For non-negative inger n, let
Assuming cos−1x takes values in [0,π] which of the following options is/are correct?
A line l passing through the origin is perpendicular to the lines l1:(3+t)i^+(−1+2t)j^+(4+2t)k^,∞<t<∞,l2:(3+s)i^+(3+2s)j^+(2+s)k^,∞<t<∞ then the coordinates of the point on l2 at a distance of 17 from the point of intersection of
Let f:RRbe a continuous odd function, which vanishes exactly at one point and f(1)=21˙Suppose that F(x)=∫−1xf(t)dtforallx∈[−1,2]andG(x)=∫−1xt∣f(f(t))∣dtforallx∈[−1,2]I˙G(x)f(lim)x1(F(x))=141,Then the value of f(21)is
For 3×3matrices MandN,which of the following statement (s) is (are) NOT correct ?NTMNis symmetricor skew-symmetric, according as mis symmetric or skew-symmetric.MN−NMis skew-symmetric for all symmetric matrices MandN˙MNis symmetric for all symmetric matrices MandN(adjM)(adjN)=adj(MN)for all invertible matrices MandN˙
Let a and b be two unit vectors such that a.b=0 For some x,y∈R, let c=xa+yb+(a×b If (∣c∣=2 and the vector c is inclined at same angle α to both a and b then the value of 8cos2α is
Column 1,2 and 3 contains conics, equations of tangents to the conics and points of contact, respectively.Column I, Column 2, Column 3I, x2+y2=a, (i), my=m2x+a, (P), (m2a,m2a)II, x2+a2y2=a, (ii), y=mx+am2+1, (Q), (m2+1−ma,m2+1a)III, y2=4ax, (iii), y=mx+a2m2−1, (R), (a2m2+1−a2m,a2m2+11)IV, x2−a2y2=a2, (iv), y=mx+a2m2+1, (S), (a2m2+1−a2m,a2m2+1−1)For a=2,ifa tangent is drawn to a suitable conic (Column 1) at the point of contact (−1,1),then which of the following options is the only CORRECT combination for obtaining its equation?(I) (ii) (Q) (b) (III) (i) (P)(II) (ii) (Q) (d) (I)(i)(P)
Let Obe the origin and let PQR be an arbitrary triangle. The point S is such thatOPO˙Q+ORO˙S=ORO˙P+OQO˙S=OQ.OR+OPO˙SThen the triangle PQ has S as its:circumcentre (b) orthocentre (c) incentre (d) centroid
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 _____.