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Statement-l: Sucrose is dextrorotatory and upon hydrolysis it becomes laevorotatory . Statement-II: Sucrose on hydrolysis gives glucose and fructose such that the laevo rotation of glucose is more than dextrorotation of fructose .

Statement-1: $NO_{2}$ is electron withdrawing group. Statement-2: Nitrobenzene is meta-directing. Statement-3: Nitrobenzene does not give Friedel Crafts alkylation :

What is the formal charge of atoms numbered as 1, 2, 3 and 4. In following structure :

Arrange following in order of $S_{N}1$ reaction : (Structures A, B, C, D are given with a $Br$ atom and $Ph$ groups) .

Arrange the given metal ion in increasing order of unpaired electron in low spin complexes formed by $Mn^{3+}, Cr^{3+}, Fe^{3+}, Co^{3+}$ :

In adiabatic compression temperature of gas becomes $4$ times while volume decreased $1/2$ times find $\gamma$ :

Given $E=10~V$, $R=10$, $L=10~mH$, $\frac{N}{e}=10^{4}$. Find energy density when current is $-\frac{1}{e}$ of max. If value is $a \frac{\pi}{e^{2}}$. Find $a$ .

Detector $D$ moves from $A$ to $B$ and observe the frequencies are differing by $10~Hz$. Source is emitting frequency $f_{0}$ as shown: Speed of detector is $35$ times less than speed of sound. Then $f_{0}$ is :

A simple pendulum with bob (mass $m$ and charge $q$) is in equilibrium in presence of horizontal electric field $E$ then tension in thread is .

Six charges (four $+q$, two $-q$) are present at circle of radius $r$ and centred at origin as shown. Electric field at origin is .

In a potentiometer null point for two resistance $R_{1}$ and $R_{2}$ is at $40~cm$ as shown. If $16~\Omega$ is connected in parallel to $R_{2}$ then null point is at $50~cm$ then $R_{1}$ and $R_{2}$ are respectively .

Match the following : \begin{tabular}{|l|l|} \hline List -1 & List-II \\ \hline (A) Spring constant & (i) $ML^{2}T^{-2}K^{-1}$ \\ \hline (B) Thermal conductivity & (ii) $ML^{0}T^{-2}$ \\ \hline (C) Boltzmann constant & (iii) $ML^{2}T^{-2}A^{-2}$ \\ \hline (D) inductance & (iv) $ML^{2}T^{-3}K^{-1}$ \\ \hline & (v) $M^{1}L^{-1}T^{-2}$ \\ \hline & (vi) $ML^{2}T^{-2}$ \\ \hline \end{tabular}

A projectile is thrown upward at an angle $60^{\circ}$ with the horizontal. The speed of the projectile is $20~m/s$ when its direction of motion is $45^{\circ}$ with horizontal. The initial speed of particle is .

If radius and density of planet $A$ are $R$ and $\rho$ respectively and escape velocity of planet $A$ is $10~km/h$. If radius of planet $B$ is $10\%$ of planet $A$ and $\rho_B = 10\%$ planet of $A$. Calculate of escape velocity of planet $B$ .

In the given situation force at center on $1~kg$ mass is $F_{1}$. Now if $4~m$ and $3~m$ is interchanged the force is $F_{2}$ Given: $\frac{F_{1}}{F_{2}}=\frac{2}{\sqrt{\alpha}}$ Find $\alpha$ . (Diagram shows masses $4m$, $3m$, $m$, $2m$ arranged around a center point) .

Given $\vec{E}=10x\hat{i}+5y\hat{j}$. Potential at $(10, 20)$ is $500~V$. Find potential at origin .

In series R-L circuit, voltage of battery is $10~V$. Resistance and inductance are $10~\Omega$ and $10~mH$ respectively. Find energy stored in the inductor when current reaches $\frac{1}{e}$ times of maximum value :

Two disc having same moment of inertia about their axis. Thickness is $t_{1}$ and $t_{2}$ and they have same density. If $R_{1}/R_{2}=1/2$, then find $t_{1}/t_{2}$ :

Chord joining at two points $(x_{1},y_{1})$ and $(x_{2},y_{2})$ on the parabola $y^{2}=12x$ intersect at right angle at the vertex, then $x_{1}x_{2}-y_{1}y_{2}=$ .

Let $A$ satisfy the equation $\lambda\begin{bmatrix}1\\2\\3\end{bmatrix}=\begin{bmatrix}-1\\0\\3\end{bmatrix}$, and $|2\text{adj}(A+I)|=2^{\alpha}3^{\beta}11^{\gamma}$ then $\alpha+\beta+\gamma$ is equal to .