This practice test consists of AIEEE 2007 questions to help you practice for actual AIEEE main examination.

AIEEE 2007 Paper

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Question

In a geometric progression consisting of positive terms, each term equals the sum of the next two terms. Then the common ratio of this progression equals

Possible Answers

Selected	Possible Answer
	$\frac {1}{2}(1-\sqrt{5})$
	$\sqrt{5}$
	$\frac {1}{2} \sqrt{5}$
	$\frac {1}{2} (\sqrt{5}-1)$

Question

If $sin^{-1} \Bigg ( \cfrac {X}{5} \Bigg ) cosec^{-1} \Bigg ( \cfrac {5}{4} \Bigg ) = \cfrac {\pi}{2}$ then a value of x is

Possible Answers

Selected	Possible Answer
	3
	1
	4
	5

Question

In the binomial expansion of $(a-b)^n, n \underline > 5$ ,the sum of $5^{th},$ and $6^{th}$ terms is zero, then $\frac {a}{b}$ equals

Possible Answers

Selected	Possible Answer
	$\frac {6}{n-5}$
	$\frac {5}{n-4}$
	$\frac {n-5}{6}$
	$\frac {n-4}{5}$

Question

The set S = {1, 2, 3, …, 12} is to be partitioned into three sets A, B, C of equal size. Thus, $A \cup B \cup C = S, A \cap B = B \cap C = A \cap C = \phi$ the number to partition S is

Possible Answers

Selected	Possible Answer
	$\frac {12!}{3!(3!)^4}$
	$\frac {12 !}{3!(4!)^3}$
	$\frac {12!}{3!}^4$
	$\frac {12!}{4!^3}$

Question

The differential equation of all circles passing through the origin and having their centres on the x-axis is

Possible Answers

Selected	Possible Answer
	$x^2 = y^2 + 3xy \cfrac{dy}{dx}$
	$x^2 = y^2 + xy \cfrac{dy}{dx}$
	$y^2 = x^2 +2 xy \cfrac{dy}{dx}$
	$y^2 = x^2 - 2xy \cfrac{dy}{dx}$

Question

The largest interval lying in $\big (-\frac{\pi}{2}, \frac{\pi}{2}\big )$ for which function

$\big [ f(x) = 4^{-x^2} + \cos^{-1}$ $\big ( \frac{x}{2} - 1 \big )$ $+ \log (\cos x) \big ]$ is defined, is

Possible Answers

Selected	Possible Answer
	$\big [ - \frac{\pi}{4} , \frac{\pi}{2}\big )$
	$[0, \pi]$
	$\big [- \frac{\pi}{2} , \frac{\pi}{2} \big )$
	$[0 , \frac{\pi}{2} )$

Question

A body weighing 13 kg is suspended by two strings 5 m and 12 m long, their other ends being fastened to the extremities of a rod 13 m long. If the rod be so held that the body hangs immediately below the middle point. The tensions in the strings are

Possible Answers

Selected	Possible Answer
	5 kg and 12 kg
	5 kg and 13 kg
	12 kg and 13 kg
	5 kg and 5 kg

Question

A pair of fair dice is thrown independently three times. The probability of getting a score of exactly 9 twice is

Possible Answers

Selected	Possible Answer
	8/243
	1/729
	8/729
	8/9

Question

Consider a family of circles which are passing through the point (−1, 1) and are tangent to xaxis. If (h, k) are the co-ordinates of the centre of the circles, then the set of values of k is given by the interval.

Possible Answers

Selected	Possible Answer
	$k \underline < \frac{1}{2}$

	$k \underline > 1/2$
	$- \frac{1}{2} \underline <$ $k \underline < \frac{1}{2}$

Question

Let L be the line of intersection of the planes 2x + 3y + z = 1 and x + 3y + 2z = 2. If L makes an angles $\alpha$ with the positive x-axis, then $\cos \alpha$ equals

Possible Answers

Selected	Possible Answer
	$\frac{1}{2}$

	$\frac{1}{\sqrt{2}}$
	$\frac{1}{\sqrt{3}}$

Question

If p and q are positive real numbers such that p^2+q^2=1 , then the maximum value of (p+q) is

Possible Answers

Selected	Possible Answer
	1/2
	$\frac {1}{\sqrt{2}}$
	2
	$\sqrt{2}$

Question

A tower stands at the centre of a circular park. A and B are two points on the boundary of the park such that AB (= a) subtends an angle of $60^{\circ}$ at the foot of the tower, and the angle ofelevation of the top of the tower from A or B is $30^{\circ}$ . The height of the tower is

Possible Answers

Selected	Possible Answer
	$a \sqrt{3}$
	$2a \sqrt{3}$
	$\frac {a}{\sqrt{3}}$
	$2a \sqrt{3}$

Question

The Sum of the series
$^{20}C_0 - ^{20}C_1 + ^{20}C_2 -^{20}C_3$ $+ \cdot \cdot - \cdot \cdot +^{20}C_{10}$ is

