Class 11 previous year questions (PYQ)

The correct order of atomic radii in Group 13 elements is:  

Uric acid is formed by:  

Choose the correct answer from the options given below:  

If a line $L$ passing through a point $A(2, 3)$ intersects another line $4x - 3y - 19 = 0$ at the point $B$ such that $AB = 4$,then the angle made by the line $L$ with the positive $X$-axis in the anti-clockwise direction is

Identify the amino acid which has $-NH_2$,$-CO_2H$ and $-CONH_2$ groups.

If $\sin x = -\frac{3}{5}$,where $\pi \lt x \lt \frac{3\pi}{2}$,then $80(\tan^2 x - \cos x)$ is equal to:

A small sphere of mass m and radius r slides down the smooth surface of a large hemispherical bowl of radius R. If the sphere starts sliding from rest, the total kinetic energy of the sphere at the lowest point A of the bowl will be:
(given, moment of inertia of sphere = 2/5 mr^2)

Given below are two statements:
Statement $I$: The forces generated by transpiration can lift a xylem-sized column of water over $130 \text{ meters}$ in height.
Statement $II$: Transpiration cools leaf surfaces,sometimes by $10$ to $15$ degrees,through evaporative cooling.
In the light of the above statements,choose the most appropriate answer from the options given below:

Assertion $(A)$: In aqueous solution,amino acids exist in dipolar ion form.
Reason $(R)$: Most of the naturally occurring amino acids have $L$-configuration.
The correct option among the following is:

Unidirectional transmission of a nerve impulse through nerve fibre is due to the fact that  

$A$ particle is moving along a circular path with constant speed and centripetal acceleration '$a$'. If the speed is doubled,the ratio of its acceleration after and before the change is:

$A$ mass of gas occupies $11.2 \ dm^3$ at $105 \ kPa$. What is its volume if the pressure is increased to $210 \ kPa$ at constant temperature (in $dm^3$)?

For the hyperbola $x^2-y^2-4x+2y+c=0$,if the focus is $S(2+2\sqrt{2}, k)$ and the directrix that is adjacent to $S$ is $x=2+\sqrt{2}$,then $c=$

$25 \ mL$ of $0.1 \ N \ NaOH$ solution neutralises $12.5 \ mL$ of $HCl$ solution. The amount of water needed to convert $500 \ mL$ of such $HCl$ solution to $0.1 \ N$ is (in $mL$)

The density of a material in $SI$ units is $128 \ kg \ m^{-3}$. In a system of units where the unit of length is $25 \ cm$ and the unit of mass is $50 \ g$,the numerical value of the density of the material is:

If \(\alpha, \beta\) are the roots of the equation  
\(x^2 - (5 + 3\sqrt{\log_3 5} - 5\sqrt{\log_5 3})x + 3(3^{\log_3 5})^{1/3} - 5(\log_5 3)^{2/3} - 1 = 0\),  

then the equation whose roots are \(\alpha + \frac{1}{\beta}\) and \(\beta + \frac{1}{\alpha}\) is  

If the angle between the circles $x^2+y^2-12x-6y+41=0$ and $x^2+y^2+kx+6y-59=0$ is $45^{\circ}$,then a value of $k$ is

If a number is chosen at random from the four-digit numbers formed by using the digits $0, 1, 2, 3, 4, 6$ without repetition,then the probability that it is divisible by $4$ is

The number of real solutions of the equation $2 \sin 3x + \sin 7x - 3 = 0$ which lie in the interval $[-2\pi, 2\pi]$ is

The number of ways of awarding $9$ scholarships among $3$ students so that each may have $3$ scholarships is

The angle of intersection between the curves $y^2+x^2=a^2 \sqrt{2}$ and $x^2-y^2=a^2$ is

Among the following, which is not true for ultraviolet light?  

The value of \(\cos 1200^\circ+\tan 1485^\circ\) is

$A$ particle of mass $2\, kg$ is on a smooth horizontal table and moves in a circular path of radius $0.6\, m$. The height of the table from the ground is $0.8\, m$. If the angular speed of the particle is $12\, rad\, s^{-1}$,the magnitude of its angular momentum about a point on the ground right under the centre of the circle is ........ $kg\, m^2\, s^{-1}$.

