Class 12 previous year questions (PYQ)

One litre solution of \(MgCl_{2}\) is electrolysed completely by passing a current of \(1\,A\) for \(16\) min \(5\) sec. The original concentration of \(MgCl_{2}\) solution was (Atomic mass of Mg = 24)

In the circuit shown, the charge $q$ varies with time $t$ as $q = t^2 - 5$, where $q$ is in coulomb and $t$ is in second. At time $t = 3$ second, the voltage $V_{AB}$ in volt will be:

The value of $\int_{-3}^3 \sin ^7 x \cos ^{16} x \,dx$ is

$\int_{\log \frac{1}{2}}^{\log 2} \sin \left(\frac{e^x-1}{e^x+1}\right) d x=$

$\int(\sqrt{1-\sin x}+\sqrt{1+\sin x}) dx =f(x)+c$, where $c$ is the constant of integration. If $\frac{5 \pi}{2}$

$A$ resistance of $20 \Omega$ is connected to a source of an alternating potential $V = 200 \sin (10 \pi t)$. If $t$ is the time taken by the current to change from the peak value to rms value,then $t$ is (in seconds).

Angular width of the central maximum of a diffraction pattern due to a single slit does not depend upon:

Total number of moles of $AgCl$ precipitated on addition of excess of $AgNO_3$ to one mole each of the following complexes $[Co(NH_3)_4Cl_2]Cl$,$[Ni(H_2O)_6]Cl_2$,$[Pt(NH_3)_2Cl_2]$ and $[Pd(NH_3)_4]Cl_2$ is $...............$ (in $.00$)

If molten $NaCl$ contains $SrCl_2$ as impurity,crystallization can generate

Let the solution curve $y=f(x)$ of the differential equation $\frac{dy}{dx}+\frac{xy}{x^{2}-1}=\frac{x^{4}+2x}{\sqrt{1-x^{2}}}, x \in(-1,1)$ pass through the origin. Then $\int_{-\frac{\sqrt{3}}{2}}^{\frac{\sqrt{3}}{2}} f(x) dx$ is equal to

'Circle of least confusion' refers to which one of the following defects occurring in images formed by mirrors or lenses?

$\lim _{x \rightarrow 1} \frac{\log x}{1-x} =$

$\int x^{3} e^{x^{2}} dx =$

If $f(x) = \left(\frac{2^{x}-1}{1-3^{x}}\right)$ for $x \neq 0$ is continuous at $x = 0$,then $f(0) =$

$A$ ray of light is reflected by a plane mirror. $\hat{e}_0$, $\hat{e}$ and $\hat{n}$ be the unit vectors along the incident ray, reflected ray and the normal to the reflecting surface respectively. Which of the following gives an expression for $\hat{e}$?

$A$ coil is connected to an $AC$ source with peak emf, $8 \, V$ and frequency $\frac{30}{\pi} \, Hz$. The coil has a resistance of $8 \, \Omega$. If the average power dissipated by the coil is $0.4 \, W$, then the inductance of the coil is (in $, H$)

$A$ muon $(\mu^-)$ is a negatively charged particle $(|q| = |e|)$ with a mass $m_{\mu} = 200 m_e$,where $m_e$ is the mass of the electron and $e$ is the elementary charge. If a $\mu^-$ is bound to a proton to form a hydrogen-like atom,identify the correct statements:
$(A)$ The radius of the muonic orbit is $200$ times smaller than that of the electron.
$(B)$ The speed of the $\mu^-$ in the $n^{th}$ orbit is $\frac{1}{200}$ times that of the electron in the $n^{th}$ orbit.
$(C)$ The ionization energy of the muonic atom is $200$ times more than that of a hydrogen atom.
$(D)$ The momentum of the muon in the $n^{th}$ orbit is $200$ times more than that of the electron.

In the reaction: 

X and Y are:  

$\frac{d}{dx} \left( \sqrt{3} \sin \left(2x + \frac{\pi}{3} \right) + \cos \left(2x + \frac{\pi}{3} \right) \right) =$ . . . . . .

