Class XII (PCM) - Online Scholarship Test - MCQ

N atoms of a radioactive element emit n alpha particles per second at an instant. Then the half - life of the element is

Two small balls, each having equal positive charge Q are suspended by two insulating strings of equal length L from a hook fixed to a stand. If the whole set-up is transferred to a satellite in orbit around the earth, the tension in equilibrium in each string is equal to

Assume that gravitational lines of forces represent gravitational field just like electric lines of forces represent electric field. Which of the following diagram correctly represents the gravitational field lines for a pair of point masses shown in options below ?

Figure shows a uniformly charged hemispherical shell. The direction of electric field at point p, that is off-centre (but in the plane of the largest circle of the hemisphere), will be along

In which of the following cases the total number of decays will be maximum in a time interval of t = 0 to t = 4 hr. The first term represents the number of nuclei at time t = 0 and the second represents the half life of the radionuclide.

An electron of mass  m , when accelerated through a potential V has de-Broglie wavelength λ. The de-Broglie wavelength associated with a proton of mass M accelerated through the same potential difference will be :

The plates of a parallel plate capacitor have charges Q and -2Q. Its capacitance is C. The potential difference between its plates will be

Acceleration of a particle under projectile motion at the highest point of its trajectory is :

Three resistances are arranged as shown. The potential of the point O is:

A battery of internal resistance 2 ? is connected to a variable resistor whose value can vary from 4 ? to 10?. The resistance is initially set at 4 ? If the resistance is now increased then

Two identical conducting rings A & B of radius R are in pure rolling over a horizontal conducting plane with same speed (of center of mass)v but in opposite direction. A constant magnetic field B is present pointing inside the plane of paper. Then the potential difference between the highest points of the two rings, is :

Two hydrogen atoms are in excited state with electrons residing in n = 2. First one is moving towards left and emits a photon of energy E₁ towards right. Second one is moving towards left with same speed and emits a photon of energy E₂ towards left. Taking recoil of nucleus into account during emission process

Entropy change for 2 moles of an ideal monoatomic gas when it undergoes the change in state from (4 atm, 300K) to (1 atm, 150 K) is

Which of following is responsible for temporary hardness of water ?

A solution turns red litmus blue, its pH is likely to be :

10 mL of a solution of NaOH is found to be completely neutralised by 8 mL of a given solution of HCl. If we take 20 mL of the same solution of NaOH, the amount of H₂SO₄ solution (having the same molarity as that of initial HCl solution) required to neutralise it will be :

Consider the following equilibrium situation and identify the correct statement :

What is the pH of 0.01M NaOH aqueous solution ?

How many α and β particles will be emitted when this conversion occurs ?

A mixture of a definite composition of ethanol and water forms

 the major product P is

 x, y, z are respectively :

The solution set of the equation =9 is

The number of ordered pairs (x, y) satisfying |y| = cosx and y = sin^-1 (sinx) where  are

The domain of definition of function is

A function f has domain [–1, 2] and range [0, 1]. The domain and range respectively of the function g defined by g(x) = 1 – f(x 1) is

The curve y - e^xy x = 0 has a vertical tangent at