List of practice Questions

Solve the differential equation $\log\left(\dfrac{dy}{dx}\right) = 3x + 4y$.
The modulus function $f: \mathbb{R} \to \mathbb{R}^{+}$ given by $f(x) = |x|$ will be:
Evaluate: $\int x^{2}\sin(x^{3})\,dx$
If the vectors $2\hat{i} + \hat{j} - a\hat{k}$ and $\hat{i} + 4\hat{j} + \hat{k}$ are perpendicular, find the value of $a$.
Solve $\dfrac{dy}{dx} = \dfrac{x + e^x}{y}$.
If $\sin^{-1}\left(\dfrac{1}{2}\right) = \tan^{-1}x$, find the value of $x$.
If $A = \begin{bmatrix} 2 & 4 \\ 3 & 2 \end{bmatrix}$ and $B = \begin{bmatrix} 1 & 3 \\ -2 & 5 \end{bmatrix}$, then find the value of $(A + B)$ and $(A - B)$.
If $A = \begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix}$ and $B = \begin{bmatrix} 1 & 0 \\ 0 & -1 \end{bmatrix}$, then $BA$ will be:
The slope of the normal to the curve $y = 2x^{2} + 3\sin x$ at $x = 0$ will be:
The value of $\int_{1}^{\sqrt{3}} \dfrac{dx}{1+x^{2}}$ will be:
If $y = 4t$ and $x = \dfrac{4}{t}$, then the value of $\dfrac{dy}{dx}$ will be:
She gave a ____ performance of the concert that had the audience on its feet.
For any \(n≥0\) the value of \(\sum_{r=0}^n \dfrac{(4r+3).(nC_r)^2}{(2n+3)}\) is 
The set of points of the form(t^2+t+1,t^2-t+1),where t is a real number, represents a/an
Calculate and determine number of byes if 19 teams are participating in a knock-out tournament ?

Let \(\beta\) be a real number Consider the
 \(matrix\ A=\begin{pmatrix}\beta & 0 & 1 \\2 & 1 & -2 \\3 & 1 & -2\end{pmatrix}If A^7-(\beta-1) A^6-\beta A^5\) is a singular matrix, then the value of \(9 \beta\) is _____

In the Young’s double slit experiment, the intensity of light passing through each of the two double slits is 2 × 10-2 Wm-2. The screen-slit distance is very large in comparison with slit-slit distance. The fringe width is β. The distance between the central maximum and a point P on the screen is \(\frac{\beta}{3}\). Then the total light intensity at that point is
If \(\overrightarrow F=2z\hat{i}-x\hat{j}+y\hat{k}\) and Vis the region bounded by the surface x=0,y=0,x=2,y=4,z=x2,z=2, then value of \(\iiint\limits_V\overrightarrow FdV\)is
Shown below are four sides of a rectangular dice. If 3 such dice are thrown together, what is the probability of getting a total sum of 4? Consider the value of the blank side to be zero.
Rectangular dice
Which of the following body constituted under the Consumer Protection Act, 2019 is authorized to render advice on promotion and protection of consumers’ rights under the Act?
Which of the following is an object on which general funds could be spent as per section 15 of the Trade Union Act, 1926?
Compound A with molecular formula (C2H6O) on oxidation by PCC gives compound B, which on treatment with dilute alkali forms compound C (a β-hydroxy aldehyde). B on oxidation by potassium permanganate forms C.
Identify A, B, C and D and write all the chemical equations involved.
If BAG = 10, HIT = 32, then CAT = ?
Which one is the correct expression of electric potential on the axial point of a dipole whose dipole moment is р and length is 2l, at a distance of r?
Select the pair in which the numbers are similarly related as in the given pair :
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