Which of the following statements is not correct about a cloning vector?

Integrating factor of $x \frac{dy}{dx} - y = x^4 - 3x$ is

Let $\alpha, \beta \in R$ be such that $\lim _{x \rightarrow 0} \frac{x^2 \sin (\beta x)}{\alpha x-\sin x}=1$. Then $6(\alpha+\beta)$ equals

The wings of a bird and the wings of an insect are

If a charged spherical conductor of radius 10 cm has potential \( V \) at a point distant 5 cm from its centre, then the potential at a point 15 cm away from the centre will be:  

The structure of $XeOF_4$ is

The structure of $XeOF_4$ is

Aryl fluoride may be prepared from arene diazonium chloride using

An electron enters a chamber in which a uniform magnetic field is present as shown in the figure. Ignore gravity. During its motion inside the chamber:

If $\vec{u} = \hat{j} + 4\hat{k}$,$\vec{v} = \hat{i} + 3\hat{k}$ and $\vec{w} = \cos \theta \hat{i} + \sin \theta \hat{j}$ are vectors in $3$-dimensional space,then the maximum possible value of $|(\vec{u} \times \vec{v}) \cdot \vec{w}|$ is

Let $f:(-1,1) \rightarrow \mathbb{R}$ be such that $f(\cos 4 \theta) = \frac{2}{2-\sec^2 \theta}$ for $\theta \in \left(0, \frac{\pi}{4}\right) \cup \left(\frac{\pi}{4}, \frac{\pi}{2}\right)$. Then the value$(s)$ of $f\left(\frac{1}{3}\right)$ is (are):

The rate of gas phase chemical reactions generally increases rapidly with a rise in temperature. This is mainly because

The maximum number of existing transgenic animals is of which of the following?

The area bounded by the parabolas $y=4x^2$, $y=\frac{x^2}{9}$ and the line $y=2$ is

Let $C$ be the capacitance of a capacitor discharging through a resistor $R$. Suppose $t_{1}$ is the time taken for the energy stored in the capacitor to reduce to half its initial value and $t_{2}$ is the time taken for the charge to reduce to one-fourth its initial value. Then the ratio $t_{1} / t_{2}$ will be

For the reaction $A + B \rightarrow$ products,it is observed that
$(i)$ on doubling the initial concentration of $A$ only,the rate of reaction is also doubled and
$(ii)$ on doubling the initial concentration of both $A$ and $B$,there is a change by a factor of $8$ in the rate of the reaction.
The rate of this reaction is given by

The equation of the tangent to the curve $y=4 x e^{x}$ at $\left(-1, -\frac{4}{e}\right)$ is

Among the following,which is least acidic?

Which one of the following is most reactive towards electrophilic attack?

$\int \frac{dx}{\cos x + \sqrt{3} \sin x} =$

$\int \frac{\sin x+8 \cos x}{4 \sin x+6 \cos x} d x$ is equal to

At a telephone enquiry system,the number of phone calls regarding relevant enquiries follows a Poisson distribution with an average of $5$ phone calls during $10$-minute time intervals. The probability that there is at most one phone call during a $10$-minute time period is:

Two insulating plates are both uniformly charged in such a way that the potential difference between them is $V_2 - V_1 = 20\ V$ (i.e.,plate $2$ is at a higher potential). The plates are separated by $d = 0.1\ m$ and can be treated as infinitely large. An electron is released from rest on the inner surface of plate $1$. What is its speed when it hits plate $2$? $(e = 1.6 \times 10^{-19}\ C, m_e = 9.11 \times 10^{-31}\ kg)$

$3$-Phenylpropene on reaction with $HBr$ gives (as a major product)

Two sources of equal $emf$ $E$ are connected in series to an external resistance $R$. The internal resistances of the two sources are $R_1$ and $R_2$ $(R_2 \gt R_1)$. If the potential difference across the source having internal resistance $R_2$ is zero,then:

Lead concentration in blood is considered alarming if it is

Assertion : Energy is released in nuclear fission.
Reason : Total binding energy of the fission fragments is larger than the total binding energy of the parent nucleus.

