Mathematics Tes...

If \(p(x)=(4 e)^{2 x}\), then what is \(\int p(x) d x\) equal to?

If \(S =\left[\begin{array}{cc}6 & -8 \\ 2 & 10\end{array}\right]= P + Q\), where \(P\) is a symmetric & \(Q\) is a skew \(-\) symmetric matrix, then the value of \(Q\) is:

A determinant (Δ) of 3 rows (R₁, R₂, R₃) and 3 columns (C₁, C₂, C₃) has a value Δ = 15. If two columns C₂ and C₃ of determinant (Δ) are interchanged, then the value of determinant will be

If \(3 \cos \theta=5 \sin \theta\), then the value of \(\frac{5 \sin \theta-2 \sec ^3 \theta+2 \cos \theta}{5 \sin \theta+2 \sec ^3 \theta-2 \cos \theta}\) is:

Integrating factor of the differential equation\(\left(1-x^2\right) \frac{d y}{d x}-x y=1\) is:

\(\int \frac{1}{1+e^x} d x\) is equal to

On a chess board, in how many different ways can \(6\) consecutive squares be chosen on the diagonals along a straight path?

Direction: In this question, two equations (I) and (II) are given. You have to solve both the equations and give an answer.

I. 15x² – 11x + 2 = 0

II. 10y² – 9y + 2 = 0

If x = 2 + 3 cos θ and y = 1 - 3 sin θ represent a circle then the centre and radius is: