The circle C1:x2+y2=3, with centre at O, intersects the parabola x2=2y at the point P in the first quadrant. Let the tangent to the circle C1 at P touches other two circles C2andC3atR2andR3, respectively. Suppose C2andC3 have equal radii 23 and centres at Q2 and Q3 respectively. If Q2 and Q3 lie on the y-axis, then (a)Q2Q3=12(b)R2R3=46(c)area of triangle OR2R3 is 62(d)area of triangle PQ2Q3is=42
If f(x)∣cos(2x)cos(2x)sin(2x)−cosxcosx−sinxsinxsinxcosx∣,then:fprime(x)=0at exactly three point in (−π,π)fprime(x)=0at more than three point in (−π,π)f(x)attains its maximum at x=0f(x)attains its minimum at x=0
Box 1 contains three cards bearing numbers 1, 2, 3; box 2 contains five cards bearing numbers 1, 2, 3,4, 5; and box 3 contains seven cards bearing numbers 1, 2, 3, 4, 5, 6, 7. A card is drawn from each of the boxes. Let xi be the number on the card drawn from the ith box, i = 1, 2, 3.The probability that x1+x2+x3 is odd isThe probability that x1,x2,x3 are in an aritmetic progression is
Let p,qbe integers and let α,βbe the roots of the equation, x2−x−1=0,where α=β. For n=0,1,2,,letan=pαn+qβn˙FACT : If aandbare rational number and a+b5=0,thena=0=b˙If a4=28,thenp+2q=7 (b) 21 (c) 14 (d) 12
Let Xbe a set with exactly 5 elements and Ybe a set with exactly 7 elements. If αis the number of one-one function from Xto Yand βis the number of onto function from Yto X, then the value of 5!1(β−α)is _____.