List of practice Questions

A cube is painted red on two adjacent faces and on one opposite sides face, yellow on two opposite faces and green on the remaining face. It is then cut into 64 equal cubes. How many cubes have one red coloured face only?

If for a matrix $ A $, $ |A| = 6 $ and $ \text{adj } A = \begin{bmatrix} 1 & -2 & 4 \\ 4 & 1 & 1 \\ -1 & k & 0 \end{bmatrix} $, then $ k $ is equal to:

Choose the figure that will correctly replace the question mark $(?)$ in the given series.

Immunity in our body is of two types: (i) Innate immunity and (ii) acquired immunity. Innate immunity is a non-specific defence mechanism, whereas acquired immunity is pathogen-specific; it is called specific immunity too. Acquired immunity is characterised by memory. Antibodies are specific to antigens and there are different types of antibodies produced in our body: they are IgA, IgE, IgG and IgM. It shows primary response when it encounters the pathogen for the first time and secondary response during the subsequent encounters with the same Antigen/Pathogen.
(a) Name the two types of specialised cells which carry out the primary and secondary immune response.
(b) Why is the antibody-mediated immunity also called as humoral immune response?
Attempt either sub-part (c) or (d):
(c) The organ transplants are often rejected if taken from suitable compatible persons.
(i) Mention the characteristic of our immune system that is responsible for the graft rejection.
(ii) Name the type of immune response and the cell involved in it.
OR
(d) How is active immunity different from passive immunity?

The question figure shows the 3D view of an object. Identify the correct view when looking in the direction of the arrow.

A cube having a side of 10 cm with unknown mass and 200 gm mass were hung at two ends of an uniform rigid rod of 27 cm long. The rod along with masses was placed on a wedge keeping the distance between wedge point and 200 gm weight as 25 cm. Initially the masses were not at balance. A beaker is placed beneath the unknown mass and water is added slowly to it. At given point the masses were in balance and half volume of the unknown mass was inside the water. (Take the density of the unknown mass is more than that of the water, the mass did not absorb water and water density is 1 gm/cm$^3$.) The unknown mass is ______ kg.

A square Lamina OABC of length 10 cm is pivoted at $ O $. Forces act at Lamina as shown in figure. If Lamina remains stationary, then the magnitude of $ F $ is:

A uniform rod of mass 250 g having length 100 cm is balanced on a sharp edge at the 40 cm mark. A mass of 400 g is suspended at the 10 cm mark. To maintain the balance of the rod, the mass to be suspended at the 90 cm mark is:

Find the roots of the quadratic equation $ 2x^2 - 4x - 6 = 0 $.

Displacement of a wave is expressed as $$ x(t) = 5 \cos \left( 628t + \frac{\pi}{2} \right) \, \text{m}. $$ The wavelength of the wave when its velocity is 300 m/s is:

If $ \mathbf{p} $ and $ \mathbf{q} $ are unit vectors, then which of the following values of $ \mathbf{p} \cdot \mathbf{q} $ is not possible?

Your school is organizing an Education Fair in the school premises. As the Head boy / Head girl of Sunshine Public School, Agra, draft a notice informing students of Classes IX – XII about the fair. Include other necessary details. You are Muskan / Manoj. Put your notice in a box.

Moment of inertia of a rod of mass $ M $ and length $ L $ about an axis passing through its center and normal to its length is $ \alpha $. Now the rod is cut into two equal parts and these parts are joined symmetrically to form a cross shape. Moment of inertia of cross about an axis passing through its center and normal to the plane containing cross is:

Considering Bohr’s atomic model for hydrogen atom :
(A) the energy of H atom in ground state is same as energy of He+ ion in its first excited state.
(B) the energy of H atom in ground state is same as that for Li++ ion in its second excited state.
(C) the energy of H atom in its ground state is same as that of He+ ion for its ground state.
(D) the energy of He+ ion in its first excited state is same as that for Li++ ion in its ground state.

Liquid A and B form an ideal solution. The vapour pressure of pure liquids A and B are 350 and 750 mm Hg respectively at the same temperature. If $ x_A $ and $ x_B $ are the mole fraction of A and B in solution while $ y_A $ and $ y_B $ are the mole fraction of A and B in vapour phase then :

The correct orders among the following are:
[A.] Atomic radius : $B<Al<Ga<In<Tl$
[B.] Electronegativity : $Al<Ga<In<Tl<B$
[C.] Density : $Tl<In<Ga<Al<B$
[D.] 1st Ionisation Energy :
In$<Al<Ga<Tl<B$
Choose the correct answer from the options given below :

The total number of structural isomers possible for the substituted benzene derivatives with the molecular formula $C_7H_{12}$ is __

The roots of the quadratic equation $ 3x^2 - px + q = 0 $ are the 10th and 11th terms of an arithmetic progression with common difference $ \frac{3}{2} $. If the sum of the first 11 terms of this arithmetic progression is 88, then $ q - 2q $ is equal to:

Which of the following is the correct IUPAC name of the given organic compound (X)?
The structure of compound $ X $ is as follows:

$ \text{H}_3\text{C} - \text{CH}_3 - \text{CH} = \text{CH} - \text{H} - \text{Br} $

For a set of $ n $ integers in arithmetic progression, the difference between twice the median of the set and the range of the set is equal to twice the first term.

A certain financial institution reported that its assets totaled Rs.2,377,366.30 on a certain day. Of this amount, Rs.31,724.54 was held in cash. Approximately what percent of the reported assets was held in cash on that day?