Possible Answers

Selected	Possible Answer

	$^{20}C_{10}$
	$- ^{20}C_{10}$
	$\frac {1}{2}^{20}C_{10}$

Question

The normal to a curve at P(x, y) meets the x-axis at G. If the distance of G from the origin is twice the abscissa of P, then the curve is a

Possible Answers

Selected	Possible Answer
	circle
	parabola
	ellipse, hyperbola
	hyperbola
	ellipse

Question

If $|z+4| \underline < 3$ , then the maximum vlaue of |z+1| is

Possible Answers

Selected	Possible Answer
	6
	0
	4
	10

Question

The resultant of two forces P N and 3 N is a force of 7 N. If the direction of 3 N force were reversed, the resultant would be $\sqrt{19}$ N. The value of P is

Possible Answers

Selected	Possible Answer
	5N
	6N
	4N
	3N

Question

if then D is

Possible Answers

Selected	Possible Answer
	divisible by x but not y
	divisible by neither x nor y
	divisible by y but not x
	divisible by both x and y

Question

For the hyperbola $\cfrac {x^2}{\cos^2\alpha} -$ $\cfrac {y^2}{\sin^2 \alpha } =1$ , which of the following remains constant when $\alpha$ varies?

Possible Answers

Selected	Possible Answer
	abscissae of vertices
	eccentricity
	directrix
	abscissae of foci

Question

If a line makes an angle of $\frac {\pi}{4}$ with the positive directions of each of x-axis and y-axis, then the angle that the line makes with the positive direction of the z-axis is

Possible Answers

Selected	Possible Answer
	$\frac{\pi}{4}$
	$\frac{\pi}{3}$
	$\frac{\pi}{6}$
	$\frac{\pi}{2}$

Question

A value of C for which the conclusion of Mean Value Theorem holds for the function f(x) = log_e x on the interval [1, 3] is

Possible Answers

Selected	Possible Answer

	$\frac {1}{2} log_e 3$

Question

The Funcation $f(x)= \tan^{-1}$ $(\sin x + \cos x )$ is an increasing function in

Possible Answers

Selected	Possible Answer
	$\Bigg ( - \frac {\pi}{4},$ $\frac {\pi}{2} \Bigg )$
	$\Bigg ( \frac {\pi}{4},$ $\frac {\pi}{2} \Bigg )$
	$\Bigg ( 0,$ $\frac {\pi}{2} \Bigg )$
	$\Bigg (- \frac {\pi}{2},$ $\frac {\pi}{4} \Bigg )$

Question

Let if |A^2|= 25 , then $| \alpha |$ equals

Possible Answers

Selected	Possible Answer
	1
	1/5

	5

Question

The sum of the series $\frac {1}{2!}$ $- \frac {1}{3!}$ $+ \frac {1} {4!}-$ ..... upto infinity is

Possible Answers

Selected	Possible Answer
	$e^{-2}$
	$e^{- 1/2}$
	$e^{-1}$
	$e^{1/2}$

Question

If $\hat{u}$ and $\hat{v}$ are unit vectors and $\theta$ is the acute angle between them, then $2 \hat {u} * 3 \hat {v}$ is a unit vector for

Possible Answers

Selected	Possible Answer
	no value of $\theta$
	exactly two values of $\theta$
	exactly one value of $\theta$
	more than two values of $\theta$

Question

A particle just clears a wall of height b at distance a and strikes the ground at a distance c from the point of projection. The angle of projection is

Possible Answers

Selected	Possible Answer
	$45^{\circ}$
	$tan ^{-1} \cfrac {bc}{a(c-a)}$
	$tan ^{-1} \cfrac {b}{ac}$
	$tan ^{-1} \cfrac {bc}{a}$

Question

The average marks of boys in a class is 52 and that of girls is 42. The average marks of boys and girls combined is 50. The percentage of boys in the class is

Possible Answers

Selected	Possible Answer
	60
	40
	20
	80

Question

The equation of a tangent to the parabola y ^2 = 8 x is y = x+2 The point on this line from which the other tangent to the parabola is perpendicular to the given tangent is

Possible Answers

Selected	Possible Answer
	(2, 4)
	(−2, 0)
	(−1, 1)
	(0, 2)

Question

If (2, 3, 5) is one end of a diameter of the sphere x^2 + y^2 +z^2 -6x -12y -2z +20 =0 , then the coordinates of the other end of the diameter are

Possible Answers

Selected	Possible Answer
	(4, 9, -3)
	(4, -3, 3)
	(4, 3, -3)
	(4, 3, 5)

Question

Let A(h, k), B(1, 1) and C(2, 1) be the vertices of a right angled triangle with AC as its hypotenuse. If the area of the triangle is 1, then the set of values which ‘k’ can take is given by

Possible Answers

Selected	Possible Answer
	{-3,-2}
	{-1,3}
	{1,3}
	{0,2}

Question

Let P = (-1,0) , Q = (0,0) and $R = ( 3 ,3 \sqrt{3})$ be three points. The equation of the bisector of the angle PQR

Possible Answers

Selected	Possible Answer
	$\sqrt {3} x +y =0$
	$x + \sqrt {3} y =0$
	$\frac { \sqrt {3}}{2} x + y =0$
	$x + \frac {\sqrt {3}}{2} y =0$

Question

If one of the lines of my^2 + (1-m^2) xy - mx^2 = 0 is a bisector of the angle between the lines xy = 0 , then m is

Possible Answers

Selected	Possible Answer
	2
	1
	-1/2
	-2

Question

Let $F(x) = f(x) + f \Bigg ( \frac {1}{x} \Bigg )$ , where $f(x) = \overset {x} {\underset {1}{\int}}$ $\cfrac {\log t }{ 1+t} dt$ . Then F(e) equals

Possible Answers

Selected	Possible Answer
	0
	1/2
	2
	1

Question

Let f: R $\rightarrow$ R be a function defined by f(x) = Min {x + 1, |x| + 1}. Then which of the following is true?

