Let L1 and L2 denote the lines r=i+λ(−i^+2j^+2k^),λ∈R and r=μ(2i^−j^+2k^),μ∈R
Respectively if L3 is a line which is perpendicular to both L1 and L2 and cuts both of them, then which of the following options describe(s) L3?
Let x, y and z be three vectors each of magnitude V2 tion on and the angle between each pair of them is E. If a is a let non-zero vector perpendicular to x and yx z and b is a non-zero tor perpendicular to y and z x x, then 1.
Let f(x)=∣1−x∣1−x(1+∣1−x∣)cos(1−x1) for x=1. Then: (A)(lim)n→1−f(x) does not exist (B)(lim)n→1+f(x) does not exist (C)(lim)n→1−f(x)=0 (D)(lim)n→1+f(x)=0
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
Let a,b,xandy be real numbers such that a−b=1andy=0. If the complex number z=x+iy satisfies Im(z+1az+b)=y , then which of the following is (are) possible value9s) of x? (a)−1−1−y2 (b) 1+1+y2(c)−1+1−y2 (d) −1−1+y2
Let fprime(x)=2+sin4πx192x3forallx∈Rwithf(21)=0.Ifm≤∫211f(x)dx≤M, then the possible values of mandM are (a)m=13,M=24 (b) m=41,M=21(c)m=−11,M=0 (d) m=1,M=12
Let PR=3i^+j^−2k^andSQ=i^−3j^−4k^determine diagonals of a parallelogram PQRS,andPT=i^+2j^+3k^be another vector. Then the volume of the parallelepiped determine by the vectors PT, PQand PSis5b. 20c. 10d. 30
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
A circle C of radius 1 is inscribed in an equilateral triangle PQR. The points of contact of C with the sides PQ, QR, RP are D, E, F, respectively. The line PQ is given by the equation 3x+y−6=0 and the point D is (3 sqrt3/2, 3/2). Further, it is given that the origin and the centre of C are on the same side of the line PQ. (1)The equation of circle C is (2)Points E and F are given by (3)Equation of the sides QR, RP are