Scholarship Test (CLASS – 12) (PCM) (10.04.2022)

The dimensional formula of ε₀  is  [MⁿL^m T^p A^k ]. The value of (n+m+p+k) is

For a given surface the Gauss’s law is stated asFrom this we can conclude that

Two concentric metallic spherical shells of radii R and 2R are given charges charge in ratio Q1:Q2 respectively. It is found that surface charge densities of the surfaces are same. The ratio Q1:Q2 is

The power in pure inductive circuit P1 and power in pure capacitive circuit is P2 then

A charge +q having a mass m enters into an electric field E which is perpendicular to its initial velocity. See figure.

If the point where it enters the electric field is (0,0), then the ordered pair (x,y) after time ‘t’ is

Two Capacitors C1 and C2 are having 60V and 120V respectively. They are being connected in such a way that potential on each one can be made zero. The ratio of C1:C2 is :

The variation of electric potential in solid metallic sphere is shown below. Choose the right answer :

The magnetic fields lines due to a bar magnet are correctly shown in :

A rectangular loop carrying a current ‘I’ is placed near a long straight wire(see figure). If steady current of same magnitude ‘I’ is established in the wire as shown in the figure, the loop will 

An electron and a proton are moving on straight parallel paths with same velocity. They enter a semi-infinite region of uniform magnetic field perpendicular to the velocity. Which of the following statement is true ?

In the circuit shown in fig the heat produced in the 5 ohm resistor due to the current flowing through it is 20J per second. The heat generated in the 4 ohm resistor is

In the circuit shown , the reading of the galvanometer is same with switch S open or closed, then choose the correct option.

The capacitance of a parallel plate capacitor is C. If the distance between the plates increased to twice and area reduced to half, The capacitance becomes :

A capacitor is charged to a voltage of 400V and has a resistance of 20 ohm. Calculate the final value of charging current.

An electric bulb has a rating 200V/100W. The resistance of the bulb is :

Two balls projected horizontally from buildings opposite to each other with velocities 20 m/s and 50 m/s. After what time(in secs) their velocities will be perpendicular to each other?

A spring of force constant k is cut into two pieces such that one piece is double the length of the other. Then the long piece will have a force constant of ?

The speed of a particle ‘v’ varies with time with a rule v=5t. The correct representation of distance ‘s’ with time ‘t’ is ?

The angle (in degrees) between vectors ( i+j ) and   (i+√3j) is :

A block of  mass 10 kg is being held by a horizontal  force of 50N as shown. The minimum value of coefficient of friction between the vertical wall and the block is

m=2 kg ; g=10m/s²; N=50N.

The total number of ions present in 50 g of CaCl₂ is

The element with atomic number 35 belongs to

The reduction in atomic size with increase in atomic number is a characteristic of elements of :

A gas deviates from ideal behaviour at a high pressure because its molecules:

In van der Waals equation of state of gas laws, the constant b is a measure of

Amorphous substances have _______.

(i) definite heat of fusion

(ii) only short range order

(iii) only long range order

(iv ) indefinite heat of fusion

Ice has three dimensional crystal structure in which _________ of total volume is unoccupied.

Which of the following crystallises in bcc structure?

Out of molality , molarity , formality  and mole fraction , those which are independent of temperature are

The molal elevation constant depends upon

Atomic mass is equal to

Which of the following solutions shows positive deviation from Raoult’s law?

The set with correct order of acidity is
(a) HClO < HClO₂ < HClO₃ < HClO₄
(b) HClO₄ < HClO₃ < HClO₂ < HClO
(c) HClO < HClO₄ < HClO₃ < HClO₂
(d) HClO₄ < HClO₂ < HClO₃ < HClO

The shape of XeF₄ is

Single bond length between carbon-carbon is

Which of the following compounds can yield only one monochlorinated product upon free radical chlorination?

In the above reaction, the product D is

Maltose is made up of

What are the hydrolysis products of sucrose?

Which of the following is a non-reducing sugar?

Let 𝑓(𝑥)=(𝑥−1) / (𝑥+1) , then f(f(x)) is

The number of bijective functions from set A to itself when A contains 106 elements is

The number of binary operations that can be defined on a set of 2 elements is

If |𝑎⃗ | = 4 and -3 ≤ λ ≤ 2 then the range of |𝜆𝑎⃗ | is

A vector equally inclined to axes is

What type of a relation is R = {(1, 3), (4, 2), (2, 4), (2, 3), (3, 1)} on the set A : {1, 2, 3, 4}

Function f should be _____ on [a,b] according to Rolle’s theorem.

Objective function of a linear programming problem is

The maximum value of the object function Z = 5x + 10 y subject to the constraints x + 2y ≤ 120, x + y ≥ 60, x – 2y ≥ 0, x ≥ 0, y ≥ 0 is

Maximize Z = 4x + 6y, subject to 3x + 2y ≤ 12, x + y ≥ 4, x, y ≥ 0

The area of a triangle with vertices (-3, 0), (3, 0) and (0, k) is 9 sq. units. The value of k will be

If the points (3, -2), (x, 2), (8, 8) are collinear, then find the value of x.

A function f∶N→N is defined by f(x)=x²+12. What is the type of function here?

The minor M_ij of an element a_ij of a determinant is defined as the value of the determinant obtained after deleting the​

If A and B are any 2 × 2 matrices , then det. (A+B) = 0 implies

The value of p in the quadratic x²  + 4x +p =0; was decided by throw of a dice. The number comes on dice is to be assigned to p. Probability that the root of the quadratic equation is real?

If p is the smallest value of x satisfying the equation 2^x + 15/2^x= 8 then the value of 4^p  is equal to-

The number of solution of the equation log₄ (x–1) = log₂ (x–3)   is:

A dice is thrown twice. Find the probability that both the toss gives prime numbers :

In a triangle ABC,  a=5 , b=7 and sinA= 3/4 . How many such triangles are possible –