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You have gone to a game show where the objective is to win a car. The host leads you to a room where there are three absolutely identical doors. You are told that behind one of the doors is the car, and behind the other two i ...
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Find the common area of the regions x2+y2≤100 and sin(x+y)>0. ...
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Consider an equilateral triangle ABC with side length 2.1cm. Find the minimum number of equilateral triangles with side length 1cm which can be placed over ΔABC so that it is completely covered. ...
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∫ sin(n+ 1/2 )x/sinx .dx. Integration from 0 to π. n is a natural number. ...
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A smooth sphere of radius R is made to translate in a straight line with constant acceleration a=g. A particle kept on the top of the sphere is released from there at zero velocity with respect to the sphere. The speed of the ...
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Point P(a, b) is in the first quadrant. A circle of radius r, centre P and containing points in each quadrant is drawn. If AK is the area inside the circle in the Kth quadrant, K=1, 2, 3, 4, then A1-A2+A3-A4= (a) ab (b) 2ab ( ...
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This is a great problem which you can probably approach in a number of different ways. All natural numbers are arranged as follows. 1 3 6 10 15 . 2 5 9 14 . . 4 8 13 . . . 7 12 . . . . 11 . . . . . and so on. Find the row and ...
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In a meter bridge experiment, the resistance to be measured is connected in the right gap and a known resistance in the left gap has a value of 50±0.2 Ω when the null point is judged to be at 60±0.2 cm. The student notes t ...
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A micrometer screw gauge with pitch of 0.5 mm and 50 divisions on circular scale is used to measure the diameter of a thin wire. Initially, when the gap is closed, the fourth division coincides with the reference line. Three ...
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A steady current I flows through a wire of resistivity Ï, length L and radius r. The current produces heat in the wire. The rate of heat loss in the wire is proportional to its surface area. The steady temperature of the wir ...
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Let S={1,2,3,...,n} and A={(a,b)l1≤a,b≤n}=S X S. A subset B of A is said to be a good subset if (x,x) belongs to B for every x belonging to S. Then the number of good subsets of A is A. 1 B. 2n C.2n(n-1) D.2n2 The answer ...
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When any three points are selected from a circle, what is the probability that they will form an obtuse-angled triangle? ...
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A filled water bottle is lying on the ground. You pick it up and put it on a table which is at some height from the ground. Thus the potential energy of the bottle increases. Does the internal energy of the water molecules in ...
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It is given that a1=1 and an=n(an-1+1). Define a sequence pn as pn=(1+ 1/a1 )(1+ 1/a2 )...(1+ 1/an ). Find lim(n→∞)pn. ...
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If Im,n = ∫cosmx.sin(nx).dx, then find 7I4,3 - 4I3,2. ...
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Among all cyclic quadrilaterals inscribed in a circle of radius R with one of its angles equal to 120°, consider the one with maximum possible area. Its area is: (a) √2R2 (b) 2R2 (c) √3R2 (d) 2√3R2 ...
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A sphere of radius R and surface charge density σ is rotating about an axis passing through its centre with angular velocity ω. Find the magnetic induction at the centre of the sphere. ...
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If p(x) is an 11th degree polynomial such that p(x) = 1/1+x for x = 1, 2, 3,...11, then find p(12). ...
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The equation of a curve is y = f(x). The tangents at (1, f(1)), (2, f(2)) and (3, f(3)) make angles π/6 , π/3 and π/4 respectively with the positive direction of the x-axis. Then the value of 23∫f'(x).f"(x).dx +13∫f"(x ...
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What is the condition that the equation ax2+bx+c has a root in [0, 1]? In class, we integrated the given expression and arrived at the condition a/3 + b/2 +c=0. However, if we take the equation (x-2)(x-0.5)=0 ie x2- 5/2 x+1=0 ...
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Let f:R-->R be a continuous function such that f(x)-2f( x/2 )+f( x/4 ) = x2. f(3) is equal to (A) f(0) (B) 4+f(0) (C) 9+f(0) (D) 16+f(0). The equation f(x)-x-f(0) = 0 has exactly (A) No solution (B) One solution (C) Two so ...
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Prove that the net internal torque on a body is zero if and only if the action-reaction forces between all pairs of its particles act along the line joining the two particles. ...
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lim (x-> 0) [f(x)+log {1-(1/ef (x))}-log (f(x))]=0. Find f (0). ...
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Can anyone please suggest how to prepare for KVPY Interview i.e. what topics to study, what type of questions to expect etc. ...