$A$ minimum value of $\int_0^x t e^{t^2} d t$ is

People recovering from a long illness are advised to include the alga $Spirulina$ in their diet because it:

In the following reaction,$X$ and $Y$ respectively are:
$C_2H_5OH$ $\xrightarrow{KMnO_4 / H^+} X$ $\xrightarrow{C_2H_5OH / H_2SO_4, \Delta} CH_3COOC_2H_5$

The exon part of $m-RNA$ codes for .............

Anemophilous pollination is mainly observed in

If $h(x) = x^{x^x}$, then at $x = 1$, $\frac{h^{\prime}(x)}{h(x)}$ is equal to

Electrolytic reduction of alumina to aluminium by the Hall-Heroult process is carried out in the presence of:

Which of the following is a common feature between $DNA$ and $RNA$?

The resistance of $0.01 \ N$ $NaCl$ solution at $25 \ ^oC$ is $200 \ \Omega$. The cell constant of the conductivity cell is $1 \ cm^{-1}$. The equivalent conductance is:

In an isolated parallel plate capacitor of capacitance $C$,the four surfaces have charges $Q_1$,$Q_2$,$Q_3$,and $Q_4$ as shown. The potential difference between the plates is

$A$ metal rod moves at a constant velocity in a direction perpendicular to its length. $A$ constant uniform magnetic field exists in space in a direction perpendicular to the rod as well as its velocity. Select the correct statement$(s)$ from the following.

The chemical knives of $DNA$ are:

The ability of an ion to bring about coagulation of a given colloid depends upon

The branch of medicine which is associated with the diagnosis,prevention,and treatment of mental disorders is:

Which one of the following is an exotic fish species introduced in India?

Phenol is treated with bromine water and shaken well. The white precipitate formed during the process is

Which one of the following causes plague?

Let $f(x) = (x + 1)^2 - 1$ for $x \ge -1$. Then the set $S = \{ x : f(x) = f^{-1}(x) \}$ is

The frequency of a mutant gene in a population is expected to increase, if the gene is

In $F_{2}$-generation,quantitative inheritance $1: 4: 6: 4: 1$ is obtained instead of

In Mr. Kapoor,there is a pair of autosomal genes $Bb$ and a sex-linked factor $d$. What will be the proportion of $Bd$ in his sperm?

Increasing the temperature of an aqueous solution will cause

The energy released in a typical nuclear fusion reaction is approximately..........$MeV$.

Usually,the recessive character is expressed only when present in a double recessive condition. However,a single recessive gene can express itself in human beings when the gene is present on

The unfertilized egg of a human contains,or when released from the ovary,the human egg contains:

$CH_2=CH_2$ is a

The dehydrohalogenation of neopentyl bromide with alcoholic $KOH$ mainly gives

$\int \frac{\cos \sqrt{x}}{\sqrt{x}} dx =$

$n$ equal resistors are first connected in series and then connected in parallel. What is the ratio of the maximum to the minimum resistance?

Which of the following is not known?

Two particles $X$ and $Y$ having equal charges are being accelerated through the same potential difference. Thereafter,they enter normally into a region of uniform magnetic field and describe circular paths of radii $R_1$ and $R_2$ respectively. The mass ratio of $X$ and $Y$ is:

If $a, b, c$ are three non-coplanar vectors and $p, q, r$ are defined by the relations $p = \frac{b \times c}{[a, b, c]}, q = \frac{c \times a}{[a, b, c]}, r = \frac{a \times b}{[a, b, c]}$,then $(a+b) \cdot p + (b+c) \cdot q + (c+a) \cdot r =$

The number of vectors of unit length perpendicular to vectors $a = (1, 1, 0)$ and $b = (0, 1, 1)$ is

