Diameter of plano-convex lens is 6 cm and thickness at the centre is 3 mm. If speed of light in material of lens is 2 × 10⁸m/s, the focal length of the lens is

A bob of mass m attached to an inextensible string of length t is suspended from a vertical support. The bob rotates in a horizontal circle with an angular speed co rad/s about the vertical. About the point of suspension:

Proton, Deuteron and alpha particle of the same kinetic energy are moving in circular trajectories in a constant magnetic field. The radii of proton, deuteron and alpha particle are respectively r_p, r_d and r_α. Which one of the following relations is correct?

Two stones are projected from the top of a cliff h meters high, with the same speed u so as to hit the ground at the same spot. If one of the stones is projected horizontally and the other is projected at an angle θ to the horizontal then tan θ equals

The limiting molar conductivities Λ ° for NaCl, KBr and KCl are 126, 152 and 150 S cm² mol^-1 respectively. The Λ ° for NaBr is

The reaction of zinc with dilute and concentrated nitric acid, respectively, produces:

Which of the following on heating with aqueous KOH, produces acetaldehyde?

Tertiary alkyl halides are practically inert to substitution by S_N2 mechanism because of

If  are non-coplanar vectors and λ is a real number then 

  for

If the roots of the quadratic equation x² + px + q = 0 are tan30 ° and tan 15 °, respectively then the value of 2 + q – p is

The value of x for which 4 sin^–1x + cos^–1x = π will be

The line parallel to the x-axis and passing through the intersection of the lines ax + 2by + 3b = 0 and bx - 2ay - 3a = 0, where (a, b) ≠ (0, 0) is