List of top Questions asked in CBSE CLASS XII

The order and degree of the differential equation : \(\dfrac{d}{dx}(\sin y) = y^2\) respectively are

Check whether the lines given by \(\dfrac{x-1}{2} = \dfrac{y-2}{3} = \dfrac{z-3}{4}\) and \(\dfrac{x-4}{5} = \dfrac{y-1}{2} = z\) are parallel or not. If parallel, find the distance between them, otherwise find their point of intersection, if the lines are intersecting.

Evaluate : \(\displaystyle\int_{0}^{1} x\tan^{-1}x\,dx\).

Find the particular solution of the differential equation

\(xy\dfrac{dy}{dx} = (x+2)(y+2)\), given that \(y(1) = -1\).

Find the general solution of the following differential equation:

\(x^{2}\dfrac{dy}{dx} = x^{2} + xy + y^{2}\)

If \(x = \cos t\), \(y = \cos mt\), prove that \((1-x^{2})\dfrac{d^{2}y}{dx^{2}} - x\dfrac{dy}{dx} + m^{2}y = 0\).

Find \(\displaystyle \int \sqrt{\frac{x+2}{x-2}}\,dx\).

Find the vector of magnitude \(14\) in the direction of \(\overrightarrow{QP}\), where P and Q are the points \((1,\ 3,\ 2)\) and \((-1,\ 0,\ 8)\) respectively.

The least value of \( f(x) = x^3 - 12x,\ x \in [0, 3] \) is

Assertion (A) : Lines given by \( x = py + q \), \( z = ry + s \) and \( x = p^{\prime}y + q^{\prime} \), \( z = r^{\prime}y + s^{\prime} \) are perpendicular to each other when \( pp^{\prime} + rr^{\prime} = 1 \).

Reason (R) : Two lines \( \vec{r} = \vec{a}_1 + \lambda\vec{b}_1 \) and \( \vec{r} = \vec{a}_2 + \mu\vec{b}_2 \) are perpendicular to each other if \( \vec{b}_1 \cdot \vec{b}_2 = 0 \).

A room freshner bottle in the shape of an inverted cone sprays the perfume at regular intervals such that volume of the perfume in the bottle decreases at the steady rate of \(1\ \text{mm}^3/\text{min}\). Find the rate at which level of perfume is dropping at an instant when level of perfume in the bottle is \(10\ \text{mm}\), if the semi-vertical angle of conical bottle is \(\dfrac{\pi}{6}\).

The length of perpendicular drawn from point \( (2, 5, 7) \) on line \( \dfrac{x}{1} = \dfrac{y}{0} = \dfrac{z}{0} \) is

The order and degree of the differential equation \( \dfrac{d}{dx}\left(e^{y}\right) = 0 \) respectively are

If A and B are skew symmetric matrices of same order, then which of the following matrices is also skew symmetric ?

If \( 2\cos^{-1}x = y \), then

Which of the following cannot be the order of a row-matrix ?

(a) Define 'Denatured Protein' with an example.

(b) What happens when glucose reacts with HCN ? Write the reaction involved.

(c) Name the disease caused by the deficiency of Vitamin C.

Conductivity of \( 2.5 \times 10^{-4} \) M methanoic acid solution is \( 5.25 \times 10^{-5} \) S cm\(^{-1}\).

(a) Calculate its molar conductivity.

(b) Calculate its degree of dissociation.

[Given : \( \lambda^{\circ}_{(\mathrm{H^+})} = 349.5 \) S cm\(^2\) mol\(^{-1}\) and \( \lambda^{\circ}_{(\mathrm{HCOO^-})} = 50.5 \) S cm\(^2\) mol\(^{-1}\)]

Explain the Finkelstein reaction.

Write the reactions taking place at anode and cathode in a lead storage battery, when it is in use.

A reaction \( \mathrm{A \rightarrow B} \) follows second order kinetics. How will the rate of reaction be affected if the concentration of (i) A is increased by three times, and (ii) A is reduced to half ?

(i) Give a chemical test to distinguish between Propanal and Propanone.

(ii) Which of the given acids is stronger and why ? \( \mathrm{F_3C{-}C_6H_4{-}COOH} \) or \( \mathrm{H_3C{-}C_6H_4{-}COOH} \)

(iii) Complete the given reaction sequence :

\[ \mathrm{CH_3CH_2CH_2COOC_2H_5} \xrightarrow{\mathrm{NaOH}} \mathrm{A + C_2H_5OH} \]

\[ \mathrm{A} \xrightarrow{\mathrm{H_3O^+}} \mathrm{B} \]

(a) Write two structural differences between DNA and RNA.

(b) Which component of starch is a branched chain polymer of \( \alpha \)-D-(+)-glucose ? Write its one characteristic feature.

(c) Which types of bonds hold the polypeptide chains in fibrous proteins ?