List of practice Questions

Given below are two statements :
Statement I : None of the alkaline earth metal hydroxides dissolve in alkali.
Statement II : Solubility of alkaline earth metal hydroxides in water increases down the group.
In the light of the above statements, choose the most appropriate answer from the options given below :

Which one of the following compounds of Group-14 elements is not known ?

The correct order of following 3d metal oxides, according to their oxidation numbers is :
(a) $CrO_3$
(b) $Fe_2O_3$
(c) $MnO_2$
(d) $V_2O_5$
(e) $Cu_2O$

The value of aluminium susceptibility is $2.2 \times 10^{-5}$. The percentage increase in the magnetic field if space within a current carrying toroid is filled with Aluminium is $\frac{x}{10^4}$. Then the value of x is __________.

Sodium stearate $CH_3(CH_2)_{16}COO^- Na^+$ is an anionic surfactant which forms micelles in water. Choose the correct statement for it from the following :

A body of mass 2 kg moving with a speed of 4 m/s makes an elastic collision with another body at rest and continues to move in the original direction but with one fourth of its initial speed. The speed of the two body centre of mass is $\frac{x}{10}$ m/s. Then the value of $x$ is ________.

A particle of mass 'm' is moving in time 't' on a trajectory given by \[ \vec{r} = 10 \alpha t^2 \hat{i} + 5 \beta (t - 5) \hat{j} \] Where $\alpha$ and $\beta$ are dimensional constants. The angular momentum of the particle becomes the same as it was for $t=0$ at time $t = $________ seconds.

Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A : Moment of inertia of a circular disc of mass 'M' and radius 'R' about X, Y axes (passing through its plane) and Z-axis which is perpendicular to its plane were found to be $I_x, I_y, & I_z$, respectively. The respective radii of gyration about all the three axes will be the same.
Reason R : A rigid body making rotational motion has fixed mass and shape.
In the light of the above statements, choose the most appropriate answer from the options given below :

Two wires of same length and radius are joined end to end and loaded. The Young's moduli of the materials of the two wires are $Y_1$ and $Y_2$. The combination behaves as a single wire then its Young's modulus is :

What should be the order of arrangement of de-Broglie wavelength of electron ($\lambda_e$), an $\alpha$-particle ($\lambda_\alpha$) and proton ($\lambda_p$) given that all have the same kinetic energy?

A particle of mass 4M at rest disintegrates into two particles of mass M and 3M respectively having non zero velocities. The ratio of de-Broglie wavelength of particle of mass M to that of mass 3M will be :

A parallel plate capacitor with plate area 'A' and distance of separation 'd' is filled with a dielectric. What is the capacity of the capacitor when permittivity of the dielectric varies as : \[ \epsilon(x) = \epsilon_0 + kx, \text{ for } \left( 0<x \le \frac{d}{2} \right) \] \[ \epsilon(x) = \epsilon_0 + k(d-x), \text{ for } \left( \frac{d}{2} \le x \le d \right) \]

Water droplets are coming from an open tap at a particular rate. The spacing between a droplet observed at 4th second after its fall to the next droplet is 34.3 m. At what rate the droplets are coming from the tap? (Take $g = 9.8 \text{ m/s}^2$)

In Amplitude Modulation, the message signal $V_m(t) = 10 \sin(2\pi \times 10^5 t)$ volts and Carrier signal $V_c(t) = 20 \sin(2\pi \times 10^7 t)$ volts. The modulated signal now contains the message signal with lower side band and upper side band frequency, therefore the bandwidth of modulated signal is $\alpha \text{ kHz}$. The value of $\alpha$ is :

Some nuclei of a radioactive material are undergoing radioactive decay. The time gap between the instances when a quarter of the nuclei have decayed and when half of the nuclei have decayed is given as : (where $\lambda$ is the decay constant)

The half-life of $^{198}\text{Au}$ is 3 days. If atomic weight of $^{198}\text{Au}$ is 198 g/mol then the activity of 2 mg of $^{198}\text{Au}$ is [in disintegration/second] :

Four identical pieces of wood of length 50 cm x 8 cm x 2 cm are arranged as shown in the figure. Another larger square is generated by rotating all the wooden panels along the outer edges and extending the outermost edges till they touch each other. What is the area of this larger square thus constructed?

Reference image of a square pyramid, P, is provided on the left. Assume Q as an identical pyramid created by mirroring P in upward direction. Q was rotated by 135 degrees around the vertical axis and then brought down so that the two pyramids intersect. Which of the options is the resultant view as seen from the given direction arrow?

In the container given below of dimensions (40 cm X 20 cm X 20 cm), four objects are dipped in water. Objects P and Q are made of some light material while objects R and S are made of iron and copper, respectively. The object P is a cube of edge 4 cm with 1/10^th floating above water; object Q displaces 50 cc of water while floating. The volumes of objects R and S are 295.4 cc and 397 cc, respectively. If all the objects are removed from the container, what would be the new water level inside the container measured from the bottom?

A rhombus is inscribed in a rectangle which in turn is inscribed in a circle as shown in the figure below. P is the centre of all three shapes, PQ=QR=5 units. What is the perimeter of the rhombus?

Three circles of radius 10 cm are drawn inside an equilateral triangle as shown below. The area of the red coloured region (in sq. cm., up to two decimal places) in the figure is ____.

Two identical cubes P and Q are made of smaller cubes in 3×3×3 and 5×5×5 configurations, respectively as shown below. Alternate cubes are painted green and white as indicated. Identify the correct option.

The figure shows views of the same solid. Count the number of surfaces.

Four views of a convex solid are shown. How many surfaces does the solid have?

On a race track shown below choose the correct starting configuration. The athletes are not allowed to change the tracks. Each grid is 2 m x 2 m.