List of practice Questions

Which one is the correct expression of electric potential on the axial point of a dipole whose dipole moment is р and length is 2l, at a distance of r?

Select the pair in which the numbers are similarly related as in the given pair :
5:35

One mole of an ideal gas undergoes two different cyclic processes I and I, as shown in the P-V diagrams below. In cycle, I processes a, b, c and d are isobaric, isothermal, isobaric, and isochoric, respectively. In cycle II, processes a',b',c', and d' are isothermal, isochoric, isobaric, and isochoric, respectively. The total work done during cycle I is 𝑊_I and that during cycle II is 𝑊_II. The ratio W_I/W_II is

A triangular pyramid with equal sides can be flipped on its edges without slipping or sliding as shown on the left. What is the minimum number of flips needed for the pyramid to reach the finishing line if the starting position is as shown on the right?

Ki are possible values of K for which lines $Kx + 2y + 2 = 0$, $2x + Ky + 3 = 0$, $3x + 3y + K = 0$ are concurrent, then $∑k_i$ has value.

A dice throw can result in the numbers 2,3,5 or 6. Every 4th throw will result in 3. What is the minimum number of times the dice has to be thrown for the pawn to move from zero to reach exactly at 100?

The range of the function $f(x)=\sqrt{3-x}+\sqrt{2+x}$ is:

In absence of instruction by the prescriber, unless otherwise directed, the dose given for the mixture preparation should be stated on the label as

If $\int \sqrt{\sec 2 x-1} d x=\alpha \log _e\left|\cos 2 x+\beta+\sqrt{\cos 2 x\left(1+\cos \frac{1}{\beta} x\right)}\right|+$ constant, then $\beta-\alpha$ is equal to_______

Temperature of 25 ºC in Fahrenheit and Kelvin scale respectively are

A small block of mass 100 g is tied to a spring of spring constant 7.5 N/m and length 20 cm. The other end of spring is fixed at a particular point A. If the block moves in a circular path on a smooth horizontal surface with constant angular velocity 5 rad/s about point A, then tension in the spring is-

Which of the following correctly represents the variation of electric potential (V) of a charged spherical conductor of radius (R) with radial distance (r) from the center?

Pipes A and C are fill pipes while Pipe B is a drain pipe of a tank. Pipe B empties the full tank in one hour less than the time taken by Pipe A to fill the empty tank. When pipes A, B and C are turned on together, the empty tank is filled in two hours. If pipes B and C are turned on together when the tank is empty and Pipe B is turned off after one hour, then Pipe C takes another one hour and 15 minutes to fill the remaining tank. If Pipe A can fill the empty tank in less than five hours, then the time taken, in minutes, by Pipe C to fill the empty tank is

Identify the total number of differences in the images shown below.

In a gravimetric estimation of Al, a sample of 0.1000 g AlCl₃ is precipitated with 8-hydroxyquinoline. The weight of the precipitate is _____ g.
[Given: atomic weight of Al is 26.98; molecular weight of AlCl₃ is 133.34; and molecular weight of 8-hydroxyquinoline is 145.16]
(round off to 4 decimal places)

Let f : $\R^2 → \R^2$ be defined by f(x, y) = (e^x cos(y), e^x sin(y)). Then the number of points in $\R^2$ that do NOT lie in the range of f is

If $p(\frac{1}{q}+\frac{1}{r}),q(\frac{1}{r}+\frac{1}{p}),r(\frac{1}{p}+\frac{1}{q})$ are in A.P., then p, q, r

The rms value of conduction current in a parallel plate capacitor is $69\, \mu A$ The capacity of this capacitor, if it is connected to $230 \, V$ ac supply with an angular frequency of $600\, rad / s$, will be :

Select the correct statements from the following :

A. Atoms of all elements are composed of two fundamental particles.
B. The mass of the electron is 9.10939 x 10^-31 kg.
C. All the isotopes of a given element same chemical properties.
D. Protons and electrons are collected known as nucleons.
E. Dalton’s atomic theory, regarded atom as an ultimate particle of matter.
Choose the correct answer from the options given below :

The number of bijective functions $f :\{1,3,5$, $7, \ldots \ldots 99\} \rightarrow\{2,4,6,8, \ldots \ldots , 100\}$, such that $f (3) \geq f (9) \geq f (15) \geq f (21) \geq \ldots f (99), $ is _____

1 L, 0.02 M solution of [Co(NH₃)₅SO₄]Br is mixed with 1 L, 0.02 M solution of [Co(NH₃)₅Br]SO₄. The resulting solution is divided into two equal parts (X) and treated with excess of AgNO₃ solution and BaCl₂ solution respectively as shown below:
1 L Solution (X) + AgNO₃ solution (excess) → Y
1 L Solution (X) + BaCl₂ solution (excess) → Z
The number of moles of Y and Z respectively are

In a given code, SISTER is coded as 535301, UNCLE as 84670, and BOY as 129. How is RUSTIC written in that code?

A wheel is rolling on a plane surface. A point on the rim of the wheel at the same level as the Centre has a speed of 4m/s. The speed of the Centre of the wheel is:

The potential energy of a long spring when stretched by 2 cm is U. If the spring is stretched by 8 cm, potential energy stored in it will be:

The set of all values of $a$ for which $\displaystyle\lim _{x \rightarrow a}([x-5]-[2 x+2])=0$,where $[\propto]$ denotes the greatest integer less than or equal to $\propto$ is equal to