Question Paper (Section wise)

If Surface tension (S), Moment of Inertia (I) and Planck’s constant (h), were to be taken as the fundamental units, the dimensional formula for linear momentum would be:

A convex lens (of focal length 20 cm) and a concave mirror, having their principal axes along the same lines, are kept 80 cm apart from each other. The concave mirror is to the right of the convex lens. When an object is kept at a distance of 30 cm to the left o the convex lens, its image remains at same position even if the concave mirror, by itself would produce a virtual image would be:

In the circuit shown, a four wire potentiometer is made of a 400 cm long wire, which extends between A and B. The resistance per unit length of the potentiometer wire is r=0.01Ω/cm, If an ideal voltmeter is connected as shown with jockey J at 50 cm from end A, the expected reading of the voltmeter will be.

The electric field in a region is given by where E is in NC^-1 and x in meters. The values of constants are A = 20 SI unit and B = 10 SI unit. If the potential at x = 1 is V₁ and that at x = -5 is V₂ then V₁ – V₂ is:

Young’s moduli of two wires A and B are in the ration 7:4 Wire A is 2 m long and has radius R. Wire A is 2 m long and has radius r. Wire B is 1.5 m long and has radius 2 mm. If the two wires stretch by the same length for a given load, then the value of R is closed to:

In a simple pendulum experiment for determination of acceleration due to gravity (g), times taken for 20 oscillation is measured by using a watch of 1 second least count. The mean value of time the taken comes out to be 30s. The length of pendulum is measured by using a meter scale of least count 1 mm and the value obtained is 55.0 cm. percentage error in the determination of g is close to:

A cell of internal resistance r drives current through an external resistance R. The power delivered by the cell to the external resistance will be maximum when:

A parallel plate capacitor has 1_μF capacitance. One of its two plates is given + 2_μC charge and the other plate, +4_μC charge. The potential difference developed across the capacitor is:

The percentage composition of carbon by mole in methane is:

Calculate the standard cell potential (in V) of the cell in which following reaction takes place:

Fe² + (aq) + Ag⁺ (aq) → Fe³⁺(aq)+ Ag (s)

Given that:

The structure of Nylon – 6 is:

If p is the momentum of the fastest electron ejected from a metal surface after the irradiation of light having wavelength λ, then for (A) 5 p momentum of the photoelectron, the wavelength of the light should be:

(Assume kinetic energy of ejected photoelectron to be very high in comparison to work function)

For a reaction scheme,  if the rate formation of B is set to be zero then the concentration of B given by

The major product of the following reaction is:

The statement that is INCORRECT about the interstitial compound is:

The ion that has sp³d² hybridization for the central atom is

The major product obtained in the following reaction is:

The major product of the following reaction is:

Let f(x) = a^x (a > 0) be written as f(x) = f₁(x) + f₂(x), where f₁(x) is an even function and f₂(x) is an odd function.

Then f₁(x + y) + f₁(x - y) equals

Which one of the following statements is not a tautology?

If  , then ( 1 + iz + z⁵ + iz⁸ )⁹ is equal to:

, were g is a non-zero even function. If f( x + 5) = g(x), then  equals

Let S(λ) = { (x, y) : y²≤ 4x, 0 ≤  x  ≤  λ } and A(λ) is the area of the region S(λ). If for λ, 0 < λ < 4, A(λ) : A(4) = 2 : 5 then λ equals:

If the system of linear equations

x - 2y + kz = 1

2x + y + z = 2

3x – y – kz =3

Has a solution (x, y, z), z ≠ 0, then (x, y) lies on the straight line whose equation is:

A student score the following marks in five tests: 45, 54, 41, 57, 43. His score is not known for the sixth test. If the mean score is 48 in the six tests, then the standard deviation of the marks in six tests is:

If f(1)=1 and f’(1)=3, the derivative of f(f(f(x)))+(f(x))² at x = 1 is:

Given that the slope of the tangent to a curve y = y(x) at any point (x, y) is . If the curve passes through the center of the circle x² + y² - 2x - 2y = 0, then its equation is:

Suppose that the points (h, k), (1, 2) and (–3, 4) lie on the line L₁. If a line L₂ passing through the points (h, k) and (4, 3) is perpendicular to L₁, then  equals: