Three lines L1,L2,L3 are given by L1:r=λi^,L2:r=μj^+k^,L3:r=i^+j^+γk^ which of the following point Q can be taken on L2 so that the point P on line L1 point Q on L2 and point R on L2 are collinear
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
Let Xbe the set consisting of the first 2018 terms of the arithmetic progression 1, 6, 11, ,¨and Ybe the set consisting of the first 2018 terms of the arithmetic progression 9, 16, 23, ¨. Then, the number of elements in the set X∪Yis _____.
Suppose that p,qandr are three non-coplanar vectors in R3. Let the components of a vector s along p,qandr be 4, 3 and 5, respectively. If the components of this vector s along (−p+q+r),(p−q+r)and(−p−q+r) are x, y and z, respectively, then the value of 2x+y+z is
If 2x−y+1=0 is a tangent to the hyperbola a2x2−16y2=1 then which of the following CANNOT be sides of a right angled triangle? (a)a,4,2 (b) a,4,1(c)2a,4,1 (d) 2a,8,1
In R', consider the planes P1,y=0 and P2:x+z=1. Let P3, be a plane, different from P1, and P2, which passes through the intersection of P1, and P2. If the distance of the point (0,1,0) from P3, is 1 and the distance of a point (α,β,γ) from P3 is 2, then which of the following relation is (are) true ?
For a point Pin the plane, let d1(P)andd2(P)be the distances of the point Pfrom the lines x−y=0andx+y=0respectively. The area of the region Rconsisting of all points Plying in the first quadrant of the plane and satisfying 2≤d1(P)+d2(P)≤4,is
Consider the hyperbola H:x2−y2=1 and a circle S with centre N(x2,0) Suppose that H and S touch each other at a point (P(x1,y1) with x1>1andy1>0 The common tangent to H and S at P intersects the x-axis at point M. If (l,m) is the centroid of the triangle ΔPMN then the correct expression is (A) dx1dl=1−3x121 for x1>1 (B) dx1dm=3(x12−1)x!)forx1>1 (C) dx1dl=1+3x121forx1>1 (D) dy1dm=31fory1>0
Consider the family of all circles whose centers lie on the straight line `y=x`. If this family of circles is represented by the differential equation `P y^(primeprime)+Q y^(prime)+1=0,`where `P ,Q`are functions of `x , y`and `y^(prime)(h e r ey^(prime)=(dy)/(dx),y^=(d^2y)/(dx^2)),`then which of the following statements is (are) true?(a)`P=y+x`(b)`P=y-x`(c)`P+Q=1-x+y+y^(prime)+(y^(prime))^2`(d)`P-Q=x+y-y^(prime)-(y^(prime))^2`