The order of decreasing ease of abstraction of hydrogen atoms in the following molecule is:

The total length of a sonometer wire between fixed ends is $110 \ cm$. Two bridges are placed to divide the length of the wire in the ratio $6 : 3 : 2$. The tension in the wire is $400 \ N$ and the mass per unit length is $0.01 \ kg/m$. What is the minimum common frequency with which the three parts can vibrate in $Hz$?

$A$ glass flask of volume $1 \ L$ is filled completely with mercury at $0^{\circ} C$. The flask is now heated to $100^{\circ} C$. The coefficient of volume expansion of mercury is $1.82 \times 10^{-4} /{ }^{\circ} C$ and the coefficient of linear expansion of glass is $0.1 \times 10^{-4} /{ }^{\circ} C$. During this process, the amount of mercury which overflows is (in $cc$)

$A$ ray of light along $x + \sqrt{3}y = \sqrt{3}$ gets reflected upon reaching the $x$-axis. The equation of the reflected ray is:

Given the circle $C$ with the equation $x^2+y^2-2x+10y-38=0$. Match the List-$I$ with the List-$II$ given below concerning $C$.

It is possible to project a particle with a given velocity in two possible ways so as to make them pass through a point $P$ at a horizontal distance $r$ from the point of projection. If $t_1$ and $t_2$ are times taken to reach this point in two possible ways,then the product $t_1 t_2$ is proportional to

Let $a_1, a_2, a_3, \ldots, a_{100}$ be an arithmetic progression with $a_1=3$ and $S_p=\sum_{i=1}^p a_i, 1 \leq p \leq 100$. For any integer $n$ with $1 \leq n \leq 20$,let $m=5n$. If $\frac{S_m}{S_n}$ does not depend on $n$,then $a_2$ is

Assertion: Bulliform cells are useful in the unrolling of leaf.
Reason: Bulliform cells store water.

The sum of the angles of elevation of the top of a tower from two points distant $a$ and $b$ from the base and in the same straight line with it is $90^{\circ}$. Then,the height of the tower is

Assertion : Benzene removes a butter stain from a table cloth.
Reason : Butter has an affinity towards benzene.

Assertion : Both $Be$ and $Al$ can form complexes such as $BeF_4^{2-}$ and $AlF_6^{3-}$ respectively,$BeF_6^{3-}$ is not formed.
Reason : In case of $Be$,no vacant $d-$ orbitals are present in its outermost shell.

If the mean deviation of the numbers $1, 1+d, 1+2d, \dots, 1+100d$ from their mean is $255$,then $d$ is equal to:

Methoxy methane and ethanol are:

The sum of the fourth powers of the roots of the equation $x^3+x+1=0$ is

$A$ particle executing simple harmonic motion has a kinetic energy $K = K_0 \cos^2(\omega t)$. The maximum values of the potential energy and the total energy are respectively:

The inverse point of $(1, 2)$ with respect to the circle $x^2 + y^2 - 4x - 6y + 9 = 0$ is

The concentration of oxalic acid is '$x$' $mol \ L^{-1}$. $40 \ mL$ of this solution reacts with $16 \ mL$ of $0.05 \ M$ acidified $KMnO_4$. What is the $pH$ of '$x$' $M$ oxalic acid solution? (Assume that oxalic acid dissociates completely)

If $\alpha, \beta, \gamma$ are the roots of the equation $x^3-6x^2+11x+6=0$,then $\Sigma \alpha^2 \beta+\Sigma \alpha \beta^2$ is equal to :

In $\Delta ABC$,the expression $a(\cos^2 B + \cos^2 C) + \cos A(c \cos C + b \cos B)$ is equal to:

In $\Delta ABC$,the expression $a(\cos^2 B + \cos^2 C) + \cos A(c \cos C + b \cos B)$ is equal to:

Reaction of $HBr$ with propene in the presence of peroxide gives

$A$ ball is released from the top of a tower of height $h$ meters. It takes $T$ seconds to reach the ground. What is the position of the ball in $\frac{T}{3}$ seconds?