Methyl ethyl ketone is prepared by the oxidation of

The solution of the differential equation $x \frac{dy}{dx} = y(\log y - \log x + 1)$ is

In the electrolysis of alumina $(Al_2O_3)$,cryolite $(Na_3AlF_6)$ is added to:

$A$ convex lens $A$ of focal length $20 \, cm$ and a concave lens $B$ of focal length $5 \, cm$ are kept along the same axis with a distance $d$ between them. If a parallel beam of light falling on $A$ leaves $B$ as a parallel beam,then the distance $d$ in $cm$ will be:

If $a = (1, 1, 1)$ and $c = (0, 1, -1)$ are two vectors and $b$ is a vector such that $a \times b = c$ and $a \cdot b = 3$,then $b$ is equal to

The capacity of a capacitor is $4 \times 10^{-6} \, F$ and its potential is $100 \, V$. The energy released on discharging it fully will be ....... $J$.

The system of equations $\lambda x + y + z = 0, -x + \lambda y + z = 0, -x - y + \lambda z = 0$ will have a non-zero solution if real values of $\lambda$ are given by

If $a = i + 2j + 2k$ and $b = 3i + 6j + 2k,$ then a vector in the direction of $a$ and having magnitude as $|b|$ is

$\int_0^{\pi /4} {\frac{{\sin x + \cos x}}{{9 + 16\sin 2x}}\,dx = }$

$A$ determinant is chosen at random from the set of all determinants of order $2$ with elements $0$ or $1$ only. The probability that the value of the chosen determinant is positive is:

In the manufacture of iron,limestone is added to the blast furnace. The calcium ion ends up in the form of:

Which substance eliminates bromine from $KBr$ solution?

If uranium (mass number $238$ and atomic number $92$) emits an $\alpha$-particle,what are the mass number and atomic number of the product?

One of the constituents of German silver is:

What is the composition of Lucas reagent?

In the figure below,what is the potential difference between the points $A$ and $B$ and between $B$ and $C$ respectively in steady state?

If $f(x) = x \tan^{-1} x$,then $f'(1) =$

$\mathop {\lim }\limits_{x \to a} \frac{{\sqrt {a + 2x} - \sqrt {3x} }}{{\sqrt {3a + x} - 2\sqrt x }} = \dots$ (where $a \ne 0$)

$\int \frac{x}{1 + x^4} \, dx =$

$\int \frac{1 + x^2}{\sqrt{1 - x^2}} dx =$

$\int (\log x)^2 \, dx =$

$\mathop {\lim }\limits_{x \to 1} \frac{x - 1}{2x^2 - 7x + 5} =$

$\mathop {\lim }\limits_{\theta \to \pi /2} (\sec \theta - \tan \theta ) =$

$\int {\frac{{{x^5}dx}}{{\sqrt {1 + {x^3}} }}} =$

The probability that $A$ speaks the truth is $\frac{4}{5}$,while the probability that $B$ speaks the truth is $\frac{3}{4}$. What is the probability that they contradict each other when asked to speak on a fact?

$\mathop {\lim }\limits_{x \to 0} \frac{{\tan x - \sin x}}{{{x^3}}} =$

$\int x^2 \sin 2x \, dx =$

$\mathop {\lim }\limits_{x \to \pi /2} \frac{2x - \pi}{\cos x} =$

If $f(x) = \begin{cases} \frac{x^2 - 4x + 3}{x^2 - 1}, & x \ne 1 \\ 2, & x = 1 \end{cases}$,then:

$\int x \cos^2 x \, dx =$

$\int (\log x)^2 \, dx =$

$\mathop {\lim }\limits_{x \to 0} \frac{{\tan 2x - x}}{{3x - \sin x}} =$

The ratio between the total intensity of the magnetic field at the equator to the poles is:

The area of the triangle formed by the points $(a, b + c)$,$(b, c + a)$,and $(c, a + b)$ is: