Class 11 previous year questions (PYQ)

Directions: In the question below, a statement of Assertion (A) is followed by a statement of Reason (R). Choose the correct option:

Assertion (A): Systemic arteries have thick, elastic muscular walls compared to veins.

Reason (R): Arterial blood flows under high, pulsatile hydrostatic pressure generated by ventricular systole.

Refer to the Case Study 'Case Study: Parabolic Cable Geometry in Civil Engineering Suspension Bridges' to answer:

What is the vertical height of the suspension cable at a horizontal distance of $25\text{ m}$ from the bridge center?

Which hormone inhibits morphogenesis?  

Which part of the brain is responsible for thermoregulation?  

The main product of the following reaction is

Identify the step in the tricarboxylic acid cycle,which does not involve oxidation of the substrate.

Which activity from the following is exhibited by a $Lewis$ base according to its definition?

Which of the following reactions is not correct?

Which of the following statements with respect to endoplasmic reticulum is incorrect?

A car accelerates from rest at a constant rate of \(2\ \text{m/s}^2\) for some time. Then, it retards at a constant rate of \(4\ \text{m/s}^2\) and comes to rest. If the total time for which it remains in motion is \(3\ \text{s}\), what is the total distance travelled?

Through the point $(4, 5)$,a straight line is drawn making positive intercepts on the coordinate axes. The area of the triangle thus formed is least,when the ratio of the intercepts on the $X$ and $Y$ axes is

If $(4,7)$ and $(-2,-1)$ are ends of a diameter of a circle which intersects $X$-axis at $A$ and $B$,then $AB$ is equal to

A gas is compressed adiabatically, which one of the following statement is NOT true.  

The increasing order of reactivity of alkaline earth metals with water is

Let the length of the latus rectum of an ellipse with its major axis along the $x$-axis and center at the origin be $8$. If the distance between the foci of this ellipse is equal to the length of its minor axis,then which one of the following points lies on it?

The transverse section of a plant shows following anatomical features:  
(a) Large number of scattered vascular bundles surrounded by bundle sheath.  
(b) Large conspicuous parenchymatous ground tissue.  
(c) Vascular bundles conjoint and closed.  
(d) Phloem parenchyma absent.  
Identify the category of plant and its part:  

$A$ bead of mass $m = 100 \,g$ is attached to one end of a spring of natural length $L$ and spring constant $k = \frac{(\sqrt{3}+1) mg}{L}$. The other end of the spring is fixed at point $A$ on a smooth vertical ring of radius $R$. The bead is at point $B$ such that the spring makes an angle of $30^{\circ}$ with the horizontal diameter. The normal reaction at $B$ just after it is released to move is (take $g = 9.8 \,ms^{-2}$): (in $\,N$)

The normal at a point $\theta$ to the curve $x=a(1+\cos \theta), y=a \sin \theta$ always passes through the fixed point

The converse of \(((\sim p) \wedge q) \Rightarrow r\) is  

In the manufacture of hydrogen from water gas $(CO + H_2)$,which of the following is the correct statement?

The sum of all $4$-digit numbers that can be formed using the digits $2, 3, 4, 5, 6$ without repetition is:

A solid sphere is rotating freely about its symmetry axis in free space. The radius of the sphere is increased keeping its mass same. Which of the following physical quantities would remain constant for the sphere?

Which statements(s) is (are) false for the periodic classification of elements?

In a data,if the number $i$ is repeated $i$ times for $i=1, 2, \ldots, n$,then the mean of the data is

The locus of the foot of the perpendicular drawn from the centre of the ellipse $x^2 + 3y^2 = 6$ to any tangent to it is:

Density of carbon monoxide is maximum at

Accumulation of lactic acid $(HC_3H_5O_3),$ a monobasic acid in tissues,leads to pain and a feeling of fatigue. In a $0.10 \ M$ aqueous solution,lactic acid is $3.7 \%$ dissociated. The value of the dissociation constant,$K_a,$ for this acid will be:

Which of the following represents the correct order of increasing first ionization enthalpy for $Ca, Ba, S, Se$ and $Ar$?

