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 \(7 \sin \theta+24 \cos \theta=25\), then what is the value of \((\sin \theta+\cos \theta) ?\)

The angle \(\theta\) between the vectors \(\vec{a}=5 \hat{i}-\hat{j}+\hat{k}\) and \(\vec{b}=\hat{i}+\hat{j}-\hat{k}\) is:

Consider a differential equation \(\frac{d y(x)}{d x}-y(x)= x\) with the initial condition \(y(0)=0\). Using Euler's first order method with a step size of \(0.1\), the value of \(y(0.3)\) is-

Axis of a parabola lies along x-axis. If its vertex and focus are at distances \(2\) and \(4\) respectively from the origin, on the positive x-axis then which of the following points does not lie on it?

If \(f(x)=2^{x}+1\), then \(f(-3), f(1)\) and \(f(3)-1\) are in:

Find the general solution of the equation, \(2 \cos (\frac{x}{3})+\sqrt{2}=0 ?\)

The coefficient of \(x^{5}\) in the expansion of \((1+x)^{21}+(1+x)^{22}+\ldots+(1+x)^{30}\) is:

Represent the complex number \(Z=-2-i 2 \sqrt{3}\) in the polar form.

The complex number \(\frac{(-\sqrt{3}+3 i)(1-i)}{(3+\sqrt{3} i)(i)(\sqrt{3}+\sqrt{3} i)}\) when represented in the Argand diagram is:

The image of the point \(P(1,3,4)\) in the plane \(2 x-y+z=0\) is:

Find the equation of a circle touching both the x-axis and y-axis and has centre at (-2, -2).

A straight line through \(P(1,2)\) is such that its intercept between the axes is bisected at \(P\). Its equation is: