IIT JEE - Jan 29, 11:54

Solution

Correct: A

The maximum height attained by a body projected vertically upwards can be calculated using the equation v^2 = u^2 + 2as, where v = 0 at the highest point. Substituting the values, we get 0 = (12)^2 - 2*9.8*h, which gives h = 7.29 m

Solution

Correct: A

The centripetal force acting on a particle moving in a circle is given by the equation F = mv^2/r, where m is the mass, v is the velocity and r is the radius of the circle

Solution

Correct: A

The de Broglie wavelength of a particle is given by the equation λ = h/mv, where h is Planck's constant, m is the mass of the particle and v is the velocity of the particle. For an electron, λ = (6.626 * 10^-34)/(9.11 * 10^-31 * 2 * 10^6) = 3.63 * 10^-10 m

Solution

Correct: A

At STP, 1 mole of CO2 occupies a volume of 22.4 liters and weighs 44 g. The number of moles of CO2 required to produce 8.8 g is (8.8/44) = 0.2

Solution

Correct: B

To evaluate the integral, we can use partial fractions. Let (x^2 + 1)/(x^2 - 4) = A/(x - 2) + B/(x + 2). Solving for A and B gives A = B = 1/4. So the integral becomes ∫(1/4)(1/(x - 2) + 1/(x + 2)) dx = (1/4)log|x - 2| + (1/4)log|x + 2| + c

Solution

Correct: B

The given curve is y = a * e^(bx). Taking logarithm on both sides, we get log(y) = log(a) + bx*log(e). Differentiating both sides with respect to x, we get (1/y)*(dy/dx) = b. So, dy/dx = b*y

Solution

Correct: A

The given curve is x^2 + 3y^2 = 4. Differentiating both sides with respect to x, we get 2x + 6y*(dy/dx) = 0. So, dy/dx = -x/3y. At the point (1, 1), the slope is -1/3. The equation of the tangent is y - 1 = (-1/3)*(x - 1), which simplifies to 3y - 3 = -x + 1, or x + 3y - 4 = 0. None of the options match this equation exactly. The closest is 2x + 6y - 8 = 0

Solution

Correct: D

Orbitals have a definite shape. Atomic orbitals are mathematical functions that describe the wave-like behavior of electrons in an atom. Each orbital has a unique shape, size, and orientation in space, which determines the probability of finding an electron within that region

Solution

Correct: D

For a spontaneous reaction, ΔG is negative. The equation ΔG = ΔH - TΔS shows that ΔG is negative when ΔH is negative and ΔS is positive

Solution

Correct: D

At 0°C, the entropy change for the transformation of 1 mole of ice to 1 mole of water can be calculated using the equation ΔS = Q/T. Since the transformation is isothermal, Q is equal to the molar heat of fusion of ice, which is 18.0 J/g. For 1 mole of ice (18.0 g), Q = 18.0 g * 334 J/g = 6012 J. So, ΔS = 6012 J / 273 K = 22.0 J/K

Solution

Correct: B

The radius of a nucleus is directly proportional to the cube root of the mass number A. So, R ∝ A^(1/3)

Solution

Correct: A

According to Newton's second law of motion, F = m*a. If the force is increased from 100 N to 200 N, the acceleration will double. So, the new acceleration is 10 ms^-2

Solution

Correct: A

The molar mass of helium is 4 g/mol. So, the number of atoms in 1 g of helium is (6.023 * 10^23 / 4) = 1.50575 * 10^23. However, since helium is a noble gas, it exists as single atoms. Therefore, the number of atoms is 1.50575 * 10^23, but among the given options, the closest is 6.023 * 10^22 * (1/4) = 1.50575 * 10^22 * 10 = 1.50575 * 10^23 / 10 = 1.50575 * 10^22

Solution

Correct: B

The force of static friction is given by the equation F = μs*N, where μs is the coefficient of static friction and N is the normal force. In this case, the normal force is equal to the weight of the block, which is 2 kg * 9.8 m/s^2 = 19.6 N. So, the force of static friction is 0.5 * 19.6 N = 9.8 N. Since the applied force is 2.5 N, which is less than the force of static friction, the block will not move

Solution

Correct: A

The reaction is exothermic, so the heat of reaction is -21 kcal. This means that heat is evolved during the reaction. When the temperature is increased, the reaction will shift to the left, as the system tries to absorb heat and reduce the temperature

Solution

Correct: A

The radius of the orbit of the electron in the ground state of hydrogen is given by the equation r = a0, where a0 is the Bohr radius. For He+, the radius is given by r = a0/Z, where Z is the atomic number. Since Z = 2 for He+, the radius is r = a0/2. So, the ratio of the radii is a0 : a0/2 = 2:1

Solution

Correct: A

The rate of the reaction is given by the equation rate = k[A]^m[B]^n. If the concentration of A is doubled, the new rate will be k(2[A])^m[B]^n = 2^m * k[A]^m[B]^n = 2^m * rate. If the concentration of B is halved, the new rate will be 2^m * k[A]^m(1/2[B])^n = 2^m * (1/2)^n * rate. So, the new rate of the reaction will be 2^m * (1/2)^n * rate

Solution

Correct: A

For strong electrolytes, the molar conductivity is constant and does not vary with concentration. This is because strong electrolytes are completely dissociated in solution, so the conductivity is dependent on the number of ions present, which is constant

Solution

Correct: A

The heat of neutralization of a strong acid with a strong base is 57.3 kJ/mol. This is because the reaction between a strong acid and a strong base is highly exothermic, releasing a large amount of heat

Solution

Correct: B

The electronic configuration of Fe (Z=26) is [Ar] 3d^6 4s^2. However, the electrons can be arranged in different ways, giving rise to different configurations. Using the Aufbau principle and the Pauli exclusion principle, the possible configurations are [Ar] 3d^6 4s^2, [Ar] 3d^7 4s^1, and [Ar] 3d^8. However, only [Ar] 3d^6 4s^2 and [Ar] 3d^7 4s^1 are stable