The value of the expression tan (sin−1 x + cos−1 x2), when x = √32 is.

The pair of lines represented by 3ax2+5xy+(a2−2)y2=0 are perpendicular to each other for

Let f(θ)=sin(tan−1(sinθ√cos2θ));−π4<θ<π4, Then the value of d(d(tanθ))(f(θ)) is

If x, y, z are the 15th, 20th, 25th term of a G.P., then find the value ofΔ = ∣∣∣∣lnx151lny201lnz251∣∣∣∣

If the normal at θ on the ellipse 5x2+14y2=70 cuts the curve again at a point 2θ, then cosθ =

If |z−3|≤2, then maximum of |z+1| is

Let O be the origin, and −−→OX,−−→OY,−−→OZ be three unit vectors in the directions of the sides −−→QR,−−→RP,−−→PQ, respectively, of a triangle PQR. If the triangle PQR varies, then the minimum value of cos(P+Q)+cos(Q+R)+cos(R+P)

Let two tangents are drawn to the curve y2−4(x+y)=3sinθ+4cosθ−15, x,y,θ∈R from the origin whose slopes are m1,m2. If the vertex of the curve is at maximum distance from the origin, then the value of ∣∣∣1m1m2∣∣∣ is

If α, β and γ are the roots of x3+8=0, then the equation whose roots are α2,β2 and γ2 is

If PM is the perpendicular from P (2,3) on to the line x+y=3 then the co-ordinates of M are

A normal is drawn on the hyperbola x216−y29=1 at a point given by parameter π3. What is the x-intercept of the normal.

Verify Rolle's theorem for the function f(x)=x2+2x−8,xϵ[−4,2]

Find the values of cos−1x in terms of given options.

The distance of the point P(3, 8, 2) from the line x−12=y−34=z−23 measured parallel to the plane 3x+2y–2z+15 = 0 is ___