Mathematics Tes...

The value of the term independent of \(x\) in the expansion of \(\left(x^{2}-\frac{1}{x}\right)^{9}\) is:

If \(\int \frac{b x \cos 4 x-a \sin 4 x}{x^{2}} d x=\frac{a \sin 4 x}{x},\) then a and \(b\) may be-

If \(a, b, c\) are three unit vectors such that \(\vec{a} \times(\vec{b} \times \vec{c})=\frac{1}{2} \vec{b}\) and \(\mathrm{b}\) is not parallel to \(c\), then the angle between a and \(\mathrm{c}\) is:

If \(f(x)=\left[\sqrt{2}-x^{2}\right]\) (where \([.]\) is g.i.f. \(),\) then which of the following statements is/are wrong?

The equation of a tangent to the circle x² + y² = 25 passing through the point (-2, 11) is

In how many ways seven different books be distributed to two persons if each person receives at least one book ?

If the roots of the equation \(\left(\mathrm{a}^{2}+\mathrm{b}^{2}\right) \mathrm{x}^{2}-2 \mathrm{~b}(\mathrm{a}+\mathrm{c}) \mathrm{x}+\left(\mathrm{b}^{2}+\mathrm{c}^{2}\right)=0\) are equal, then which one of the following is correct?

The equation \(|z-\omega|^{2}+\left|z-\omega^{2}\right|^{2}=\lambda\) represents the equation of a circle with \(\omega, \omega^{2}\) as extremities of a diameter, then \(\lambda\) is, (where \(\omega, \omega^{2}\) are cube roots of unity)

A function \(f: R \rightarrow R\) satisfies the functional relation \(f(x+2)=\sqrt{2} f(x+1)-f(x)\), then

Tangent at any point to a curve in the first quadrant meets the coordinate axes at A and B such that area of triangle OAB is always 2 square units. If the curve passes through (1, 1), then-

Find the length of longer diagonal of the parallelogram constructed on \(5 a+2 b\) and \(a-3 b\), if it is given that \(|a|=2 \sqrt{2},|b|=3\) and the angle between \(a\) and \(b\) is \(\frac{\pi}{4},\) is

If '\(M\)' and \(\sigma^2\) are mean and variance of random variable X, whose distribution is given by -

The projection of the line joining the points (3,4,5) and (4,6,3) on the line joining the points (-1,2,4) and (1,0,5) is :