Mathematics Tes...

How many 4-digit numbers can be formed using digits 1, 2, 3, 4, 7, 9 lying between 3000 and 5000, if repetition of digits is allowed?

If \(\log x+\log 5=\log x^{2}-\log 14\), the \(x\) is equal to:

If \(\mathrm{X}=\left\{8^{\mathrm{n}}-7 \mathrm{n}-1, \mathrm{n} \in \mathbf{N}\right\}\) and \(\mathrm{Y}=49(\mathrm{n}-1), \mathrm{n} \in \mathbf{N},\) then: \((\) given \(\mathrm{n}>1)\)

If \(\alpha, \beta\) are the roots of \(a x^{2}+b x+c=0,\) find the value of \((1+\alpha)(1+\beta)\):

Consider the function:-

Let \(z=\left(\frac{\sqrt{3}}{2}+\frac{i}{2}\right)^5+\left(\frac{\sqrt{3}}{2}-\frac{i}{2}\right)^5\). If \(R(z)\) and \(I(z)\) respectively denote the real and imaginary parts of \(z\), then:

Given function \(f(x)=\left(\frac{e^{2 z}-1}{e^{2 z}+1}\right)\) is:

Find the angle between the vector \(\vec{a}=\hat{i}+\hat{j}-\hat{k}\) तथा \(\vec{b}=\hat{i}-\hat{j}+\hat{k}\).

For what values of \(k\), the equations:

\(x+y+z=1\)

\(2 x+y+4 z=k\)

\(4 x+y+10 z=k^{2}\)

have a solution?

If \(A=\left[\begin{array}{lll}3 & 1 & 2 \\ 4 & 2 & 1 \\ 2 & a & 1\end{array}\right]\) is a singular matrix, then value of \(a\):