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A particle moves with velocity
\[
v(t) = 3t^2 + 2t \ \text{m/s}.
\]
What is its acceleration at \(t = 2\,\text{s}\)?

sove $\sqrt{x}+5+\sin x=\frac{dy}{dx}$

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Find number of solutions of $\tan^{-1}4x+\tan^{-1}6x=\frac{\pi}{6}$ in $(\frac{-1}{2\sqrt{6}},\frac{1}{2\sqrt{6}})$ .

Let $A=\begin{bmatrix}2&3\\3&5\end{bmatrix}$ , then $|A^{2025}-3A^{2024}-A^{2023}|$ is equal to .

The number of real solutions of equation $x|x+4|+3|x+2|+10=0$ is equal to .

If sum of first 4 terms of an A.P. is 6 and sum of first 6 terms is 4, then sum of first 12 terms of an A.P. is :

Consider the following statements: (A) Propanal and propanone are functional isomers; (B) Ethoxyethane and methoxypropane are metamers; (C) But-2-ene shows optical isomerism; (D) But-1-ene and but-2-ene are functional isomers; (E) Pentane and 2,2-dimethylpropane are chain isomers. The correct statements are:

$C_{6}H_{12}O_{3}$ gives positive iodoform test. On hydrolysis with dilute acid, the product formed gives both Tollens' test and iodoform test. Find the correct structure.

In the binomial expansion of $(ax^{2}+bx+c)(1-2x)^{26}$, the coefficients of $x$, $x^{2}$, $x^{3}$ are 56, 0 and 0 respectively. Then the value of $(a+b+c)$ is:

Out of the following, how many compounds have tetrahedral geometry? $NH4^{+}$, $XeF4$, $[NiCl4]^{2-}$, $[PtCl4]^{2-}$, $[Cu(NH3)4]^{2+}$, $BF3$, $[Ni(CO)4]$

Given below are two statements. Statement I: All the pairs of molecules $(PbO,PbO_{2})$; $(SnO,SnO_{2})$ and $(GeO,GeO_{2})$ contain amphoteric oxides. Statement II: $AlCl_{3}$, $BH_{3}$, $BeH_{2}$ and $NO_{2}$ all have incomplete octet.

An ideal solenoid is kept with its axis vertical. A current $I_{0}$ is flowing in the solenoid. A charge q is thrown vertically downward inside the solenoid. The acceleration of the charged particle is:

In the following reaction, $MnO4^{2-} \xrightarrow{H^{+}}$ ?. Manganate ion undergoes disproportionation to form:

Consider a set $S=\{a,b,c,d\}$. Then the number of reflexive as well as symmetric relations from $S\rightarrow S$ is: