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Q 1.
If the magnetic field in a plane electromagnetic wave is given by \(\vec{B}=3*10^{-8} sin(1.6*10^3+ 48*10 ^{10}t)T \) , Then what will be expression for electric field?

Q 2.
The time period of revolution of electron in its ground state orbit in a hydrogen atom is \(1.6*10^{–16}\). The frequency of revolution of the electron in its first excited state (in \(s^{-1}\) ) is

Q 3.
Consider a circular coil of wire carrying current I, forming a magnetic dipole. The magnetic flux through an infinite plane that contains the circular coil and excluding the circular coil area is given by ϕi. The magnetic flux through the area is given by ϕ0. Which of the following is correct?

Q 4.
Visible light of wavelength\( 6000 × 10^{–8 }\)cm falls normally on a single slit and produces a diffraction pattern. If it is found that the second diffraction minimum is at 60° from the central maximum. if the first minimum is produced at \(θ_1, the θ_1\) is close to

Q 5.
 The radius of gyration of a uniform rod if length l, about an axis passing through a point \(1/ 2 \)away from the centre of the rod, and perpendicular to it, is

Q 6.
A 60 HP electric motor lifts an elevator having a maximum total load capacity of 2000 kg. If the frictional force on the elevator is 4000 N, the speed of the elevator at full load is close to: \((1 HP = 746 W, g = 10 ms^{–2} )\)

Q 7.

Two infinite planes each with uniform surface charge density +σ are kept in such a way that the angle but them is 30°. The electric field in the region shown between them is given by

Q 8.
A satellite of mass m launched vertically upwards with an initial speed u from the surface of the earth. After it reaches height R (R = radius of the earth), it ejects a rocket of mass m/10 so that subsequently the satellite moves in a circular orbit. The kinetic energy of the rocket is (G is the gravitational constant; M is the mass of the earth)

Q 9.
A polarizer-analyser set is adjusted such that intensity of light coming out of the analyser is just 10% of the original intensity. Assuming that the polarizer. Analyser set does not absorb any light, the angle by which the analyser need to be rotated further to reduce the output intensity to be zero, is

Q 10.
A long solenoid of radius R carries a time (t) - dependent current I(t) = I0t (1-t). A ring of radius 2R is placed coaxially hear its middle. During the time interval 0 ≤ t ≤ 1, the induced current\( (I_R) \)and the induced EMF \((V_R)\) in the ring changes as

Q 11.
Which of the following a reversible operation?

Q 12.
Speed of a transverse wave on a straight wire (mass 6.0 g, length 60 cm and area of cross-section\( 1.0 mm^2 ) is 90 ms^–1 \). If the Young's modules of wire is \(16 × 10^{11} Nm^–2 \), the extension of wire over its natural length is

Q 13.

As shown in the figure, a bob a mass m is tied by a massless string whose other end portion is wound on a fly wheel (disc) of radius r and mass m. When released from rest the bob starts falling vertically. When it has covered a distance of h, the angular speed of the wheel will be

Q 14.
A LCR circuit behaves like a damped harmonic oscillator comparing it with a physical spring-mass damped oscillator having damping constant ‘b’, the correct equivalence would be

Q 15.

Three point particles of masses 1.0 k.g., 1.5 kg and 2.5 kg are placed at three corners of a right ∆ of sides 4.0 cm, 3.0 cm and 5.0 cm as shown. The centre of mass of the system is at a pt.

Q 16.

The current I1 (in A) flowing through 1Ω resistor in the following circuit is

Q 17.
If we need a magnification of 375 from a compound microscope of tube length 150 mm and an objective of focal length 5m, the focal length of the eye-piece, should be close to

Q 18.
: If we need a magnification of 375 from a compound microscope of tube length 150 mm and an objective of focal length 5m, the focal length of the eye-piece, should be close t

Q 19.
: A litre of dry air at STP expands adiabatically to a volume of 3 litres. If γ = 1.40, the work done by air is: (\(3^{1.4 }= 4.6555) \)[Take air to be an ideal gas]

Q 20.

A parallel plate capacitor has plates of area A separated by distance 'd' between them. It is filled with a dielectric which has a dielectric constant that varies as k(x) = K(1 + x) where 'x' is the distance measured from one of the plates. If (d) << 1, the total capacitance of the system is best given by the expression

Q 21.
Let P be a plane passing through the points (2, 1, 0), (4, 1, 1) and (5, 0, 1) and R be any point (2, 1, 6). Then the image of R in the plane P is

Q 22.

 If the system of linear equations

2x + 2ay + az = 0

2x + 3by + bz = 0

2x + 4cy + cz = 0

where a,b,c ∈ R are non-zero and distinct; has non-zero solution then

Q 23.
The greatest positive integer k, for which 49k + 1 is a factor of the sum \(49^{125 }+ 49^{124 }+….+ 49^2 + 49 + 1, is\)

Q 24.

Q 25.

Q 26.
If the distance between the foci of an ellipse is 6 and the distance between its directrices is 12, then the length of its latus rectum is

Q 27.
: If y = mx + 4 is a tangent to both the parabolas.\( y^2 = 4x and x^2 = 2by\), then b is equal to

Q 28.

Q 29.
Total number of 6 digit numbers in which only and all the five digits 1, 3, 5, 7 and 9 appears is

Q 30.
Five numbers are in A.P., whose sum is 25 and product is 2520. If one of these five numbers is –1/2, then the greatest number amongst them is

Q 31.
The logical statement (p ⇒ q) ∧ (q ⇒ ∼p) is equivalent to

Q 32.

Q 33.

Q 34.

Q 35.

Q 36.
The area of the region enclosed by the circle \(x^ 2 + y^ 2 = 2\) which is not common to the region bounded by the parabola \(y ^2 = x\) and the straight line y = x, is

Q 37.
An unbiased coin is tossed 5 times. Suppose that a variable X is assigned the value k when k consecutive heads are obtained for k = 3, 4, 5, otherwise X takes the value -1. Then the expected value of X is

Q 38.

Q 39.

Q 40.

Q 41.
Amongst the following statements, that which was not proposed by Dalton was Options:

Q 42.
A solution of m-chloroaniline, m-chlorophenol and m-chlorobenzoic acid in ethyl acetate was treated initially with a saturated solution of NaHCO3 to give fraction A. The left-over organic phase was extracted with dilute NaOH solution to give fraction B. The final organic layer was labelled as fraction C. Fractions A, B and C contain respectively

Q 43.
The atomic radius of Ag is closest to

Q 44.
1-methyl-ethylene oxide when treated with an excess of HBr produces

Q 45.
Given that the standard potentials \((E°) of Cu^2+/Cu\) and Cu+ /Cu are 0.34 V and 0.522 V respectively, the E° of \(Cu^2+/Cu+ is\)

Q 46.

The increasing order of\( pK_b \)for the following compounds will be

Q 47.

What is the product of following reaction?

Q 48.
At 35°C, the vapour pressure of \(CS_2\) is 512 mm Hg and that of acetone is 344 mm Hg. A solution of\( CS_2\) in acetone has a total vapour pressure of 600 mm Hg. The false statement amongst the following is

Q 49.
Oxidation number of potassium in \(K_2O, K_2O_2 and KO_2\), respectively is

Q 50.
The dipole moments of \(CCl_4, CHCl_3 and CH_4\) are in order

Q 51.
In comparison to the Zeolite process for the removal of permanent hardness, the synthetic resins method is

Q 52.
: The theory that can completely/properly explain the nature of bonding in\( [Ni(CO)_4]\) is

Q 53.
The IUPAC name of the complex \([Pt(NH_3)_2Cl(CH_3NH_2)]\) is

Q 54.
The number of orbitals associated with quantum numbers n = 5, ms = +½ is

Q 55.
The electron gain enthalpy (in kJ/mol) of fluorine, chlorine, bromine, iodine respectively is

Q 56.

Match the following:

Q 57.
The purest form of commercial iron is

Q 58.
The relative strength of interionic/intermolecular forces is decreasing order is

Q 59.

Consider the following reactions:

Q 60.

Consider the following reaction:

Q 61.
For the reaction \(A_{(l)} → 2B_{(g)} ΔU = 2.1 kcal, ΔS = 20 cal K^{–1 }at 300 K\). Hence ΔG in kcal is.
Q 62.
During the nuclear explosion one of the products of \(^{90}Sr\) with half life of 6.93 years. If 1 μg of \(^{90}Sr\) was absorbed in the bones of a newly born baby in place of Ca, how much time, in years, is required to reduce it by 90% if it is not lost metabolically _____
Q 63.
The number of chiral carbons in chloramphenicol is ______.
Q 64.
Two solutions A and B, each of 100 L was made by dissolving 4g of NaOH and 9.8 g of\( H_2SO_4\) in water, respectively. The pH of the resultant solution obtained from mixing 40 L of solution A and 10 L of solution B is _______.
Q 65.
Chlorine reacts with hot and concentrated NaOH and produces compounds (X) and (Y). Compound (X) gives white precipitate with silver nitrate solution. The average bond order between CI and O atoms in (Y) is _____.
Q 66.
Let S be the set of points, where the function \(f(x)=|2-|x-3||,\in{R}\) , is not differentiable, then \(\displaystyle\sum_{x\in{y}}f(f(x))\) is equal to
Q 67.
If the variance of the first n natural numbers is 10 and the variance of the first m even natural numbers is 16, then m + n is equal to______
Q 68.
Let A(1, 0), B(6, 2) and \(C(\frac{3}{2},6) \)be the vertices of a triangle ABC. If P is a point inside the ΔABC such that the triangles APC, APB and BPC have equal areas, then the length of the line segment PQ, where Q is the point \((\frac{-7}{6},\frac{-1}3) \) is_____
Q 69.

Q 70.
: If the sum of the coefficients of all even powers of x in the product \((1 + x + x^2 + ….. + x^{2n}) (1 – x + x^2 – x^3 + …. + x^{2n})\) is 61, then n is equal to _____
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