An open vessel at $300 \ K$ is heated until $2/5$ of the air in it is expelled. Assuming that the volume of the vessel remains constant,the temperature to which the vessel is heated is $..... \ K$.

The statement that is $TRUE$ among the following is:

$A$ box is moved along a straight line by a machine delivering constant power. The distance moved by the body in time $t$ is proportional to

The decreasing order of wavelength of infrared,microwave,ultraviolet,and gamma rays is:

Identify the components labelled $A, B, C$ and $D$ in the diagram below from the list $(i)$ to $(viii)$ given along with:
Components:
$(i)$ Cristae of mitochondria
$(ii)$ Inner membrane of mitochondria
$(iii)$ Cytoplasm
$(iv)$ Smooth endoplasmic reticulum
$(v)$ Rough endoplasmic reticulum
$(vi)$ Mitochondrial matrix
$(vii)$ Cell vacuole
$(viii)$ Nucleus
The correct components are:

$A$ buffer solution contains $0.1 \ mol$ of sodium acetate in $1000 \ cm^{3}$ of $0.1 \ M$ acetic acid. To the above buffer solution,$0.1 \ mol$ of sodium acetate is further added and dissolved. The $pH$ of the resulting buffer is equal to

From the following bond energies:

$A$ planet revolves around the sun in an elliptical orbit. The linear speed of the planet will be maximum at

The alkali metals form salt-like hydrides by direct synthesis at elevated temperatures. The thermal stability of these hydrides decreases in which of the following orders?

The velocity of electromagnetic radiation in a medium of permittivity $\varepsilon_0$ and permeability $\mu_0$ is given by:

$A$ plant requires magnesium for

Calculate the change in internal energy $(\Delta U)$ if $\Delta H = -92.2\, kJ$,$P = 40\, atm$,and $\Delta V = -1\, L$.

Observe the following statements:
$I$. The circle $x^2+y^2-6x-4y-7=0$ touches the $y$-axis.
$II$. The circle $x^2+y^2+6x+4y-7=0$ touches the $x$-axis.
Which of the following is a correct statement?

Two solid spheres $A$ and $B$ made of the same material have radii $r_A$ and $r_B$ respectively. Both the spheres are cooled from the same temperature under the conditions valid for Newton's law of cooling. The ratio of the rate of change of temperature of $A$ and $B$ is :

Which one of the following statements regarding enzyme inhibition is correct?

An electron is moving in Bohr's fourth orbit. Its de-Broglie wavelength is $\lambda$. What is the circumference of the fourth orbit?

The shape of $O_2F_2$ is similar to that of

In the given conformation,if $C_2$ is rotated about the $C_2-C_3$ bond anticlockwise by an angle of $120^{\circ}$,then the conformation obtained is:

The focal chord to $y^2 = 16x$ is tangent to $(x - 6)^2 + y^2 = 2$. Then,the possible values of the slope of this chord are:

Assertion : $trans-2-Butene$ on reaction with $Br_2$ gives $meso-2,3-dibromobutane$.
Reason : The reaction involves $syn-addition$ of bromine.

Which type of cartilage is found at the ends of long bones?

In a compound,$C$,$H$,and $N$ atoms are present in $9 : 1 : 3.5$ by weight. The molecular weight of the compound is $108$. What is the molecular formula of the compound?

Two particles having mass $M$ and $m$ are moving in a circular path having radius $R$ and $r$. If their time periods are the same,then the ratio of their angular velocities will be:

In a $\triangle ABC$,the expression $\frac{\cos C+\cos A}{c+a}+\frac{\cos B}{b}$ is equal to

Plants absorb $Zn$ in the form of:

Which of the following has the highest nucleophilicity?

Which of the following helps in the absorption of water and mineral salts?

