If A = \(\left[ \begin{matrix} 2 & 3 \\ 5 & -2 \end{matrix} \right] \) be such that λA⁻¹ = A, then λ is

If A is a non-singular matrix such that A^-1 = \(\left[ \begin{matrix} 5 & 3 \\ -2 & -1 \end{matrix} \right] \), then (A^T)⁻¹ =

If A, B and C are invertible matrices of some order, then which one of the following is not true?

If the planes \(\vec { r } .(2\hat { i } -\lambda \hat { j } +\hat { k } )=3\) and \(\vec { r } .(4\hat{i}+\hat { j } -\mu \hat { k } )=5\) are parallel, then the value of λ and μ are

Distance from the origin to the plane 3x − 6y + 2z + 7 = 0 is

The angle between the line \(\vec { r } =(\hat { i } +2\hat { j } -3\hat { k } )+t(2\hat { i } +\hat { j } -2\hat { k } )\) and the plane \(\vec { r } .(\hat { i } +\hat { j } )+4=0\) is

The angle between the lines \(\frac{x-2}{3}=\frac{y+1}{-2}, z=2 \text { and } \frac{x-1}{1}=\frac{2 y+3}{3}=\frac{z+5}{2}\) is

The volume of the parallelepiped with its edges represented by the vectors \(\hat { i } +\hat { j } ,\hat { i } +2\hat { j } ,\hat { i } +\hat { j } +\pi \hat { k } \) is

If a vector \(\vec { \alpha } \) lies in the plane of \(\vec { \beta } \) and \(\vec { \gamma } \), then

An ellipse has OB as semi minor axes, F and F′ its foci and the angle FBF′ is a right angle. Then the eccentricity of the ellipse is

Area of the greatest rectangle inscribed in the ellipse \(\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1\) is

If P(x, y) be any point on 16x² + 25y² = 400 with foci F₁ (3, 0) and F₂ (-3, 0) then PF₁  + PF₂ is

If \(\sin ^{-1} \frac{x}{5}+\operatorname{cosec}^{-1} \frac{5}{4}=\frac{\pi}{2}\), then the value of x is

If \(\sin ^{-1} x+\cot ^{-1}\left(\frac{1}{2}\right)=\frac{\pi}{2}\), then x is equal to

If cot^-1 2 and cot^-1 3 are two angles of a triangle, then the third angle is

\(\tan ^{-1}\left(\frac{1}{4}\right)+\tan ^{-1}\left(\frac{2}{9}\right)\) is equal to

The domain of the function defined by \(f(x)=\sin ^{-1} \sqrt{x-1}\) is

If (1+i)(1+2i)(1+3i)...(1+ni) = x + iy, then \(2\cdot 5\cdot 10...\left( 1+{ n }^{ 2 } \right) \) is

The number of positive zeros of the polynomial \(\overset { n }{ \underset { j=0 }{ \Sigma } } { n }_{ C_{ r } }\)(-1)^rx^r is

The number of real numbers in [0, 2π] satisfying sin⁴x - 2sin²x + 1 is

If α, β and γ are the zeros of x³ + px² + qx + r, then \(\Sigma \frac { 1 }{ \alpha } \) is

A polynomial equation in x of degree n always has

A zero of x³ + 64 is

If |z₁| = 1, |z₂| = 2, |z₃| = 3 and |9z₁z₂ + 4z₁z₃ + z₂z₃| = 12, then the value of |z₁+z₂+z₃| is 

If |z| = 1, then the value of \(\frac { 1+z }{ 1+\overline { z } }\) is