Mathematics Tes...

Let \(f(x)=e^{(x-1)}-a x^{2}+b \& g(x)=\left[\begin{array}{ll}e^{x-1} & \text { for } x \leq 1 \\ x^{2}+1 & \text { for } x>1\end{array}\right.\) with \(f^{\prime}(1)=2 \cdot\) The values of a and \(b\) for which the function \(h(x)=f(x) \cdot g(x),\) is differentiable at \(x=1,\) are respectively

The function \(f(x)=\frac{\log _{e}(\pi+x)}{\log _{e}(e+x)}\) is

\(\int x^{\mathrm{x}^{2}}\left(2 \mathrm{x} \log _{\mathrm{e}} \mathrm{x}+\mathrm{x}\right) \mathrm{dx}\) is equal

The value of the definite integral \(\int_{0}^{1} \frac{d x}{\left(x^{2}+2 x \cos \alpha+1\right)}\) for \(0<\alpha<\pi,\) equal to

The solution to \(\frac{d y}{d x}+\frac{\tan y}{x}=\frac{1}{x^{2}} \tan y \sin y\) is :

In a triangle ABC, the angle B is greater than angle A . If the values of the angle A and B satisfy the equation \(3 \sin x-4 \sin ^{3} x-k=0\), 0 < k < 1, then value of C is

Coordinates of the orthocentre of the triangle whose sides are x=3, y=4 and 3x+4y=6, will be:

The area bounded by the curves \(x+2|y|=1\) and \(x=0\) is:

none of these equation of the hyperbola whose foci are (6,5), (-4,5)and eccentricity $\frac{5}{4}$ is

An equilateral triangle is inscribed in the parabola y²=4axwhose vertex is at the vertex of the parabola. The length of its side is