Class 12th

If (a + √2bcos x)(a – √2bcos y) = a² – b², where a > b > 0, then dy/dx at (π/4, π/4) is

Let x₀ be the point of local maxima of f(x) = a · (b * c) where a = xî − 2ĵ + 3k, b = −2î + xĵ − k and c = 7î – 2ĵ + xk. Then the value of a · b + b · c + c · a at x = x₀ is

Let f be a twice differentiable function on (1,6). If f(2) = 8, f'(2) = 5, f'(x) ≥ 1 and f''(x) ≥ 4, for all x ∈ (1,6), then:

Let f(x) = |x − 2| and g(x) = f(f(x)), x ∈. Then ∫?³ (g(x) – f(x))dx is equal to:

In the line spectra of hydrogen atom, difference between the largest and the shortest wavelengths of the Lyman series is 304Å. The corresponding difference for the Paschan series in Å is:

In a compound microscope, the magnified virtual image is formed at a distance of 25 cm from the eye-piece. The focal length of its objective lens is 1 cm. If the magnification is 100 and the tube length of the microscope is 20 cm, then the focal length of the eyepiece lens (in cm ) is

A battery of 3.0 V is connected to a resistor dissipating 0.5 W of power. If the terminal voltage of the battery is 2.5 V, the power dissipated within the internal resistance is:

Two charged thin infinite plane sheets of uniform surface charge density σ+and σ−, where |σ+| > |σ−|, intersect at right angle. Which of the following best represents the electric field lines for this system.

A two point charges 4q and –q are fixed on the x-axis at x = −d/2 and x = d/2, respectively. If a third point charge ' q ' is taken from the origin to x = d along the semicircle as shown in the figure, the energy of the charge will:

A small bar magnet placed with its axis at 30° with an external field of 0.06 T experiences a torque of 0.018Nm. The minimum work required to rotate it from its stable to unstable equilibrium position is: