Q 2.

\(aK_2Cr_2O_7 + bKCI + c H_2SO_4 \to x Cr O_2Cl_2 + y KHSO_4 + z H_2O \)

Q 3.

 What is the correct order of dehydration of the following compounds in presence of acidic medium?

Q 4.

Very pure hydrogen (99.9%) can be made by which of the following processes?

Q 5.

 Identify A and B in the following reaction.

Q 6.

 Among the following, the least thermally stable is

Q 7.

A deliquescent white crystalline solid hydroxide ‘X’ reacts with nitrate ‘Y’ to form another hydroxide which decomposes to give an insoluble brown layer of its oxide. X is a powerful cautery and breaks down the proteins of skin flesh to a pasty mass. X and Y are

Q 8.

Boron cannot form which one of the following anions?

Q 9.

The composition of common glass is

Q 10.

Which one of the following has the most nucleophlic nitrogen ?

Q 11.

The critical temperatures of \(​CO,CH_4, HCl \ and ​\ SO_2\) are 134K, 190K, 324K and 430K respectively. The order of extension of adsorption of these gases on charcoal is

Q 12.

Q 13.

Select the incorrect statement about liquid junction potential.

Q 14.

If Ag I crystallize in \(I^-\) zinc blende structure with ions at lattice points, what fraction of tetrahedral voids is occupied by \(Ag^+\) ions

Q 15.

Which of the following can be distinguished from an aliphatic carboxylic acid using sodium bicarbonate solution?

Q 16.

The F .pt(in° C) of a solution containing 0.1 g of \(K_3[ Fe(CN)_6]\) (mol wt. 329) in 100 g of water \((k_f=1.86 \ K\ kg/ mol)\) is

Q 17.

A first order reaction in aqueous solution was too fast to be detected by a procedure that could have followed a reaction having a half life of at least 2.0ns. The minimum value of the rate constant of the reaction is

Q 18.

 Identify the major product in the following reaction.

Q 19.

The rate of a reaction is given by rate if the rate \(r=K[H^+]^n\) becomes 100 times when the pH changes from 2 to 1, the order of the reaction is

Q 20.

When a \(CS_2\) layer containing Bromine and Iodine is shaken with excess of chlorine water, the violet colour due to iodine disappears and orange colour of bromine appears. The disappearance of violet colour is due to the formation of

Q 21.

Figure shows the vertical section of a frictionless surface. A block of mass 2 kg is released from rest from position A; its KE as it reaches position C is \((g = 10 m/s^2)\)

Q 22.

Two travelling waves\( y_1 = A sin [K(x + ct)] and y_2 = A sin[K(x – ct)]\) are superposed on a string. The distance between the adjacent nodes will be

Q 23.

In the circuit shown in fig. A and B are two cells of the same emf E and of internal resistances rA and rB respectively. L is an ideal inductor and C is an ideal capacitor. The key K is closed. When the current in the circuit becomes steady, what should be the value of R so that the potential difference across the terminals of cell A is zero.

Q 24.

 A light rod of length ‘L’ is suspended from a support horizontally by means of two vertical wires A and B of equal length as shown. Crosssection area of ‘A’ is half that of B. A weight ‘w’ is hung on the rod as shown. The value of ‘x’ so that the stress in ‘A’ is same as that in ‘B’, is

Q 25.

A charged particle enters a uniform magnetic field with velocity vector making an angle of 30º with the magnetic field. The particle describes a helical trajectory of pitch x. The radius of the helix is

Q 26.

Two concentric spheres of radii \(r_1 and r_2\) carry charges \(q_1 and q_2 \)respectively. If the surface charge density (σ) is the same for both the spheres, the electric potential at the common centre will be

Q 27.

 An alternating current (in ampere) varies with time t as I = 3 sin ωt + 4 cos ωt The rms value of the current is

Q 28.

The coefficient of static friction between the two blocks shown in the figure is ‘μ’ and the table is smooth. The maximum value of ‘F’ so that both blocks moves together, is

Q 29.

A uniform rope having some mass hangs vertically from a rigid support. A transverse wave pulse is produced at the lower end. The speed (v) of the wave pulse varies with height (h) from the lower end as:

Q 30.

If de-Broglie wavelength of an electron in the nth Bohr orbit is \(λ_n\) and angular momentum is \(J_n\) then

Q 31.

When electrons in a hydrogen atom jumps from first orbit to one of the higher energy orbits, the orbital velocity is reduced to (1/3)rd the initial value. If the radius of the first orbit is r, the radius of the higher energy orbit is

Q 32.

A plano convex lens \((μ =\frac 3 2 )\)has radius of curvature R = 10 cm, and is placed at a distance of ‘b’ from a concave lens of focal length 20 cm as shown in the figure. At what distance ‘a’ should a point object be placed from plano convex lens, so that position of the final image is independent of ‘b’?

Q 33.

The introduction of a metal plate between the plates of a parallel plate capacitor increases its capacitance by 4.5 times. If d is the separation of the two plates of the capacitor, the thickness of the metal plate introduced is

Q 34.

Two coherent sources \(S_1\) and \(S_2 \)are situated on the x-axis, screen ‘S’ is in y –z plane(as shown). The shape of the fringe on the screen is

Q 35.

The convex reflecting surface is represented by the equation \(2x = y^2\) as shown in figure. A ray travelling horizontally along positive x-axis becomes vertical after reflection. The co-ordinates of the point of incidence can be

Q 36.

A transverse wave is passing through a light string shown in the figure. The equation of wave is y = Asin(ωt – kx). The area of cross section of string is ‘A’ and density is ‘ρ’. The hanging mass is:

Q 37.

The current I through 10 Ω resistor in the circuit with ideal diodes shown in the figure is

Q 38.

A beam of light is incident on a glass plate at an angle of incidence 60°. The reflected ray is polarized. The angle of refraction when the angle of incidence is 45° is

Q 39.

From a given sample of uniform wire, two circular loops P and Q are made, P of radius r and Q of radius nr. If the moment of inertia of Q about it axis is four times that of P about its axis (assuming wire diameter much smaller, than either radius), the value of n is

Q 40.

 For an electron in the \(nth\) Bohr orbit of hydrogen atom, what will be the ratio of radius of orbit to its de-Broglie wavelength

Q 41.

OPQR is a square and M, N are the middle points of the sides PQ and QR respectively, then the ratio of the areas of the square and the triangle OMN is

Q 42.

Let the maximum and minimum distance from origin to the curve \((z\bar z)-\frac{3}{2 \sqrt 2}[(z+\bar z)-i(z-\bar z)]-\sqrt 2=0\) are \(r_1\) and \(r_2\)respectively then \(r_1+r_2=\)

Q 43.

The angle between the tangents drawn from the point (1, 4) to the parabola \(y^2 = 4x\) is. 

Q 44.

Evaluate 

Q 45.

Mean of 100 items is 49. It was discovered that three items which should have been 60, 70, 80 were wrongly read as 40, 20, 50 respectively. Correct mean will be

Q 46.

If the roots of the equation \(x^2 – (p+1)x +p^2 + p – 8 = 0 \) are on opposite sides with respect to the line x = 2 then the range of ‘p’ is

Q 47.

p→ (q ∨ r) is false, then the true valves of p, q , r respectively are

Q 48.

The area enclosed between the curves \(y = ax^2\ and\ x = ay^2 (a > 0) \ is \ 1\) sq. unit. Then the value of ‘a’ is

Q 49.

Q 50.

The total number of ways of selecting 10 balls out of an unlimited number of identical white, red and blue balls is

Q 51.

\(Sin^{−1}x + Sin^{−1 }y = π/2 \ then\ \frac {dy}{ dx}=\)

Q 52.

The sum of the series \( 3^ n C_0 -8^ n C_1 + 13^ n C_2 – 18.^ n C_3 + --- is\)

Q 53.

The tangent at \(A (2, 4)\ on\ y = x^3 – 2x^2 + 4\) cuts the x axis at T then AT =

Q 54.

The co-efficent of \(a^8 b^4 c ^9 d^9\) in \((abc+abd+acd+bcd)^{10}\) is

Q 55.

The value of ‘a’ for which the function \(f(x) = a sin x + \frac{1 }{3 }sin 3x \) has an extremum at x = π/3 is

Q 56.

The sub-tangent at any point of the curve \(x^m.y^n = a^{m+n }\) varies as

Q 57.

The quadratic equation \( 3ax^2 + 2bx + c = 0\) has at least one root between 0 and 1 if

Q 58.

Number of non-differentiable Points of the curve f(x) = min.{|log|x||, |Tan x|} in \(\left [-\frac {\pi}{ 2 }, \frac {\pi }{2} \right]\)

Q 59.

Let A, B, C and D be four non-empty sets. The Contrapositive statement of “If A ⊆ B and B ⊆ D then A ⊆ C ” is :

Q 60.

Q 61.

A block is placed on an inclined plane moving towards right horizontally with an acceleration \(a_0=g\). The length of the plane AC = 1m. Friction is absent everywhere. Find the time taken (in seconds) by the block to reach from C to A.

Q 62.

The balancing length for a cell is 560 cm in a potentiometer experiment. When an external resistance of 10 Ω is connected in parallel to the cell, the balancing length changes by 60 cm. If the internal resistance of the cell is N/10 Ω, where N is an integer then value of N is ______.

Q 63.

A charged particle of mass m = 1 mg and charge q = 1 μC enters along AB at point A in a uniform magnetic field B = 1.2 T existing in the rectangular region of size a×b, where a = 4 m and b = 3m. The particle leaves the region exactly at corner point C. What is the speed v (in ms^–1) of the particle?

Q 64.

A Carnot engine operates between two reservoirs of temperature 900 K and 300 K. The engine performs 1200 J of work per cycle. The heat energy (in J) delivered by the engine to the low temperature reservoir, in a cycle, is

Q 65.

In the given figure, find the horizontal velocity u (in ms^-1) of a projectile so that it hits the inclined plane perpendicularly. Given H = 6.25 m:

Q 66.

A uniform cylinder rests on a cart as shown. The coefficient of static friction between the cylinder and the cart is 0.5. If the cylinder is 4 cm in diameter and 10 cm in height, then what is the minimum acceleration (in m/s²) of the cart needed to cause the cylinder to tip over?

Q 67.

M grams of steam at 100°C is mixed with 200g of ice at its melting point in a thermally insulated container. If it produces liquid water at 40°C [heat of vaporization of water is 540 cal/g and heat of fusion of ice is 80 cal/g], the value of M is______.

Q 68.

 The figure shows three particles A, B and C on the x-axis. They are given velocities \(v_1=3m/s,v_2=2m/s,\;and\;v_3=5m/s\),respectively, in the direction shown. The position of centre of mass of A, B and C at time t = 1 s will be x = k (m), where k is:

Q 69.

In the circuit shown in figure, find the ratio of currents \(\frac{i_1}{i_2}\)

Q 70.

The centers of two identical small conducting spheres are 1m apart. They carry charges of opposite kind and attract each other with a force F. When they are connected by a conducting thin wire, they repel each other with a force F/3. The ratio of the magnitude of charges carried by the spheres initially is n : 1. Find the value of n.

Q 71.

From the following sets of quantum numbers, state which are not possible.
a. n = 0, l = 0, m = 0, s = +1/2
b. n = 1, l = 0, m = 0, s = –1/2
c. n = 1, l = 1, m = 0, s = +1/2
d. n = 1, l = 0, m = +1, s = +1/2
e. n = 3, l = 0, m = –1, s = –1/2
f. n = 2, l = 2, m = 0, s = –1/2
g. n = 2, l = 1, m = 0, s = –1/2

Q 72.

The number of sp2 hybridised carbons present in ''Aspartame'' is ______

Q 73.

200g impure CaCO₃ on heating gives 5.6L. CO₂ gas at STP. Find the percentage of Calcium in the limestone sample.

Q 74.

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 75.

NO → N₂O + NO₂
In this reaction equivalent weight of NO is \(\frac xy\) M then x + y will be

Q 76.

How many bonds are greater than 90° in XeOF₄?

Q 77.

10 g impure NaOH is completely neutralised by 1000 ml of \(\frac{1}{10}\) N HCI. Calculate the percentage purity of the impure NaOH.

Q 78.

 An acidic solution of dichromate is electrolyzed for 8 minutes using 2A current. As per the following equation \(Cr^2O_7^2+14\;H^++6e^-\rightarrow2C^{3+}+7H_2O\) The amount of Cr3+ obtained was 0.104 g. The efficiency of the process (in%) is (Take : F = 960000 C, At. mass of chromium = 52)

Q 79.

Then weight of MgSO₄ will be formed in this series is

Q 80.

How many of the following compounds have sp³ hybridisation?

Q 81.

If the mean and variance of eight numbers 3, 7, 9, 12, 13, 20,

Q 82.

Q 83.

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 84.

If the foot of perpendicular drawn from the point (1, 0, 3) on a line passing through \((\alpha,7,1)\) is \(\left(\frac 5 3, \frac 7 3 ,\frac {17} {3} \right)\), then \(\alpha\) is equal to

Q 85.

The value of x satisfying the equation
\(log_{17}log_2(5\sqrt x-\sqrt{25x-4)})=0\), is \(\frac{k}{25}\) then k is

Q 86.

Q 87.

The sum of squares of all integral values of a for which the quadratic expression (x−a)(x−10)+1 can be factored as a product (x+α)(x+β) of two factors and α,β∈I, must be equal to

Q 88.

If \(f(x)=tan^{−1}(sin⁡x+cos⁡x)^3\) is an increasing function, then the value of x in (0,2π) is \(x∈(\frac {aπ}{4},\frac{ bπ}{4})∪(\frac{cπ}{4},\frac{dπ}{4})\). Then the value of a+10b+100c+1000d must be

Q 89.

The equation of a curve whose slope at any point is thrice its abscissa and which passes through (–1, –3) is 2y=λ(x²−3) then the value of λ must be

Q 90.

The sum of two digit even numbers which do not end with zero is