Which one of the following is not a buffer solution?

$\frac{1}{2!} + \frac{1+2}{3!} + \frac{1+2+3}{4!} + \ldots$ is equal to :

Vessels are found in $..........$.

The value of $\sum_{k=1}^3 \cos ^2\left((2 k-1) \frac{\pi}{12}\right)$ is equal to

$A$ child is swinging on a swing. The minimum and maximum heights of the swing from the earth's surface are $0.75\,m$ and $2\,m$ respectively. The maximum velocity of this swing is ............. $m/s$.

One litre of hard water contains $12.00 \ mg$ of $Mg^{2+}$. The milli-equivalents of washing soda $(Na_2CO_3)$ required to remove its hardness is:

Mortar is a mixture of

Birds are:

The antherozoids of $Funaria$ are ....

$ABA$ is involved in:

$A$ plant hormone used for inducing morphogenesis in plant tissue culture is

The position of both an electron and a helium atom is known within $1.0 \, nm$ and the momentum of the electron is known within $50 \times 10^{-26} \, kg \, m \, s^{-1}$. The minimum uncertainty in the measurement of the momentum of the helium atom is

The first use of quantum theory to explain the structure of the atom was made by

Which of the following statements is true for viruses?

The structure and hybridisation of $Si(CH_3)_4$ is

Which of the following is a micronutrient for plants?

$A$ homogeneous solid cylinder of length $L$ $(L \lt H/2)$ and cross-sectional area $A/5$ is immersed such that it floats with its axis vertical at the liquid-liquid interface with length $L/4$ in the denser liquid as shown in the figure. The lower density liquid is open to the atmosphere having pressure $P_0$. Then,the density $D$ of the solid is given by:

What is the structure of a prokaryotic flagellum?

Radial symmetry is generally exhibited by animals that have:

If the kidneys fail to reabsorb water,what effect will be observed on the tissues?

Pulses belong to which family?

$A$ solid sphere,a disc,and a solid cylinder,all of the same mass and made of the same material,are allowed to roll down from rest on an inclined plane. Then,which of the following is true?

The blastopore is the ....................

Turpentine is obtained from

$A$ particle of mass $m = 5$ is moving with a uniform speed $v = 3\sqrt{2}$ in the $XOY$ plane along the line $Y = X + 4$. The magnitude of the angular momentum of the particle about the origin is .......

What is the effect of Abscisic Acid $(ABA)$?

Zymogen cells and chief cells secrete

For the reaction ${H_2}_{(g)} + {I_2}_{(g)} \rightleftharpoons 2HI_{(g)}$ at $721 \ K$,the value of the equilibrium constant $({K_c})$ is $50$. When the equilibrium concentration of both is $0.5 \ M$,the value of ${K_p}$ under the same conditions will be:

If $a$ and $b$ are real numbers between $0$ and $1$ such that the points $z_1 = a + i$,$z_2 = 1 + bi$,and $z_3 = 0$ form an equilateral triangle,then

The gases respectively absorbed by alkaline pyrogallol and oil of cinnamon are:

$A$ cylinder of radius $R$ made of a material of thermal conductivity $K_1$ is surrounded by a cylindrical shell of inner radius $R$ and outer radius $2R$ made of material of thermal conductivity $K_2$. The two ends of the combined system are maintained at two different temperatures. There is no loss of heat across the cylindrical surface and the system is in steady state. The effective thermal conductivity of the system is

Where is $NADP^+$ reduced to $NADPH$?

Which of the following is not formed by the reaction of $Cl_2$ on $CH_4$ in sunlight?

Which of the following molecules has a zero dipole moment?