Possible Answers

Selected	Possible Answer
	f(x) is not differentiable at x = 0
	f(x) is differentiable everywhere
	f(x) is not differentiable at x = 1
	$\underline > 1$ for all $x \in R$

Question

The Funcation $f: R \sim {0 }\rightarrow R$ Given by
$f (x) = \cfrac {1}{x} - \cfrac {2} {e^{2x}-1}$
Can be made continous at x = 0 b defining f(0) as

Possible Answers

Selected	Possible Answer
	2
	1
	0
	-1

Question

The solution for x of the equation

$\overset {x}{\underset {\sqrt {2}}{\int}}$ $\cfrac {dt}{\sqrt {t^2-1}} = \cfrac {\pi}{2}$ is

Possible Answers

Selected	Possible Answer
	$- \sqrt{2}$
	$2 \sqrt{2}$
	$\frac {\sqrt{3}}{2}$
	$\pi$

Question

$\int dx / (\cos x + \sqrt {3} \sin x)$ equals

Possible Answers

Selected	Possible Answer
	$\log \tan$ $\Big ( \frac {\pi}{2}$ $- \frac {\pi}{12} \Big ) +c$
	$\frac {1}{2} \log \tan$ $\Big ( \frac {\pi}{2}$ $+ \frac {\pi}{12} \Big ) +c$
	$\log \tan$ $\Big ( \frac {\pi}{2}$ $+ \frac {\pi}{12} \Big ) +c$
	$\frac {1}{2} \log \tan$ $\Big ( \frac {\pi}{2}$ $- \frac {\pi}{12} \Big ) +c$

Question

The area enclosed between the curves y^2 = x and y = |x| is

Possible Answers

Selected	Possible Answer
	2/3
	1/3
	1
	1/6

Question

If the difference between the roots of the equation x^2 + ax + 1 = 0 is less than $\sqrt {5}$ , then the set of possible values of a is

Possible Answers

Selected	Possible Answer
	$(- \infty, -3)$
	$(-3, \infty)$

	$(3,\infty)$

Question

Let $\overset {-}{a}$ $= \hat {i}+ \hat {j} + \hat {k}$ $, \overset {-}{b} = \hat {i}$ $- \hat {j} + 2 \hat {k}$ and $\overset {- }{c} = x \hat {i}$ $+ (x-2) \hat {j}= \hat {k}$ if If the vector $\overset {-}{c}$ lies in the plane of $\overset {-}{a}$ and $\overset {-}{b}$ , then x equals

Possible Answers

Selected	Possible Answer
	-4
	1
	-2
	0

Question

The displacement of an object attached to a spring and executing simple harmonic motion is given by $x = 2 * 10^{-2} \cos \pi t$ metres. The time at which the maximum speed first occurs is

Possible Answers

Selected	Possible Answer
	0.75 s
	0.5 s
	0.125 s
	0.25 s

Question

In an a.c. circuit the voltage applied is $E = E_0 \sin \quad \omega t$ The resulting current in the circuit is $l = l_0 \sin$ $\Big ( \omega t - \frac {\pi}{2} \Big )$ The power consumption in the circuit is given by

Possible Answers

Selected	Possible Answer
	$P = \frac {E_0 l_0}{2}$
	$P \sqrt {2}E_0l_0$

	$P = \frac {E_0 l_0}{\sqrt{2}}$

Question

An electric charge $10^{-3} \mu C$ is placed at the origin (0, 0) of X–Y co-ordinate system. Two points A and B are situated at $( \sqrt {2} , \sqrt {2})$ and (2, 0) respectively. The potential difference between the points A and B will be

Possible Answers

Selected	Possible Answer
	4.5 volt
	9 volt
	zero
	2 volt

Question

A battery is used to charge a parallel plate capacitor till the potential difference between the plates becomes equal to the electromotive force of the battery. The ratio of the energy stored in the capacitor and the work done by the battery will be

Possible Answers

Selected	Possible Answer
	1/4
	1/2
	1
	2

Question

An ideal coil of 10H is connected in series with a resistance of $5 \Omega$ and a battery of 5V. 2 second after the connection is made the current flowing in amperes in the circuit is

Possible Answers

Selected	Possible Answer
	$e^{-1}$


	$(1-e^{-1})$

Question

A long straight wire of radius ‘a’ caries a steady current i. The current is uniformly distributed across its cross section. The ratio of the magnetic field at $\cfrac {a}{2}$ and 2a is

