Mathematics Tes...

Consider the following statements:

1. The function \(f(x)=|x|\) is not differentiable at \(x=1\).

2. The function \(f(x)=e^{x}\) is differentiable at \(x=0\).

Which of the above statements is/are correct?

The area enclosed between the curves \(y=\sin x, y=\cos x, 0 \leq x \leq \frac{\pi}{2}\) is

The set of all values of \(\lambda\) for which the system of linear equations \(x-2 y-2 z=\lambda x\)

\(x+2 y+z=\lambda y\)

\(-x-y=\lambda z\) has a non-trivial solution:

Given that N = {1, 2, 3, …, 100}, then write B, the subset of N whose elements are represented by x + 2, where x is ∈ N.

The term independent of \({x}\) in \(\left({x}^{2}-\frac{1}{{x}^{3}}\right)^{10}\) is:

Let X be a square matrix. Consider the following two statements on X.

I. X is invertible.

II. Determinant of X is non-zero.

Which one of the following is TRUE?

For any two sets A and B, find the value of \([(A-B) \cup B]^{C}\):

Solve the linear inequality:

\(\frac{x}{4}<\frac{(5 x-2)}{3}-\frac{(7 x-3)}{5}\)

If \({y}=\sqrt{{x}+\sqrt{{x}+\sqrt{{x}+\ldots \infty}}}\), then \(\frac{{dy}}{{dx}}=?\)

The perpendicular distance between the straight lines 6x + 8y + 15 = 0 and 3x + 4y + 9 = 0 is: