Mathematics Tes...

If for the non-singular matrix \(A, A^{2}=I\), then find \(A^{-1}\).

Let P(x₁, y₁) and Q(x₂, y₂), y₁ < 0, y₂ < 0 be the end points of the latus rectum of the ellipse x₂ + 4y₂ = 4. The equation(s) of parabolas with latus rectum PQ is/are-

Let \(a, b, c\) are the Arithmetic means between two numbers such that \(a+b+c=15\) and \(p, q, r\) be Harmonic mean between same numbers such that \(\frac{1}{p}+\frac{1}{q}+\frac{1}{r}=\frac{5}{3}\) then the numbers are

The number of values of \(\lambda\) for which the given system of equations has No solution

\(x+2 y+3 z=5\)

\(4 x+6 y+2 \lambda z=21\)

\(x+\lambda y+3 z=3\)

In a triangle ΔPQR, cos(P - R) cos(Q) + cos(2Q) = 0

Which of the following options is/are correct?

If \(p \rightarrow(p \wedge \sim q)\)

is false, then truth value of \(p\) and \(q\) are respectively

If \((\mathrm{n}+1) !=12 \times(\mathrm{n}-1) !\), then the value of \(\mathrm{n}\) is?

Find the equation of ellipse whose eccentricity is \(\frac{1}{2}\), length of latus rectum is 4 and the center is \((0,0)\).

If the mean and standard deviation of 10 observations are 20 and 2 respectively. The sum of squares of all the observations is—

The internal bisector of ∠A of a triangle ABC meets side BC at D. A line drawn through D perpendicular to AD intersects the side AC at E and side AB at F. If a, b and c represent the sides of ΔABC, then-

Find the equation(s) of common tangent(s) to y = x² and y = - x² + 4x - 4.

The value of \({ }^{21} \mathrm{C}_{1}+{ }^{21} \mathrm{C}_{2}+\ldots .21 \mathrm{C}_{10}\) is \(-\)

The angles of elevation of top of a pole from two points \(A\) and \(B\) on the horizontal line lying on opposite side of the pole are observed to be \(30^{\circ}\) and \(60^{\circ}\) If \(A B=100 \mathrm{m}\) then height of the pole is

\(\int \frac{x^{2}-1}{\left(x^{2}+1\right)\left(x^{4}+1\right)^{1 / 2}} d x\)

Find the number of four digit numbers that are less than 2000 that can be formed with the digits 1,2,3,4 such that each digit can be repeated any number of times