Possible Answers

Selected	Possible Answer


	$\frac {1}{4}$
	$\frac {1}{2}$

Question

A current I flows along the length of an infinitely long, straight, thin walled pipe. Then

Possible Answers

Selected	Possible Answer
	the magnetic field is zero only on the axis of the pipe (
	the magnetic field at any point inside the pipe is zero
	the magnetic field is different at different points inside the pipe (
	the magnetic field at all points inside the pipe is the same, but not zero

Question

If MO is the mass of an oxygen isotope $_8O^{17} , M_p$ and M_N are the masses of a proton and a neutron respectively, the nuclear binding energy of the isotope is

Possible Answers

Selected	Possible Answer

Question

In gamma ray emission from a nucleus

Possible Answers

Selected	Possible Answer
	there is no change in the proton number and the neutron number.
	only the proton number changes
	both the neutron number and the proton number change
	only the neutron number changes

Question

If in a p-n junction diode, a square input signal of 10V is applied as shown Then the output signal across R_L

will be

Possible Answers

Selected	Possible Answer

Question

Photon of frequency ν has a momentum associated with it. If c is the velocity of light, the momentum is

Possible Answers

Selected	Possible Answer

	v/c
	hvc

Question

The velocity of a particle is v = v_0 + gt + ft^2 . If its position is x = 0 at t = 0, then its displacement after unit time (t = 1) is

Possible Answers

Selected	Possible Answer

Question

For the given uniform square lamina ABCD, whose centre is O

Possible Answers

Selected	Possible Answer
	$l_{AC}$ $= l_{EF}$
	$l_{AD}$ $= 3l_{EF}$
	$l_{AC}$ $= \sqrt {2} l_{EF}$
	$\sqrt {2} l_{ac}$ $= l_{EF}$

Question

A point mass oscillates along the x-axis according to the law $x = x_0 \cos (\omega t - \pi / 4)$ . If the acceleration of the particle is written as $a = A \cos ( \omega t + \delta)$

Possible Answers

Selected	Possible Answer
	$A = x_0 \omega ^2 , \delta = - \pi / 4$
	$A = x_0 \omega ^2 , \delta = - \pi / 4$
	$\delta = - \pi /4$
	$A = x_0 \omega ^2 , \delta = 3 \pi / 4$

Question

Charges are placed on the vertices of a square as shown. Let E be the electric field and V the potential at the centre. If the charges on A and B are interchanged with those on D and C respectively, then

Possible Answers

Selected	Possible Answer
	Both $\overset {\rightarrow }{E}$ and V Change
	$\overset {\rightarrow }{E}$ remains unchanged, V changes
	$\overset {\rightarrow }{E}$ and V remains unchanged
	$\overset {\rightarrow }{E}$ changes, V remains unchanged

Question

The half-life period of a radio-active element X is same as the mean life time of another radioactive element Y. Initially they have the same number of atoms. Then

Possible Answers

Selected	Possible Answer
	X and Y have same decay rate initially
	X and Y decay at same rate always.
	Y will decay faster than X
	X will decay faster than Y

Question

A Carnot engine, having an efficiency of $\eta = 1/10$ as heat engine, is used as a refrigerator. If the work done on the system is 10 J, the amount of energy absorbed from the reservoir at lower temperature is

Possible Answers

Selected	Possible Answer
	100 J
	99 J
	1 J
	90 J

Question

Carbon, silicon and germanium have four valence electrons each. At room temperature which one of the following statements is most appropriate?

Possible Answers

Selected	Possible Answer
	The number of free conduction electrons is negligible small in all the three.
	The number of free electrons for conduction is significant in all the three.
	The number of free conduction electrons is significant in C but small in Si and Ge.
	The number of free electrons for conduction is significant only in Si and Ge but small in C.

Question

A charged particle with charge q enters a region of constant, uniform and mutually orthogonal fields $\overset {\rightarrow }{E}$ and $\overset {\rightarrow }{B}$ with a velocity $\overset {\rightarrow }{v}$ perpendicular to both $\overset {\rightarrow }{E}$ and $\overset {\rightarrow }{B}$ , and comes out without any change in magnitude or direction of $\overset {\rightarrow }{v}$ . Then

Possible Answers

Selected	Possible Answer
	$\overset {\rightarrow }{v}=$ $\overset {\rightarrow }{B} *$ $\overset {\rightarrow }{E} / E^2$
	$\overset {\rightarrow }{v}=$ $\overset {\rightarrow }{B} *$ $\overset {\rightarrow }{E} / B^2$
	$\overset {\rightarrow }{v}=$ $\overset {\rightarrow }{E} *$ $\overset {\rightarrow }{B} / B^2$
	$\overset {\rightarrow }{v}=$ $\overset {\rightarrow }{E} *$ $\overset {\rightarrow }{B} / E^2$

Question

The potential at a point x (measured in $\mu m$ ) due to some charges situated on the x-axis is given by V(x) = 20 / (x^2 -4) volts. The electric E at $x = 4 \mu m$ is given by

Possible Answers

Selected	Possible Answer
	$10/9 \quad Volt/ \mu m$ and in the – ve x direction
	$10/9 \quad Volt/ \mu m$ and in the + ve x direction
	$5/3 \quad Volt/ \mu m$ and in the -ve x direction
	$5/3 \quad Volt/ \mu m$ and in the +ve x direction

Question

Which of the following transitions in hydrogen atoms emit photons of highest frequency?