Cystoliths, sometimes deposited in plant cells, are crystals of (aggregation of)

Which one among the following chemicals is used for causing defoliation of forest trees?

$A$ few organisms are known to grow and multiply at temperatures of $100-105^{\circ}C$. They belong to:

Haemoglobin is

$A$ black body is at a temperature of $500 \; K$. It emits energy at a rate which is proportional to:

Bryophytes are called the amphibians of the plant kingdom because:

The specimen used for the original publication by the author is known as:

Which one of the following statements about glycogen is correct?

$A$ simple pendulum with a bob of mass $m$ oscillates from $A$ to $C$ and back to $A$ such that $PB$ is $H$. If the acceleration due to gravity is $g$,then the velocity of the bob as it passes through $B$ is

The equation $2x^2 + 3y^2 - 8x - 18y + 35 = k$ represents:

The table shown below gives the bond dissociation energies $E_{diss}$ for single covalent bonds of carbon $C$ atoms with elements $A, B, C$ and $D.$ Which element has the smallest atoms?

For $0 \lt \phi \lt \frac{\pi}{2}$,if $x = \sum_{n=0}^\infty \cos^{2n}\phi$,$y = \sum_{n=0}^\infty \sin^{2n}\phi$,and $z = \sum_{n=0}^\infty \cos^{2n}\phi \sin^{2n}\phi$,then:

Which of the following is of considerable economic importance?

In which of the following plants,cotyledons form the first pair of leaves?

Epipetalous and syngenesious stamens occur in

The vectors $\vec{A}$ and $\vec{B}$ are such that $|\vec{A}+\vec{B}|=|\vec{A}-\vec{B}|$. The angle between the two vectors is: (in $^{\circ}$)

The dimensional formula of permeability of free space $\mu_0$ is

An enthusiastic professor,wanting to demonstrate a physiological process,placed soaked mustard seeds in a glass jar and kept it in a corner before starting the lecture. At the end of the lecture,a sudden explosion occurred,and the glass jar shattered into pieces. Which of the following processes was the professor trying to demonstrate?

The maximum range of a gun on horizontal terrain is $16 \, km$. If $g = 10 \, m/s^2$,what must be the muzzle velocity of the shell in $m/s$?

If we use phenolphthalein as an indicator in a titration of $Na_2CO_3$ with $HCl$,the usual result is:

The pigment phytochrome is involved in:

The cork cambium (phellogen) is formed from:

The dimensional formula for angular momentum is

If $\frac{2x}{2x^2 + 5x + 2} \gt \frac{1}{x + 1}$,then

The bond between carbon atom $(1)$ and carbon atom $(2)$ in compound $N \equiv C - CH = CH_2$ involves the hybridised carbon as

The atmosphere is held to the earth by

The equation of the line passing through the points of intersection of the circles $3x^2 + 3y^2 - 2x + 12y - 9 = 0$ and $x^2 + y^2 + 6x + 2y - 15 = 0$ is

The molecules of a given mass of a gas have a $r.m.s.$ velocity of $200 \, m/s$ at $27^{\circ}C$ and $1.0 \times 10^5 \, N/m^2$ pressure. When the temperature is $127^{\circ}C$ and pressure is $0.5 \times 10^5 \, N/m^2$,the $r.m.s.$ velocity in $m/s$ will be

$A$ mass $m$ is moving with a constant velocity $v$ along a line parallel to the $X$-axis. Its angular momentum with respect to the origin or the $Z$-axis is:

The equations of two equal sides of an isosceles triangle are $7x - y + 3 = 0$ and $x + y - 3 = 0$. If the third side passes through the point $(1, -10)$,then the equation of the third side is:

The $IUPAC$ name of $(CH_3)_3C-CH=CH_2$ is

$A$ student has identified a triploblastic,coelomate,segmented animal as an arthropod. Which additional character should the student have verified before identifying that animal as an arthropod?

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

What is the normality of a $1 \, M$ solution of $H_3PO_4$?

Find the total number of $9$ digit numbers which have all the digits different.

Two tangents $PQ$ and $PR$ are drawn to the circle $x^2 + y^2 - 2x - 4y - 20 = 0$ from the point $P(16, 7)$. If the centre of the circle is $C$,then the area of quadrilateral $PQCR$ is ............ $sq. \text{ units}$.

The equation $\frac{x^2}{1 - r} - \frac{y^2}{1 + r} = 1$ for $r \gt 1$ represents:

$A$ wire of length $L$ and radius $r$ is rigidly fixed at one end. On stretching the other end of the wire with a force $F$,the increase in its length is $l$. If another wire of same material but of length $2L$ and radius $2r$ is stretched with a force of $2F$,the increase in its length will be

If ${x^2} + px + 1$ is a factor of the expression $a{x^3} + bx + c$,then

If $\cos(\alpha + \beta) = \frac{4}{5}$ and $\sin(\alpha - \beta) = \frac{5}{13}$,where $0 \le \alpha, \beta \le \frac{\pi}{4}$,then $\tan 2\alpha =$

The points $(-a, -b)$,$(0, 0)$,$(a, b)$,and $(a^2, ab)$ are

Six '$X$'s have to be placed in the squares of the figure such that each row contains at least one '$X$'. In how many different ways can this be done?

If $x = a + b$,$y = a\alpha + b\beta$,and $z = a\beta + b\alpha$,where $\alpha$ and $\beta$ are complex cube roots of unity,then $xyz$ =

For every natural number $n$,${3^{2n + 2}} - 8n - 9$ is divisible by

$A$ 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:

The points on the line $x + y = 4$ which lie at a unit distance from the line $4x + 3y = 10$ are

Numbers greater than $1000$ but not greater than $4000$ which can be formed with the digits $0, 1, 2, 3, 4$ (repetition of digits is allowed),are

In how many ways can $5$ boys and $5$ girls sit in a circle so that no two boys sit together?

To double the volume of a given mass of an ideal gas at $27^{\circ}C$ keeping the pressure constant,one must raise the temperature in degrees Celsius to ....... $^{\circ}C$.

$\tan 20^\circ \tan 40^\circ \tan 60^\circ \tan 80^\circ =$

The equation of the lines which pass through the point $(3, -2)$ and are inclined at $60^o$ to the line $\sqrt{3}x + y = 1$ is:

The equation of the base of an equilateral triangle is $x + y = 2$ and the vertex is $(2, -1)$. The length of the side of the triangle is

The number of ways in which five identical balls can be distributed among ten identical boxes such that no box contains more than one ball is:

If $n$ is an integer greater than $1$,then $a - ^nC_1(a - 1) + ^nC_2(a - 2) + \dots + (-1)^n(a - n) =$

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

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

If $A, B, C, D$ are the angles of a cyclic quadrilateral,then $\cos A + \cos B + \cos C + \cos D =$

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

If $x$ is real,the expression $\frac{x + 2}{2x^2 + 3x + 6}$ takes all values in the interval

The quadratic equation in $t$,such that the $A.M.$ of its roots is $A$ and the $G.M.$ of its roots is $G$,is

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 the roots of the equation $\frac{1}{x + p} + \frac{1}{x + q} = \frac{1}{r}$ are equal in magnitude but opposite in sign,then the product of the roots will be

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

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 $\omega$ is a cube root of unity,then the value of $(1 - \omega + \omega^2)^5 + (1 + \omega - \omega^2)^5$ 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 $\sec x \cos 5x + 1 = 0$,where $0 \lt x \lt 2\pi$,then $x =$

If $\sec 4\theta - \sec 2\theta = 2$,then the general value of $\theta$ is

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

The vertices of a triangle are $(2, 1)$,$(5, 2)$ and $(4, 4)$. The lengths of the perpendiculars from these vertices to the opposite sides are

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 $OQ_1 \cdot OQ_2 \cos \angle Q_1OQ_2 =$

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:

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