For a student to qualify, he must pass at least two out of three exams. The probability that he will pass the 1st exam is p. If he fails in one of the exams, then the probability of his passing in the next exam is p/2, otherwise it remains the same. Find the probability that he will qualify?

A bag contains 5 white, 7 black and 8 red balls. A ball is drawn at random. Find the probability of getting: (i) red ball (ii) non-white ball

Find the probability of the event A if (i) odds in favour of event A are 5 : 7 (ii) odds against A are 3 : 4?

A block of mass 0.50 kg is moving with a speed of 2.00 m/s on a smooth surface. It strikes another mass of 1.00 kg and then they move together as a single body. The energy loss during the collision is?

A wave travelling along the x-axis is described by the equation y(x, t) = 0.005 cos (αx −βt). If the wavelength and the time period of the wave are 0.08 m and 2.0 s, respectively, then α and β in appropriate units are

Two coaxial solenoids are made by winding thin insulated wire over a pipe of cross sectional area A = 10 cm2 and length = 20 cm. If one of the solenoids has 300 turns and the other 400 turns, their

mutual inductance is (μ0 = 4π × 10-7 Tm A-1)

A horizontal overhead power line is at a height of 4m from the ground and carries a current of 100 A from east to west. The magnetic field directly below it on the ground is (μ0 = 4π × 10-7 T m A-1)

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Consider a uniform square plate of side ‘a’ and mass ‘m’. The moment of inertia of this plate about an axis perpendicular to its plane and passing through one of its corners is?

A planet in a distant solar system is 10 times more massive than the earth and its radius is 10 times smaller. Given that the escape velocity from the earth is 11 kms−1, the escape velocity from the surface of the planet would be

The pKa of a weak acid, HA, is 4.80. The pKb of a weak base, BOH, is 4.78. The pH of an aqueous solution of the corresponding salt, BA, will be

In a compound atoms of element Y from ccp lattice and those of element X occupy 2/3rd of tetrahedral voids. The formula of the compound will be

The vapour pressure of water at 20oC is 17.5 mm Hg. If 18 g of glucose (C6H12O6) is added to 178.2 g of water at 20oC, the vapour pressure of the resulting solution will be

The ionization enthalpy of hydrogen atom is 1.312 × 106 Jmol−1. The energy required to excite the electron in the atom from n = 1 to n = 2 is?

How many different words can be formed by jumbling the letters in the word MISSISSIPPI in which no two S are adjacent?

The line passing through the points (5, 1, a) and (3, b, 1) crosses the yz−plane at the point (0, 17/2 , -13/2) then a =? and b = ?

The perpendicular bisector of the line segment joining P (1, 4) and Q (k, 3) has y−intercept − 4. Then a possible value of k is

The point diametrically opposite to the point P(1,0) on the circle x2 +y2 +2x+4y−3=0 is

A parabola has the origin as its focus and the line x = 2 as the directrix. Then the vertex of the parabola is at

A focus of an ellipse is at the origin. The directrix is the line x = 4 and the eccentricity is 1/2. Then the length of the semi−major axis is