Possible Answers

Selected	Possible Answer
	n = 6 to n = 2
	n = 2 to n = 6
	n = 1 to n = 2
	n = 2 to n = 1

Question

A block of mass ‘m’ is connected to another block of mass ‘M’ by a spring (massless) of spring constant ‘k’. The blocks are kept on a smooth horizontal plane. Initially the blocks are at rest and the spring is unstretched. Then a constant force ‘F’ starts acting on the block of mass ‘M’ to pull it. Find the force on the block of mass ‘m’

Possible Answers

Selected	Possible Answer
	$\cfrac {mF}{M}$
	$\cfrac {MF}{(m+M)}$
	$\cfrac {(M+m)} {m}$
	$\cfrac {mF}{(m+M)}$

Question

Two lenses of power -15 D and +5D are in contact with each other. The focal length of the combination is

Possible Answers

Selected	Possible Answer
	+20 cm
	-10 cm
	-20 cm
	+10 cm

Question

One end of a thermally insulated rod is kept at a temperature T_1 and the other at T_2 . The rod is composed of two sections of lengths l_1 and l_2 and thermal conductivities k_1 and k_2 respectively. The temperature at the interface of the two sections is

Possible Answers

Selected	Possible Answer

Question

A sound absorber attenuates the sound level by 20 dB. The intensity decreases by a factor of

Possible Answers

Selected	Possible Answer
	10000
	10
	1000
	100

Question

If C_p and C_v denote the specific heats of nitrogen per unit mass at constant pressure and constant volume respectively, then

Possible Answers

Selected	Possible Answer

Question

A charged particle moves through a magnetic field perpendicular to its direction. Then

Possible Answers

Selected	Possible Answer
	the momentum changes but the kinetic energy is constant
	both momentum and kinetic energy of the particle are not constant
	both, momentum and kinetic energy of the particle are constant
	kinetic energy changes but the momentum is constant

Question

Two identical conducting wires AOB and COD are placed at right angles to each other. The wire AOB carries an electric current l_1 and COD carries a current l_2 . The magnetic field on a point lying at a distance ‘d’ from O, in a direction perpendicular to the plane of the wires AOB and COD, will be given by

Possible Answers

Selected	Possible Answer
	$\cfrac { \mu }{2 \pi d}$
	$\cfrac { \mu _0 }{2 \pi}$ $( l^2_1 + l^2 _2 ) ^{1/2}$
	$\cfrac { \mu _0 }{2 \pi}$ $\Big ( \cfrac {l_1 + l_2 }{d} \Big ) ^{1/2}$
	$\cfrac { \mu _0 }{2 \pi}$

Question

The resistance of a wire is ohm at $50^{\circ}$ C and 6 ohm at $100^{\circ}$ C. The resistance of the wire at 0 $^{\circ} C$ will be

Possible Answers

Selected	Possible Answer
	1 ohm
	2 ohm
	3 ohm
	4 ohm

Question

A parallel plate condenser with a dielectric of dielectric constant K between the plates has a capacity C and is charged to a potential V volts. The dielectric slab is slowly removed from between the plates and then reinserted. The net work done by the system in this process is

Possible Answers

Selected	Possible Answer

Question

If $g_{E}$ and g_m are the accelerations due to gravity on the surfaces of the earth and the moon respectively and if Millikan’s oil drop experiment could be performed on the two surfaces, one will find the ratio (electronic charge on the moon) $\Big/$ (electronic charge on the earth) to be

Possible Answers

Selected	Possible Answer
	0

	1

Question

A circular disc of radius R is removed from a bigger circular disc of radius 2R such that the circumferences of the discs coincide. The centre of mass of the new disc is $\alpha \Big / R$ from the centre of the bigger disc. The value of $\alpha$ is

Possible Answers

Selected	Possible Answer
	1/2
	1/4
	1/6
	1/3

Question

A round uniform body of radius R, mass M and moment of inertia ‘I’, rolls down (without slipping) an inclined plane making an angle $\theta$ with the horizontal. Then its acceleration is

Possible Answers

Selected	Possible Answer
	$\cfrac {g \sin \theta}{1 + \frac {MR^2}{l}}$
	$\cfrac {g \sin \theta}{1 - \frac {MR^2}{l}}$
	$\cfrac {g \sin \theta}{1 + \frac {l}{MR^2}}$
	$\cfrac {g \sin \theta}{1 - \frac {l}{MR^2}}$

Question

Angular momentum of the particle rotating with a central force is constant due to

Possible Answers

Selected	Possible Answer
	Zero Torque
	Constant linear momentum.
	Constant Force
	Constant Torque

Question

A 2 kg block slides on a horizontal floor with a speed of 4 m/s. It strikes a uncompressed spring, and compresses it till the block is motionless. The kinetic friction force is 15 N and spring constant is 10,000. N/m. The spring compresses by

Possible Answers

Selected	Possible Answer
	8.5 cm
	5.5 cm
	11.0 cm
	2.5 cm

Question

A particle is projected at $60 ^{\circ}$ to the horizontal with a kinetic energy K. The kinetic energy at the highest point is

Possible Answers

Selected	Possible Answer
	Zero
	k/2
	k/4
	K

Question

In a Young’s double slit experiment the intensity at a point where the path difference is $\cfrac {\lambda}{6} ( \lambda$ being the wavelength of the light used is I. If l_0 denotes the maximum intensity, $\cfrac {l}{l_0}$ is equal to

Possible Answers

Selected	Possible Answer
	1/2
	$\frac {\sqrt {3}}{2}$
	$\frac {1}{\sqrt{2}}$
	3/4

Question

Two springs, of force constants k_1 and k_2 , are connected to a mass m as shown. The frequency of oscillation of the mass is f. If both k_1 and k_2 are made four times their original values, the frequency of oscillation becomes

Possible Answers

Selected	Possible Answer
	f/4
	f/2
	4f
	2f

Question

When a system is taken from state i to state f along the path iaf, it is found that Q = 50 cal and W = 20 cal. Along the path’ ibf Q = 36 cal. W along the path ibf is

Possible Answers

Selected	Possible Answer
	16 cal
	14 cal
	66 cal
	6 cal

Question

A particle of mass m executes simple harmonic motion with amplitude ‘a’ and frequency ‘ν’. The average kinetic energy during its motion from the position of equilibrium to the end is

Possible Answers

Selected	Possible Answer
	$4 \pi ^2 ma^2 v^2$
	$\pi ^2 ma^2 v^2$
	$\frac {1}{4} \pi ^2ma^2 v^2$
	$2 \pi ^2 ma^2 v^2$

Question

The energies of activation for forward and reverse reactions for $A_2 + B_2 \leftrightharpoons 2AB$ are 180 kJ $mol^{-1}$ and 200 kJ $mol^{-1}$ respectively. The presence of catalyst lowers the activation energy of both (forward and reverse) reactions by 100 kJ $mol^{-1}$ . The enthalpy change of the reaction $(A_2 +B_2 \rightarrow 2AB)$ in the presence of catalyst will be (in kJ $mol^{-1}$ )

Possible Answers

Selected	Possible Answer
	300
	280
	20
	120

Question

The cell, $Zn| Zn^{2+} ( 1M)||Cu^{2+}$ $(1M)| Cu(E^0 _{cell} =1.10 V)$ , was allowed to be completely discharged at 298 k . the relative concentration $Zn^{2+}$ to $Cu^{2+}$ $\Bigg[ \big [ Zn^{2+}] /[Cu^{2+}\big ]\Bigg]$ is

Possible Answers

Selected	Possible Answer



	$10^{37.3}$

Question

The pKa of a weak acid (HA) is $4 \cdot 5$ . The pOH of an aqueous buffered solution of HA in which $50 \%$ of the acid is ionized is

Possible Answers

Selected	Possible Answer
	2.5
	9.5
	4.5
	7.0

Question

consider the reaction
$2A + B \rightarrow Products$
When concentration of B alone was doubled, the half-life did not change. When the concentration of A alone was doubled, the rate increased by two times. The unit of rate constant for this reaction is

Possible Answers

Selected	Possible Answer
	$L mol ^{-1} s^{-1}$
	$s^{-1}$
	$mol L ^{-1} s^{-1}$
	no unit

Question

Identify the incorrect statement among the following

Possible Answers

Selected	Possible Answer
	La and Lu have partially filled d orbitals and no other partially filled orbitals
	The chemistry of various lanthanoids is very similar
	d-Block elements show irregular and erratic chemical properties among themselves
	4f and 5f orbitals are equally shielded

Question

which one of the following has a square planer geometry>

Possible Answers

Selected	Possible Answer
	$[ CoCl_4 ]^{2-}$
	$[ PtCl_4 ]^{2-}$
	$[ NiCl_4 ]^{2-}$
	$[ FeCl_4 ]^{2-}$

Question

Which of the following molecules is expected to rotate the plane of plane polarized light?

Possible Answers

Selected	Possible Answer

Question

The secondary structure of a protein refers to

Possible Answers

Selected	Possible Answer
	fixed configuration of the polypeptide backbone
	hydrophobic interactions
	sequence of $\alpha -$ amino acids
	$\alpha -$ helical backbone

Question

Which of the following reactions will yield 2, 2-dibromopropane?

