of surface area $40 \, cm^2, (in\, J)$ is
In the adiabatic compression, the decrease in volume is associated with
Which one of the following is a correct set?