Exogenous application of gibberellins induces male flower formation on genetically female plants in

When $NaNO_3$ is heated in a closed vessel,$O_2$ is liberated and $NaNO_2$ is left behind. At equilibrium,

$70 \, cal$ of heat are required to raise the temperature of $2 \, moles$ of an ideal gas at constant pressure from $30^{\circ}C$ to $35^{\circ}C$. The amount of heat required to raise the temperature of the same gas through the same range ($30^{\circ}C$ to $35^{\circ}C$) at constant volume is ..... $cal$ $(R = 2 \, cal/mol \cdot K)$.

The compound that is most reactive towards electrophilic nitration is

An autonomic genome system is present in

The ${n^{th}}$ term of the series $3 \cdot 8 + 6 \cdot 11 + 9 \cdot 14 + 12 \cdot 17 + \dots$ will be

Two atoms have the same atomic mass but different atomic numbers. Such atoms are called as:

The roots of the quadratic equation $2x^2 + 3x + 1 = 0$ are:

The bond angle in a water molecule is nearly or directed bonds in water form an angle of:

If $n \in N$,then ${7^{2n}} + {2^{3n - 3}} \cdot {3^{n - 1}}$ is always divisible by

Among the given cations,the most stable carbonium ion is

The compound having both $sp$ and $sp^{2}$ hybridised carbon atoms is

The area of the circle whose centre is at $(1, 2)$ and which passes through the point $(4, 6)$ is

The thylakoids are removed and kept in a culture medium containing $CO_2$ and $H_2O$. If the setup is exposed to light,hexose sugars are not formed as the end product. The most appropriate reason for this is that

If the cube roots of unity are $1, \omega, \omega^2$,then the roots of the equation $(x - 1)^3 + 8 = 0$ are

Two vertices of a triangle are $(5, -1)$ and $(-2, 3)$. If the orthocentre is the origin,then the coordinates of the third vertex are:

If $9, x, y, z, a$ are in $A.P.$ such that $x + y + z = 15$,and $9, x, y, z, a$ are in $H.P.$ such that $\frac{1}{x} + \frac{1}{y} + \frac{1}{z} = \frac{5}{3}$,then the value of $a$ is:

One side of a rectangle lies along the line $4x + 7y + 5 = 0.$ Two of its vertices are $(-3, 1)$ and $(1, 1).$ Then the equations of the other three sides are

$A$ straight line moves such that the sum of the reciprocals of its intercepts on two perpendicular lines is constant. Then the line always passes through:

$2 \sin^2 \beta + 4 \cos(\alpha + \beta) \sin \alpha \sin \beta + \cos 2(\alpha + \beta) =$

The line $2x + 3y = 12$ meets the $x$-axis at $A$ and $y$-axis at $B$. The line through $(5, 5)$ perpendicular to $AB$ meets the $x$-axis,$y$-axis,and the $AB$ at $C, D,$ and $E$ respectively. If $O$ is the origin of coordinates,then the area of $OCEB$ is

How many numbers can be formed using the digits $0, 1, 2, 3, 4, 5$ that are greater than $3000$ (repetition is not allowed)?

$\sqrt{2} + \sqrt{3} + \sqrt{4} + \sqrt{6}$ is equal to

If ${a_1}, {a_2}, {a_3}, {a_4}$ are the coefficients of any four consecutive terms in the expansion of ${(1 + x)^n}$,then $\frac{{{a_1}}}{{{a_1} + {a_2}}} + \frac{{{a_3}}}{{{a_3} + {a_4}}}$ =

The sum of the series $6 + 66 + 666 + \dots$ up to $n$ terms is

$\frac{1}{\sin 10^\circ} - \frac{\sqrt{3}}{\cos 10^\circ} =$

The area of a parallelogram formed by the lines $ax \pm by \pm c = 0$ is

The sum of the series $1 \cdot 3^2 + 2 \cdot 5^2 + 3 \cdot 7^2 + \dots$ up to $20$ terms is

If $x = -5 + 2\sqrt{-4}$,then the value of the expression $x^4 + 9x^3 + 35x^2 - x + 4$ is

The radius of a circle which touches the $y$-axis at $(0,3)$ and cuts an intercept of $8$ units with the $x$-axis is