Possible Answers

Selected	Possible Answer
	$CH_3 CH \equiv CHBr + HBr \rightarrow$
	$CH \equiv CH + 2HBr \rightarrow$
	$CH_3 - C \equiv CH+ 2HBr \rightarrow$
	$CH_3 - CH = CH_2 + HBr \rightarrow$

Question

In the chemical reaction,

$+ 3KOH \longrightarrow (A)+(B) + 3H_2 O,$ the compoubd (A) and ( B) are respectively

Possible Answers

Selected	Possible Answer
	and
	and
	and
	and

Question

in presence of FeCl_3 gives predominantly

Possible Answers

Selected	Possible Answer
	benzoyl chloride
	benzyl chloride
	o-and p-chlorotoluene
	m-chlorotoluene

Question

Presence of a nitro group in a benzene ring

Possible Answers

Selected	Possible Answer
	deactivates the ring towards electrophilic substitution
	deactivates the ring towards nucleophilic substitution
	renders the ring basic
	activates the ring towards electrophilic substitution

Question

In which of the following ionization processes, the bond order has increased and the magnetic behaviour has changed?

Possible Answers

Selected	Possible Answer
	$N_2 \longrightarrow N^+_2$
	$O_2 \longrightarrow O^+_2$
	$NO \longrightarrow NO^+$
	$C_2 \longrightarrow C^+_2$

Question

The actinoids exhibits more number of oxidation states in general than the lanthanoids. This is because

Possible Answers

Selected	Possible Answer
	the 5f orbitals are more buried than the 4f orbitals
	the actinoids are more reactive than the lanthanoids
	there is a similarity between 4f and 5f orbitals in their angular part of the wave function
	the 5f orbitals extend further from the nucleus than the 4f orbitals

Question

Equal masses of methane and oxygen are mixed in an empty container at $25 ^{\circ} C$ . The fraction of the total pressure exerted by oxygen is

Possible Answers

Selected	Possible Answer
	$\frac {2}{3}$
	$\frac {1}{2}$
	$\frac {1}{3}$
	$\frac {1}{3} * \frac {273}{298}$

Question

A $5 \cdot 25 \%$ solution of a substance is isotonic with a $1 \cdot 5\%$ solution of urea $( molar \operatorname{ mass}= 60 g$ $mol^{-1}$ in the same solvent. If the densities of both the solutions are assumed to be equal to $1 \cdot 0$ $g \operatorname{cm} ^{-3}$ , molar mass of the substance will be

Possible Answers

Selected	Possible Answer
	$105 \cdot 0$ $g \operatorname{mol} ^{-1}$
	$90 \cdot 0$ $g \operatorname{mol} ^{-1}$
	$210 \cdot 0$ $g \operatorname{mol} ^{-1}$
	$115 \cdot 0$ $g \operatorname{mol} ^{-1}$

Question

Which one of the following conformation of cyclohexane is chiral?

Possible Answers

Selected	Possible Answer
	Twist boat
	Chair
	Rigid
	Boat

Question

Which of the following is the correct order of decreasing SN^2 reactivity

(X= A halogen)

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Selected	Possible Answer

Question

Which of the following sets of quantum numbers represents the highest energy of an atom?

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Selected	Possible Answer

Question

Which of the following hydrogen bonds is the strongest?

Possible Answers

Selected	Possible Answer
	O-H…......F
	F-H…......F
	O-H…......O
	O-H…......N

Question

Assuming that water vapour is an ideal gas, the internal energy $(\Delta U)$ when 1 mol of water is vapourised at 1 bar pressure and $100^{\circ}C,$ (Given: Molar enthalpy of vapourization of water at 1 bar and $373K=41 kjmol^{-1}$ and $R=8.3J mol^{-1} K^{-1}$ will be

Possible Answers

Selected	Possible Answer
	$37.904 KJ mol^{-1}$
	$3.7904 KJ mol^{-1}$
	$41.00 KJ mol^{-1}$
	$4.100 KJ mol^{-1}$

Question

In a sautrated solution of the sparingly soluble strong electrolyte AgLO_3 (Molecular mass = 283) the equilibrium which sets in is
$AglO_{3(s)}$ $\Leftrightarrow$ $Ag^+_{(ag)}$ $lO^-_{3(aq)}$
If the solubility product constant $K_{sp}$ of AgLO_3 at a given temperature is $1.0*10^{-8}$ what is the mass of AgLO_3 contained in 100 ml of its saturated solution?

Possible Answers

Selected	Possible Answer
	$1.0*10^{-7}g$
	$28.3*10^{-3}g$
	$1.0*10^{-4}g$
	$28.3*10^{-2}g$

Question

A radioactive element gets spilled over the floor of a room. Its half-life period is 30 days. If the initial activity is ten times the permissible value, after how many days will it be safe to enter the room?

Possible Answers

Selected	Possible Answer
	100 days
	300 days
	1000 days
	10 days

Question

In the following sequence of reactions

the compound ‘D’

Possible Answers

Selected	Possible Answer
	n-butyl alcohol
	butanal
	n-propyl alcohol
	propanal

Question

In the reaction. $2Al_{(s)} +6HCl_{(s)}\longrightarrow$ $2Al^{3+}_{(aq)}+6Cl^{-}_{(aq)}+3H_{2(g)}$

Possible Answers

Selected	Possible Answer
	$33.6 LH_{2(g)}$ is produced regardless of temperature and pressure for every mole Al that reacts
	$11.2H_{2(g)}$ at STP is produced for every mole $HCl_{(aq)}$
	$6 L HCl_{(aq)}$ is consumed for every $3L H_{2(g)}$ produced
	$67.2 LH_{2(g)}$ at STP is produced for every mole Al that reacts

Question

Regular use of which of the following fertilizer increases the acidity of soil?

Possible Answers

Selected	Possible Answer
	Urea
	Ammonium sulphate
	Potassium nitrate
	Superphosphate of lime

Question

Identify the correct statement regarding a spontaneous process

Possible Answers

Selected	Possible Answer
	Lowering of energy in the reaction process is the only criterion for spontaneity
	Endothermic processes are never spontaneous
	Exothermic processes are always spontaneous
	For a spontaneous process in an isolated system, the change in entropy is positive

Question

Which of the following nuclear reactions will generate an isotope?

Possible Answers

Selected	Possible Answer
	$\alpha$ -particle emission
	$\Beta$ -particle emission
	neutron particle emission
	positron emission

Question

Which one of the following is the strongest base in aqueous solution?

Possible Answers

Selected	Possible Answer
	Methylamine
	Dimethylamine
	Aniline
	Trimethylamine

Question

The compound formed as a result of oxidation of ethyl benzene by KMnO_4 is

Possible Answers

Selected	Possible Answer
	benzophenone
	benzoic acid
	benzyl alcohol
	acetophenone

Question

Which of the following species exhibits the diamagnetic behaviour?

Possible Answers

Selected	Possible Answer



	$O^{2-}_2$

Question

The stability of dihalides of Si, Ge, Sn and Pb increases steadily in the sequence

Possible Answers

Selected	Possible Answer

Question

Identify the incorrect statement among the following

Possible Answers

Selected	Possible Answer
	Silicon reacts with $NaOH_{aq)}$ in the presence of air to give and
	reacts with hot and strong NaOH solution to give and ,math>H_2O
	reacts with excess of to give and
	Ozone reacts with to give

Question

The IUPAC name of

Possible Answers

Selected	Possible Answer
	5, 5-diethyl-4, 4-diemthylpentane
	3-ethyl-4, 4-dimethylheptane
	1, 1-diethyl-2,2-dimethylpentane
	4, 4-dimethyl-5, 5-diethylpentane

Question

The charge/size ratio of a cation determines its polarizing power. Which one of the following sequences represents the increasing order of the polarizinig order of the polarizing power of the cationic species, $K^+, Ca^{2a}, Mg^{2+},Be^{2+}$

Possible Answers

Selected	Possible Answer
	$Mg^{2+}, Be^{2+}, K^+ ,Ca^{2+}$
	$Ca^{2+},Mg^{2+},Be^{2e},K^+$
	$Be^{2+}, K^+, Ca^{2+},Mg^{2+}$
	$K^+,Ca^{2+},Mg^{2+},Be^{2+}$

Question

The density in $g mL^{-1}$ of a 3.60 M sulphuric acid solution that is $29\%$ H_2SO_4 (Molar mass $= 98 g mol^{-1}$ by mass will be

Possible Answers

Selected	Possible Answer
	1.45
	1.64
	1.22
	1.88

Question

The first and second dissociation constants of an acid H_2A are $1.0 * 10^{-5}$ and $5.0*10^{-10}$ respectively. The overall dissociation constant of the acid will be

Possible Answers

Selected	Possible Answer
	$=5.0*10^{-5}$
	$=5.0*10^{15}$
	$=5.0*10^{-15}$
	$=0.0*10^{5}$

Question

A mixture of ethyl alcohol and propyl alcohol has a vapour pressure of 290 mm at 300 K. The vapour pressure of propyl alcohol is 200 mm. If the mole fraction of ethyl alcohol is 0.6, its vapour pressure (in mm) at the same temperature will be

Possible Answers

Selected	Possible Answer
	700
	350
	300
	360

Question

In conversion of lime-stone to lime,
$CaCO_3(s) \longrightarrow CaO(s)+CO_2 (g)$
the vales of $\Delta H^{\circ}$ and $\Delta S^{\circ}$ are $+179.1 kJ mol^{-1}$ and 160.2 J/K respectively at 298 K and 1 bar. Assuming that $\Delta H^{\circ}$ do not change with temperature, temperature above which conversion of limestone to lime will be spontaneous is

Possible Answers

Selected	Possible Answer
	1118 K
	1200
	1008 K
	845 K

Question

The equivalent conductances of two strong electrolytes at infinite dilution in H_2O (where ions move freely through a solution) at $25^{\circ}C$ are given below:

$\land^{\circ}_{CH_3COONa}$ =91.0 S cm^2 /equiv
$\land ^{\circ}_{HCl}=426.2 S cm^2/equiv$
What additional information/quantity one needs to calculate $\land ^{\circ}$ of an aqueous solution of acetic acid?

Possible Answers

Selected	Possible Answer
	$\land ^{\circ}$ of
	$\land ^{\circ}$ of chloroacetic acid (C/CH2COOH)
	The limiting equivalent conductance of $H^+ (\land^{\circ}_{H^+})$
	$\land ^{\circ}$ of

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