Mathematics Tes...

Out of \(7\) consonants and \(4\) vowels, how many words can be formed such that it contains \(3\) consonants and \(2\) vowels?

If two sides of a triangle are represented by \(x^2-7 x y+6 y^2=\) 0 and the centroid is \((1,0)\), then the equation of third side is

Integrate the function: \((4 x+2) \sqrt{x^{2}+x+1}\)

Let \(z\) and \(w\) be two non-zero complex numbers such that \(|{z}|=|{w}|\) and \(\arg ({z})+\arg ({w})=\pi,\) then \({z}\) equals:

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

Let \(P , Q , R\) and \(S\) be the points on the plane with position vectors \(-2 i-\) \(\hat{j}, 4 \hat{i}, 3 \hat{i}+3 \hat{j}\) and \(-3 \hat{i}+2 \hat{j}\) respectively. The quadrilateral \(P Q R S\) must be a:

In a survey of 600 students in a school, 150 students were found to be taking teaand 225 taking coffee, 100 were taking both tea and coffee. Find how manystudents were taking neither tea nor coffee?

If \(U=\left[\begin{array}{lll}2 & -3 & 4\end{array}\right], X=\left[\begin{array}{lll}0 & 2 & 3\end{array}\right], V=\left[\begin{array}{l}3 \\ 2 \\ 1\end{array}\right], Y=\left[\begin{array}{l}2 \\ 2 \\ 4\end{array}\right]\), then find out the value of \(U V+X Y\).

A ratio of the \(5^{\text {th }}\) term from the beginning to the \(5^{\text {th }}\) term from the end in the binomial expansion of \(\left(2^{\frac{1}{3}}+\frac{1}{2(3)^{\frac{1}{3}}}\right)^{10}\) is:

What is the distance of the point \((2,3,4)\) from the plane \(3 x-6 y+2 z+11=0\) ?