List of top Questions asked in CBSE CLASS XII

Find the intervals in which the following functions are strictly increasing or decreasing:
\((a) x^2 + 2x − 5 \)
\((b) 10 − 6x − 2x^2 \)
\((c) −2x^3 − 9x^2 − 12x + 1 \)
\((d) 6 − 9x − x^2 \)
\((e) (x + 1)^3 (x − 3)^3\)

A balloon, which always remains spherical has a variable radius. Find the rate at which its volume is increasing with the radius when the later is 10cm.

What is spectrochemical series? Explain the difference between a weak field ligand and a strong field ligand.

The integrating factor of the differential equation.
\((1-y^{2})\frac{dx}{dy}+yx=ay\)\((-1<y<1)\)\(is\)

What are the characteristics of the transition elements and why are they called transition elements? Which of the d-block elements may not be regarded as the transition elements?

A 3.0 cm wire carrying a current of 10 A is placed inside a solenoid perpendicular to its axis. The magnetic field inside the solenoid is given to be 0.27 T. What is the magnetic force on the wire?

Consider a certain reaction \(A\) \(→\) \(Products\) with \(k = 2.0 \times 10^{-2 }s^{-1}\) . Calculate the concentration of A remaining after 100 s if the initial concentration of A is 1.0 mol L^-1.

Find the integrals of the function: \(sin^3 (2x+1)\)

The displacement of a body is given to be proportional to the cube of time elapsed. The magnitude of the acceleration of the body, is

The author has used gentle humour to point out human foibles. Pick out instances of this to show how this serves to make the piece interesting.

A beam of light consisting of two wavelengths, 650 nm and 520 nm, is used to obtain interference fringes in a Young’s double-slit experiment.
(a) Find the distance of the third bright fringe on the screen from the central maximum for wavelength 650 nm.
(b) What is the least distance from the central maximum where the bright fringes due to both the wavelengths coincide?

In a Young’s double-slit experiment, the slits are separated by 0.28 mm and the screen is placed 1.4 m away. The distance between the central bright fringe and the fourth bright fringe is measured to be 1.2 cm. Determine the wavelength of light used in the experiment.

An aromatic compound ‘A’ on treatment with aqueous ammonia and heating forms compound ‘B’ which on heating with Br₂ and KOH forms a compound ‘C’ of molecular formula C₆H₇N. Write the structures and IUPAC names of compounds A, B and C

The decomposition of A into product has value of k as \(4.5 \times 10^3 s^{-1}\) at \(10°C\) and energy of activation \(60\ kJ mol^{-1 }\). At what temperature would k be \(1.5 \times 10^4 s^{-1}\)?

A reaction is second order with respect to a reactant. How is the rate of reaction affected if the concentration of the reactant is
(i) doubled
(ii) reduced to half?

Find a particular solution satisfying the given condition: \(\frac {dy}{dx}+2y\ tan\ x=sin\ x;\ y=0\ when \ x=\frac \pi3\)

Find general solution: \((x+3y^2) \frac {dy}{dx} = y,\ (y>0)\)

In a culture,the bacteria count is 1,00,000.The number is increased by \(10\%\) in 2 hours. In how many hours will the count reach 2,00,000,if the rate of growth of bacteria is proportional to the number present?

In a bank,principal increases continuously at the rate of \(5\%\) per year. An amount of Rs1000 is deposited with this bank,how much will it worth after 10years\((e^{0.5}=1.648)\).

In a bank principal increases continuously at the rate of \(r\%\) per year.Find the value of \(r\) is Rs100 doubles itself in 10years\((log_e2=0.6931).\)

At any point \((x,y)\) of a curve,the slope of a tangent is twice the slope of the line segment joining the point of contact to the point \((-4,-3)\).Find the equation of the curve given that it passes through \((-2,1)\).