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A box contains coupons labeled 1,2,3,....n. A coupon is picked at random and the number x is noted. The coupon is put back into the box and a new coupon is picked at random. The new number is y. Then the probability that one ...
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A plank is resting on a horizontal ground in the northern hemisphere of the earth at 45° latitude. Let the angular speed of the earth be ω and its radius be re. The magnitude of the frictional force on the plank will be A. ...
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A ball is rolling without slipping in a spherical shallow bowl as shown and executing SHM. If radius of the ball is doubled, the period of oscillation *Image* A) increases slightly B) is reduced by a factor of 1/2 C) is incre ...
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If f(x) is a function which is both even and odd, then f(3) - f(2) is equal to (a) +1 (b) -1 (c) 0 (d) none ...
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There are two drawers in each of three boxes that are identical in appearance. The first box contains a gold coin in each drawer, the second contains a silver in each drawer, but the third contains a gold in one drawer and a ...
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A metallic ball is suspended by an insulated string, in an uniform electric field. A X-Ray of high radiation is passed through the ball in the field. What will happen to the ball? ...
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Two curves C1 : y = x2 - 3 and C2 : y = kx2, k ε R intersect each other at two different points. The tangent drawn to C2 at one of the points of intersection A(a,y1), (a>0) meets C1 again at B (1, y2) (y1 ≠y2). The valu ...
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Equation of the line through the point ( 1/2 ,2) and tangent to the parabola y = - x2/2 + 2 and secant to the curve y = 4 - x2 is (A) 2x + 2y - 5 = 0 (B) 2x + 2y - 3 = 0 (C) y-2 = 0 (D) None of these ...
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Among various properties of continuous, we have ƒ is continuous function on [a,b] and ƒ(a)ƒ(b) < 0, then there exists a point c in (a,b) such that ƒ(x) = 0 equivalently if ƒ is continuous on [a,b] and x ε R is such t ...
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s2 = Σ(yi - a - bxi)2 = ƒ(a,b) (i= 1,2....n) Given: ∂s2/∂a = 0 ∂s2/∂b = 0 Then solve for a and b ...
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Show that a plumb line deviates from the vertical line slightly at all latitudes except 0° and 90° due to the diurnal motion of the earth. Also show that this effect is maximum at the latitude 45° and hence determine this ...
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In a test an examinee either guesses or copies or knows the answer to a multiple choice question with 4 choices. The probability that he makes a guess is 1/3 and the probability that he copies it is 1/6 . The probability that ...
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In a multiple choice question there are four alternative answers, of which one or more are correct. a candidate will get marks in the question only if he ticks all the correct answers. The candidate decides to tick the answer ...
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Let U1 and U2 be two urns such that U1 contains 3 white and 2 red balls, and U2 contains only 1 white ball. A fair coin is tossed. If head appears then 1 ball is drawn at random from U1 and put into U2. However, if tail appea ...
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A train is moving along a straight line with a constant acceleration a. A boy standing in the train throws a ball forward at an angle of 60° to the horizontal. The boy has to move forward by 1.15m inside the train to catch t ...
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A mass {{m}_{1}} hanging at the end string, draws a mass {{m}_{2}} along the surface of a smooth table if the mass on the table be doubled the tension in string becomes, 1.5 times then {{m}_{1}}/{{m}_{2}} is *Image* ...
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