The sum of number of angular nodes and radial nodes for $4 d$-orbital is

If the position of the electron was measured with an accuracy of +0.002 nm . The uncertainty in the momentum of it would be (in $\mathrm{kg} \mathrm{ms}^{-1}$ )

$$ \left(h=6.626 \times 10^{-34} \mathrm{Js}\right) $$

$$ \text { Match the following. } $$

Observe the following reactions

(i) $2 \mathrm{KClO}_3(s) \xrightarrow{\Delta} 2 \mathrm{KCl}(s)+3 \mathrm{O}_2(g)$

(ii) $2 \mathrm{H}_2 \mathrm{O}_2(a q) \xrightarrow{\Delta} 2 \mathrm{H}_2 \mathrm{O}(l)+\mathrm{O}_2(g)$

(iii) $\mathrm{AgNO}_3(a q)+\mathrm{KCl}(a q) \longrightarrow \mathrm{AgCl}(s)+\mathrm{KNO}_3(a q)$

(iv) $2 \mathrm{Na}(s)+\frac{1}{2} \mathrm{O}_2(g) \longrightarrow \mathrm{Na}_2 \mathrm{O}(s)$

The number of redox reactions in thsi list is

Which of the following sets are correctly matched?

(i) $\mathrm{B}_2 \mathrm{H}_6$ - electron deficient hydride

(ii) $\mathrm{NH}_3$ - electron precise hydride

(iii) $\mathrm{H}_2 \mathrm{O}$ - electron rich hydride

Which of the following, on thermal decomposition, form both acidic and basic oxides along with $\mathrm{O}_2$ ?

(i) $\mathrm{NaNO}_3$

(ii) $\mathrm{Ca}\left(\mathrm{NO}_3\right)_2$

(iii) $\mathrm{Be}\left(\mathrm{NO}_3\right)_2$

(iv) $\mathrm{LiNO}_3$

The correct option is

Identify the correct sets

(i) Boron fibres - bullet proof vest

(ii) Metal borides - protective shields

(iii) Borax - glass wool

Correct option is

Which of the following is /are ionic in nature?

(i) $\mathrm{GeF}_4$

(ii) $\mathrm{SnF}_4$

(iii) $\mathrm{PbF}_4$

The correct option is

Two statements are given below

Statements I : Liquids $A$ and $B$ form a non-ideal solution with positive deviation. The interactions between $A$ and $B$ are weaker than $A-A$ and $B-B$ interactions.

Statements II : For an ideal solution $\Delta_{\text {mix }} H=0$; $\Delta_{\text {mix }} V=0$

The correct answer is

At 300 K , the $E_{\text {cell }}^{\ominus}$ of

$$ A(s)+B^{2+}(a q) \rightleftharpoons A^{2+}(a q)+B(s) $$

is 1.0 V . If $\Delta_r S^\theta$ of this reaction is $100 \mathrm{JK}^{-1}$. What is $\Delta_r H^{\ominus}$ (in $\mathrm{kJ} \mathrm{mol}^{-1}$ ) of this reaction?

$$ \left(\mathrm{F}=96500 \mathrm{C} \mathrm{~mol}^{-1}\right) $$

Two statements are given below

Statements I : Adsorption of a gas on the surface of charcoal is primarily an exothermic reaction.

Statement II : A closed vessel contains $\mathrm{O}_2, \mathrm{H}_2, \mathrm{Cl}_2$, $\mathrm{NH}_3$ gases. Its pressure is $p$ (atm). About 1 g of charcoal is added to this vessel and after some time its pressure was found to be less than $p$ (atm)

The correct answer is

Arrange the following in the increasing order of their magnetic moments

I. $\left[\mathrm{Mn}(\mathrm{CN})_6\right]^{3-}$

II. $\left[\mathrm{Mn} \mathrm{Cl}_6\right]^{3-}$

III. $\left[\mathrm{Fe}(\mathrm{CN})_6\right]^{3-}$

IV. $\left[\mathrm{FeF}_6\right]^{3-}$

Toluene on reaction with the reagent $X$ gave $Y$, which dissolves in $\mathrm{NaHCO}_3$ and when reacted with $\mathrm{Br}_2 / \mathrm{Fe}$ gave $Z$. What are $X$ and $Z$ ?

Which of the following function are odd?

I. $f(x)=x\left(\frac{e^x-1}{e^x+1}\right)$

II. $f(x)=k^x+k^{-x}+\cos x$

III. $f(x)=\log \left(x+\sqrt{x^2+1}\right)$

If the system of equations $a_1 x+b_1 y+c_1 z=0, a_2 x+b_2 y+c_2 z=0$ and $a_3 x+b_3 y+c_3 z=0$ has only trivial solution, then the rank of $\left[\begin{array}{lll}a_1 & b_1 & c_1 \\ a_2 & b_2 & c_2 \\ a_3 & b_3 & c_3\end{array}\right]$ is

$(r, \theta)$ denotes $r(\cos \theta+i \sin \theta)$. If $x=(1, \alpha), y=(1, \beta), z=(1, \gamma)$ and $x+y+z=0$, then $\Sigma \cos (2 \alpha-\beta-\gamma)$ is equal to