$A$ line $4x + y = 1$ passes through the point $A(2, -7)$ and meets the line $BC$,whose equation is $3x - 4y + 1 = 0$,at the point $B$. The equation of the line $AC$ such that $AB = AC$ is

The equation of the circle whose diameter is the line segment joining the points $(-4, 3)$ and $(12, -1)$ is:

$A$ spherical balloon of radius $r$ subtends an angle $\alpha$ at the eye of an observer. If the angle of elevation of the centre of the balloon is $\beta$,then the height of the centre of the balloon is:

If $\tan \theta + \sin \theta = m$ and $\tan \theta - \sin \theta = n,$ then

The orthocentre of the triangle formed by the lines $4x - 7y + 10 = 0$,$x + y = 5$,and $7x + 4y = 15$ is

If $a^{1/x} = b^{1/y} = c^{1/z}$ and $a, b, c$ are in $G.P.$,then $x, y, z$ will be in

Let $P(a \sec \theta, b \tan \theta)$ and $Q(a \sec \phi, b \tan \phi)$ where $\theta + \phi = \frac{\pi}{2}$ be two points on the hyperbola $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$. If $(h, k)$ is the point of intersection of the normals drawn at $P$ and $Q$,then $k=$

If a root of the equation $ax^2 + bx + c = 0$ is the reciprocal of a root of the equation $a'x^2 + b'x + c' = 0$,then:

The coefficient of $x^{-7}$ in the expansion of $\left( ax - \frac{1}{bx^2} \right)^{11}$ is

If $^{15}C_{3r} = ^{15}C_{r+3}$,then the value of $r$ is

If $(1 + x)^{15} = C_0 + C_1x + C_2x^2 + ...... + C_{15}x^{15},$ then $C_2 + 2C_3 + 3C_4 + .... + 14C_{15} =$

If $x, y, z$ are in $G.P.$ and $a^x = b^y = c^z$,then

The term independent of $x$ in the expansion of ${\left( {\sqrt {\frac{x}{3}} + \frac{3}{{2{x^2}}}} \right)^{10}}$ is:

An aeroplane flying horizontally $1 \ km$ above the ground is observed at an elevation of $60^\circ$ and after $10$ seconds the elevation is observed to be $30^\circ$. The uniform speed of the aeroplane in $km/h$ is

If the vertices of a triangle are $(2, 1), (5, 2)$ and $(3, 4)$,then its circumcentre is

$A$ vertical pole consists of two parts,the lower part being one third of the whole. At a point in the horizontal plane through the base of the pole and at a distance of $20 \, m$ from it,the upper part of the pole subtends an angle whose tangent is $\frac{1}{2}$. The possible heights of the pole are

If $2\sin^2 \theta = 3\cos \theta$,where $0 \le \theta \le 2\pi$,then $\theta =$

If $\sec x \cos 5x + 1 = 0$,where $0 \lt x \lt 2\pi$,then $x =$

One diagonal of a square is along the line $8x - 15y = 0$ and one of its vertices is $(1, 2)$. Then the equations of the sides of the square passing through this vertex are:

The sum of $n$ terms of the following series $1 + (1 + x) + (1 + x + x^2) + \dots$ will be

If the line segment joining the points $A(a, b)$ and $B(c, d)$ subtends an angle $\theta$ at the origin,then $\cos \theta$ is equal to

If $O$ is the origin and the coordinates of any two points $Q_1$ and $Q_2$ are $(x_1, y_1)$ and $(x_2, y_2)$ respectively,then $OQ_1 \cdot OQ_2 \cos \angle Q_1OQ_2 =$

Find the value of $\frac{18^3 + 7^3 + 3 \times 18 \times 7 \times 25}{3^6 + 6 \times 243 \times 2 + 15 \times 81 \times 4 + 20 \times 27 \times 8 + 15 \times 9 \times 16 + 6 \times 3 \times 32 + 64}$

If $A(6, 3)$,$B(-3, 5)$,$C(4, -2)$,and $D(x, 3x)$ are four points. If the ratio of the area of $\Delta DBC$ and $\Delta ABC$ is $1 : 2$,then the value of $x$ is: