Number of complexes from the following with even number of unpaired "$$\mathrm{d}$$" electrons is ________ $$[\mathrm{V}

What will be the decreasing order of basic strength of the following conjugate bases? $${ }^{-} \mathrm{OH}, \mathrm{R}

Given below are two statements : Statements I : Acidity of $$\alpha$$-hydrogens of aldehydes and ketones is responsible

Match List I with List II : .tg {border-collapse:collapse;border-spacing:0;} .tg td{border-color:black;border-style:so

Identify B and C and how are A and C related?

Identify the correct set of reagents or reaction conditions '$$X$$' and '$$Y$$' in the following set of transformation.

In the precipitation of the iron group (III) in qualitative analysis, ammonium chloride is added before adding ammonium

The element which shows only one oxidation state other than its elemental form is :

Which of the following is the correct structure of L-Glucose?

Identify the product in the following reaction:

Number of molecules/ions from the following in which the central atom is involved in $$\mathrm{sp}^3$$ hybridization is

The correct sequence of ligands in the order of decreasing field strength is :

The Molarity (M) of an aqueous solution containing $$5.85 \mathrm{~g}$$ of $$\mathrm{NaCl}$$ in $$500 \mathrm{~mL}$$ wat

Which among the following is incorrect statement?

One of the commonly used electrode is calomel electrode. Under which of the following categories, calomel electrode come

The correct order of first ionization enthalpy values of the following elements is : (A) O (B) N (C) Be (D) F (E) B Choo

Which of the following nitrogen containing compound does not give Lassaigne's test ?

Which one of the following molecules has maximum dipole moment?

What pressure (bar) of $$\mathrm{H}_2$$ would be required to make emf of hydrogen electrode zero in pure water at $$25^{

Number of elements from the following that CANNOT form compounds with valencies which match with their respective group

$$2.5 \mathrm{~g}$$ of a non-volatile, non-electrolyte is dissolved in $$100 \mathrm{~g}$$ of water at $$25^{\circ} \mat

Only $$2 \mathrm{~mL}$$ of $$\mathrm{KMnO}_4$$ solution of unknown molarity is required to reach the end point of a titr

Consider the following transformation involving first order elementary reaction in each step at constant temperature as

The enthalpy of formation of ethane $$(\mathrm{C}_2 \mathrm{H}_6)$$ from ethylene by addition of hydrogen where the bond

$$\mathrm{Xg}$$ of ethylamine is subjected to reaction with $$\mathrm{NaNO}_2 / \mathrm{HCl}$$ followed by water; evolve

The number of the correct reaction(s) among the following is _______.

The de-Broglie's wavelength of an electron in the $$4^{\text {th }}$$ orbit is ________ $$\pi \mathrm{a}_0$$. ($$\mathrm

The number of different chain isomers for C$$_7$$H$$_{16}$$ is __________.

Number of molecules/species from the following having one unpaired electron is ________. $$\mathrm{O}_2, \mathrm{O}_2^{-

Consider the following reaction $$\mathrm{MnO}_2+\mathrm{KOH}+\mathrm{O}_2 \rightarrow \mathrm{A}+\mathrm{H}_2 \mathrm{O

$$\text { Let } f(x)=\left\{\begin{array}{lr} -2, & -2 \leq x \leq 0 \\ x-2, & 0

One of the points of intersection of the curves $$y=1+3 x-2 x^2$$ and $$y=\frac{1}{x}$$ is $$\left(\frac{1}{2}, 2\right)

Let $$\alpha \in(0, \infty)$$ and $$A=\left[\begin{array}{lll}1 & 2 & \alpha \\ 1 & 0 & 1 \\ 0 & 1 & 2\end{array}\right]

There are 5 points $$P_1, P_2, P_3, P_4, P_5$$ on the side $$A B$$, excluding $$A$$ and $$B$$, of a triangle $$A B C$$.

A square is inscribed in the circle $$x^2+y^2-10 x-6 y+30=0$$. One side of this square is parallel to $$y=x+3$$. If $$\l

Let $$\alpha, \beta \in \mathbf{R}$$. Let the mean and the variance of 6 observations $$-3,4,7,-6, \alpha, \beta$$ be 2

Let $$f(x)=x^5+2 \mathrm{e}^{x / 4}$$ for all $$x \in \mathbf{R}$$. Consider a function $$g(x)$$ such that $$(g \circ f)

Let a unit vector which makes an angle of $$60^{\circ}$$ with $$2 \hat{i}+2 \hat{j}-\hat{k}$$ and an angle of $$45^{\cir

If the domain of the function $$\sin ^{-1}\left(\frac{3 x-22}{2 x-19}\right)+\log _{\mathrm{e}}\left(\frac{3 x^2-8 x+5}{

Let the point, on the line passing through the points $$P(1,-2,3)$$ and $$Q(5,-4,7)$$, farther from the origin and at a

The vertices of a triangle are $$\mathrm{A}(-1,3), \mathrm{B}(-2,2)$$ and $$\mathrm{C}(3,-1)$$. A new triangle is formed

Three urns A, B and C contain 7 red, 5 black; 5 red, 7 black and 6 red, 6 black balls, respectively. One of the urn is s

If the solution $$y=y(x)$$ of the differential equation $$(x^4+2 x^3+3 x^2+2 x+2) \mathrm{d} y-(2 x^2+2 x+3) \mathrm{d}

Let the first three terms 2, p and q, with $$q \neq 2$$, of a G.P. be respectively the $$7^{\text {th }}, 8^{\text {th }

The sum of all rational terms in the expansion of $$\left(2^{\frac{1}{5}}+5^{\frac{1}{3}}\right)^{15}$$ is equal to :

If 2 and 6 are the roots of the equation $$a x^2+b x+1=0$$, then the quadratic equation, whose roots are $$\frac{1}{2 a+

Let the sum of the maximum and the minimum values of the function $$f(x)=\frac{2 x^2-3 x+8}{2 x^2+3 x+8}$$ be $$\frac{m}

If the system of equations $$\begin{aligned} & x+(\sqrt{2} \sin \alpha) y+(\sqrt{2} \cos \alpha) z=0 \\ & x+(\cos \alpha

Let $$\alpha$$ and $$\beta$$ be the sum and the product of all the non-zero solutions of the equation $$(\bar{z})^2+|z|=

Let $$f: \mathbf{R} \rightarrow \mathbf{R}$$ be a function given by $$f(x)= \begin{cases}\frac{1-\cos 2 x}{x^2}, & x 0\e

Let the solution $$y=y(x)$$ of the differential equation $$\frac{\mathrm{d} y}{\mathrm{~d} x}-y=1+4 \sin x$$ satisfy $$y

If the shortest distance between the lines $$\frac{x+2}{2}=\frac{y+3}{3}=\frac{z-5}{4}$$ and $$\frac{x-3}{1}=\frac{y-2}{

Let $$A$$ be a square matrix of order 2 such that $$|A|=2$$ and the sum of its diagonal elements is $$-$$3 . If the poin

If $$\lim _\limits{x \rightarrow 1} \frac{(5 x+1)^{1 / 3}-(x+5)^{1 / 3}}{(2 x+3)^{1 / 2}-(x+4)^{1 / 2}}=\frac{\mathrm{m}

Let $$A$$ be a $$3 \times 3$$ matrix of non-negative real elements such that $$A\left[\begin{array}{l}1 \\ 1 \\ 1\end{ar

If $$\int_0^{\frac{\pi}{4}} \frac{\sin ^2 x}{1+\sin x \cos x} \mathrm{~d} x=\frac{1}{\mathrm{a}} \log _{\mathrm{e}}\left

In a survey of 220 students of a higher secondary school, it was found that at least 125 and at most 130 students studie

Let the length of the focal chord PQ of the parabola $$y^2=12 x$$ be 15 units. If the distance of $$\mathrm{PQ}$$ from t

Let $$\mathrm{ABC}$$ be a triangle of area $$15 \sqrt{2}$$ and the vectors $$\overrightarrow{\mathrm{AB}}=\hat{i}+2 \hat

Let $$a=1+\frac{{ }^2 \mathrm{C}_2}{3 !}+\frac{{ }^3 \mathrm{C}_2}{4 !}+\frac{{ }^4 \mathrm{C}_2}{5 !}+...., \mathrm{b}=

An infinitely long positively charged straight thread has a linear charge density $$\lambda \mathrm{~Cm}^{-1}$$. An elec

An electron is projected with uniform velocity along the axis inside a current carrying long solenoid. Then :

A metal wire of uniform mass density having length $$L$$ and mass $$M$$ is bent to form a semicircular arc and a particl

An effective power of a combination of 5 identical convex lenses which are kept in contact along the principal axis is $

Given below are two statements : Statement I : When speed of liquid is zero everywhere, pressure difference at any two p

If a rubber ball falls from a height $$h$$ and rebounds upto the height of $$h / 2$$. The percentage loss of total energ

In an ac circuit, the instantaneous current is zero, when the instantaneous voltage is maximum. In this case, the source

Which of the following nuclear fragments corresponding to nuclear fission between neutron $$\left({ }_0^1 \mathrm{n}\rig

A body travels $$102.5 \mathrm{~m}$$ in $$\mathrm{n}^{\text {th }}$$ second and $$115.0 \mathrm{~m}$$ in $$(\mathrm{n}+2

In an experiment to measure focal length ($$f$$) of convex lens, the least counts of the measuring scales for the positi

The co-ordinates of a particle moving in $$x$$-$$y$$ plane are given by : $$x=2+4 \mathrm{t}, y=3 \mathrm{t}+8 \mathrm{t

The equation of stationary wave is : $$y=2 \mathrm{a} \sin \left(\frac{2 \pi \mathrm{nt}}{\lambda}\right) \cos \left(\fr

Which figure shows the correct variation of applied potential difference (V) with photoelectric current (I) at two diffe

P-T diagram of an ideal gas having three different densities $$\rho_1, \rho_2, \rho_3$$ (in three different cases) is sh

The electric field in an electromagnetic wave is given by $$\overrightarrow{\mathrm{E}}=\hat{i} 40 \cos \omega(\mathrm{t

The resistances of the platinum wire of a platinum resistance thermometer at the ice point and steam point are $$8 \Omeg

The value of net resistance of the network as shown in the given figure is :

A wooden block, initially at rest on the ground, is pushed by a force which increases linearly with time $$t$$. Which of

To measure the internal resistance of a battery, potentiometer is used. For $$R=10 \Omega$$, the balance point is observ

On celcius scale the temperature of body increases by $$40^{\circ} \mathrm{C}$$. The increase in temperature on Fahrenhe

A solid sphere and a hollow cylinder roll up without slipping on same inclined plane with same initial speed $$v$$. The

An infinite plane sheet of charge having uniform surface charge density $$+\sigma_{\mathrm{s}} \mathrm{C} / \mathrm{m}^2

A hydrogen atom changes its state from $$n=3$$ to $$n=2$$. Due to recoil, the percentage change in the wave length of em

A soap bubble is blown to a diameter of $$7 \mathrm{~cm}$$. $$36960 \mathrm{~erg}$$ of work is done in blowing it furthe

An elastic spring under tension of $$3 \mathrm{~N}$$ has a length $$a$$. Its length is $$b$$ under tension $$2 \mathrm{~

The magnetic field existing in a region is given by $$\vec{B}=0.2(1+2 x) \hat{k}$$. A square loop of edge $$50 \mathrm{~

Two forces $$\overline{\mathrm{F}}_1$$ and $$\overline{\mathrm{F}}_2$$ are acting on a body. One force has magnitude thr

A alternating current at any instant is given by $$i=[6+\sqrt{56} \sin (100 \pi t+\pi / 3)]$$ A. The $$r m s$$ value of

Twelve wires each having resistance $$2 \Omega$$ are joined to form a cube. A battery of $$6 \mathrm{~V}$$ emf is joined

Two wavelengths $$\lambda_1$$ and $$\lambda_2$$ are used in Young's double slit experiment. $$\lambda_1=450 \mathrm{~nm}