The cubic equation whose roots are the square of the roots of the equation is

$$ 12 x^3-20 x^2+x+3=0 $$

$\frac{4 x^2+5}{(x-2)^4}=\frac{A}{(x-2)}+\frac{B}{(x-2)^2}+\frac{C}{(x-2)^3}+\frac{D}{(x-2)^4}$, then $\sqrt{\frac{A}{C}+\frac{B}{C}+\frac{D}{C}}$ is equal to

$$ \tan ^2 \frac{\pi}{16}+\tan ^2 \frac{2 \pi}{16}+\tan ^2 \frac{3 \pi}{16}+\tan ^2 \frac{4 \pi}{16} $$

$+\tan ^2 \frac{5 \pi}{16}+\tan ^2 \frac{6 \pi}{16}+\tan ^2 \frac{7 \pi}{16}$ is equal to

$$ \begin{aligned} & \sin ^2 18^{\circ}+\sin ^2 24^{\circ}+\sin ^2 36^{\circ}+\sin ^2 42^{\circ}+\sin ^2 78^{\circ} \\ & +\sin ^2 90^{\circ}+\sin ^2 96^{\circ}+\sin ^2 102^{\circ}+\sin ^2 138^{\circ}+\sin ^2 162^{\circ} \text { is } \\ & \text { equal to } \end{aligned} $$

If $0 < x < \frac{1}{2}$ and $\alpha=\sin ^{-1} x+\cos ^{-1}\left(\frac{x}{2}+\frac{\sqrt{3-3 x^2}}{2}\right)$, then $\tan \alpha+\cot \alpha$ is equal to

$$ \text { In } \triangle A B C, \frac{r_2\left(r_1+r_3\right)}{\sqrt{r_1 r_2+r_2 r_3+r_3 r_1}} \text { is equal to } $$

The probability that $A$ speaks truth is $75 \%$ and the probability that $B$ speaks truth is $80 \%$. The probability that they contradict each other when asked to speak on a fact is

If the probability distribution of a random variable $X$ is as follows, then $k$ is equal to

$$ \begin{array}{c|l|l|l|l} \hline X=x & 1 & 2 & 3 & 4 \\ \hline P(X=x) & 2 k & 4 k & 3 k & k \\ \hline \end{array} $$

If the line through the point $P(5,3)$ meets the circle $x^2+y^2-2 x-4 y+\alpha=0$ at $A(4,2)$ and $B\left(x_1, y_1\right)$, then $P A \cdot P B$ is equal to

If $P$ is a point which divides the line segment joining the focus of the parabola $y^2=12 x$ and a point on the parabola in the ratio $1: 2$. Then, the locus of $p$ is

Let $f(x)=\left\{\begin{array}{cl}1+\frac{2 x}{a}, & 0 \leq x \leq 1 \\ a x, & 1 < x \leq 2\end{array}\right.$.If $\lim _{x \rightarrow 1} f(x)$ exists, then the sum of the cubes of the possible values of $a$ is

Let $[P]$ denote the greatest integer $\leq P$. If $0 \leq a \leq 2$, then the number of integral values of ' $a$ ' such that $\lim \limits_{x \rightarrow a}\left(\left[x^2\right]-[x]^2\right)$ does not exist is

If $\int_0^{2 \pi}\left(\sin ^4 x+\cos ^4 x\right) d x=K \int_0^\pi \sin ^2 x d x+L \int_0^{\frac{\pi}{2}} \cos ^2 x d x$ and $K, L \in N$, then the number of possible ordered pairs ( $K, L$ ) is

If $(a, \beta)$ is the stationary point of the curve $y=2 x-x^2$, then the area bounded by the curves $y=2^x, y=2 x-x^2, x=0$ and $x=\alpha$ is

Path of projectile is given by the equation $Y=P x-Q x^2$, match the following accordingly (acceleration due to gravity $=g$ )

$$ \begin{array}{llll} \hline \text { a. } & \text { Range } & \text { i } & \frac{P}{Q} \\ \hline \text { b. } & \text { Maximum height } & \text { ii } & P \\ \hline \text { c. } & \text { Time of flight } & \text { iii } & \frac{P^2}{4 Q} \\ \hline \text { d. } & \text { Tangent of projection } & \text { iv } & \left(\sqrt{\frac{2}{g Q}}\right) P \\ \hline \end{array} $$

A particle of mass $m$ at rest on a rough horizontal surface with a coefficient of friction $\mu$ is given a

velocity $u$. The average power imparted by friction before it stops

As shown in the figure, two blocks of masses $m_1$ and $m_2$ are connected to spring of force constant $k$. The blocks are slightly displaced in opposite directions to $x_1, x_2$ distances and released. If the system executes simple harmonic motion, then the frequency of oscillation of the system ( $\omega$ ) is

Energy levels $A, B$ and $C$ of a certain atom corresponding to increasing values of energy i.e $E_A < E_B < E_C$. If $\lambda_1, \lambda_2$ and $\lambda_3$ are the wavelengths of a photon corresponding to the transitions shown then.

$$ \text { The following configuration of gates is equivalent to } $$