List of practice Questions

If $2x + 3y + 12 = 0$ and $x - y + 4 \lambda = 0$ are conjugate with respect to the parabola $y^2 = 8x$, then $\lambda$ is equal to

The distance between the foci of the hyperbola $x^2 - 3y^2 - 4x - 6y -11 = 0$ is

The radius of the circle with the polar equation $r^2 - 8r( \sqrt{3} \, \cos \, \theta + \sin \, \theta) + 15 = 0$ is

If $f: R \rightarrow R$ is defined by $f(x)=[x-3]+|x-4|$ for $x \in R$, then $\displaystyle\lim _{x \rightarrow 3} f(x)$ is equal to

If $f : R \rightarrow R$ is defined by $f(x) = \begin{cases} \frac{\cos \ 3x - \cos \ x}{x^2} &, \text{for } x \neq 0 \\ \lambda &, \text{for } x = \end{cases}$ and if $f$ is continuous at $x = 0,$ then $\lambda$ is equal to

If $f(2) = 4$ and $f'(2) = 1$, then $\displaystyle\lim_{x \to 2} \frac{xf (2) - 2 f (x) }{x -2}$ is equal to

If $\overline{ M _{ W }}$ is the weight average molecular weight and $\overline{ M _{ n }}$ is the number average molecular weight of a polymer, the poly dispersity index (PDI) of the polymer is given by:

The velocities of two particles $A$ and $B$ are $0.05$ and $0.02\, ms^{-1}$ respectively. The mass of $B$ is five times the mass of $A$. The ratio of their de- Broglie's wavelength is

Two particles $A$ and $B$ initially at rest, move towards each other, under mutual force of attraction. At an instance when the speed of $A$ is $v$ and speed of $B$ is $2v$, the speed of center of mass $(CM)$ is

Which of the following correspond $(s)$ has '$Z$' configuration?

Which one of the following graphs represents "Freundlich adsorption isotherm'' ?

Which of the following is true in the case of an adiabatic process, where $\gamma = C_{p} / C_{v} $ ?

Two concentric coils of $10$ turns each are placed in the same plane. Their radii are $20\, cm$ and $40\, cm$ and carry $0.2\, A$ and $0.3\, A$. current respectively in opposite directions. The magnetic induction (in tesla) at the center is

Which of the following statements are correct for alkali metal compounds? (i) Superoxides are paramagnetic in nature. (ii) The basic strengths of hydroxides increases down the group. (iii) The conductivity of chlorides in their aqueous solutions decreases down the group. (iv) The basic nature of carbonates in aqueous solutions is due to cationic hydrolysis.

An $X$-ray tube produces a continuous spectrum of radiation with its shortest wavelength of $45 \times 10^{-2}?$. The maximum energy of a photon in the radiation in $eV $ is $(h = 6.62 \times 10^{-34} \, J-s, c = 3 \times 10^8 \, m/s)$

In $\triangle A B C$ the mid points of the sides $A B, B C$ and $C A$ are respectively $(1,0,0),(0$, $m , 0)$ and $(0,0, n )$. Then, $\frac{A B^{2}+B C^{2}+C A^{2}}{l^{2}+m^{2}+n^{2}}$ is equal to

The magnetised wire of moment $M$ and length $l$ is bent in the form of semicircle of radius $r$. Then its magnetic moment is

In a certain code ROAD is written as URDG. How is SWAN written in that code?

Which of the following will come in place of the question mark(?) in the following sequence?
6C7,8FIO, 11J14, 15019,?

Ram walks 10m South from his house, turns left and walks 23 m, again turns left and walks 40 m, then turns right and walks 5 m to reach his school. In which direction is the school from his house?

If table is called chair, chair is called cot, cot is called pot and pot is calledfilter, where does a person sit?

Off-hand is related to PERFUNCTORY, in the same way as above, Board is related to

In a class of 35 students, Kiran is placed 7th from the bottom whereas Mohan is placed 9th from the top. Sohan is placed exactly in between Kiran and Mohan. What is Kiran's position from Sohan?

If the second, third, fifth, eighth and ninth letters of the word CONTEMPLATION are combined to form a meaningful word, what will be the middle letter of the word? If more than one such word can be formed, your answer is X and if no such words can be formed your answer is Y.

Pointing to a photograph Arun said, 'She is the mother of my brother's son's wife's daughter.' How is Arun related to the lady?