List of practice Questions

The value of $\lim_{x\rightarrow 0}\frac{\sqrt{1+x} - 1}{x} = $

The value of $\lim_{x\rightarrow\infty}(1 + \frac{1}{x})^{x} = $

The equation of the ellipse with foci at ($\pm$3, 0) and the eccentricity as 1/3 is:

The length of the latus rectum and eccentricity of the Hyperbola $9x^{2} - 16y^{2} = 144$ are}

The line $y = mx + 2$ is a tangent to the parabola $y^{2} = 8x$ if}

If the parabola $y^{2} = 4ax$ passes through the point (3, 2) then the length of its latus rectum is:}

The equation of a circle whose Centre is (2, -1) and which passes through the point (3, 6) is

The equation of a circle whose Centre is $(-3, 2)$ and area is $176$ units is:

The conjugate of $(1+i)^3$ is:

If $z_1 = 4i^{40} - 5i^{35} + 6i^{17} + 2$ and $z_2 = -1 + i$, then $|z_1 + z_2| =$

The value of $\tan^{-1} 1 + \tan^{-1} 2 + \tan^{-1} 3$ is:}

The value of $\cos 6^\circ \sin 24^\circ \cos 72^\circ$ is:

If $\cos \theta = \frac{1}{2}(a + \frac{1}{a})$, then $4 \cos^3 \theta - 3 \cos \theta =$

The value of $\tan 9^\circ - \tan 27^\circ - \tan 63^\circ + \tan 81^\circ$ is:

The expression $\frac{\tan x - 1 + \sec x}{\tan x - \sec x + 1}$ is equal to:}

If $\tan \theta + \sec \theta = \sqrt{3}$ then the principal value of $\theta$ in $[0, 2\pi]$ is

If $\begin{bmatrix}x+y & 2 \\ 1& x-y\end{bmatrix}=\begin{bmatrix}4& 2 \\ 1& 2\end{bmatrix}$, then the values of $x$ and $y$ are:}

Which of the following systems has non-trivial solution?

If $A$ is a square matrix of order 3 and $|A|=5$, then the value of $|2A^{T}|$ is

If $\begin{vmatrix}2x& 5 \\ 8 & x\end{vmatrix}=\begin{vmatrix}6 &-2 \\ 7& 3\end{vmatrix}$ then the value of $x$ is

In the matrix $A=\begin{bmatrix}1& 2& 3 \\ 4& 5 & 6 \\ 7& 4 & 9\end{bmatrix}$, the minor $M_{23}$ of the $a_{23}$ is

The differential equation is \[ \frac{dy}{dx}+y\tan x=\sec x \] and \(y(0)=1\). Then the value of \(y\left(\frac{\pi}{4}\right)\) is

The general solution of the differential equation \[ \frac{dy}{dx}=e^{x-y}+x^2e^{-y} \] is

The differential equation is \[ \frac{dy}{dx}+\frac{y}{x}=0 \] and \(y(1)=2\). Then the value of \(y(3)\) is

If \(a\) and \(b\) are arbitrary constants, then the differential equation representing the family of curves \[ y=a\sin(x+b) \] is