The major product 'P' for the following sequence of reactions is :

The magnetic behaviour of $$\mathrm{Li_2O,Na_2O_2}$$ and $$\mathrm{KO_2}$$, respectively, are :

Compound that will give positive Lassaigne's test for both nitrogen and halogen is :

Identify the correct order for the given property for following compounds. Choose the correct answer from the option gi

The bond dissociation energy is highest for

Number of cyclic tripeptides formed with 2 amino acids A and B is :

The shortest wavelength of hydrogen atom in Lyman series is $$\lambda$$. The longest wavelength is Balmer series of He$$

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The increasing order of $$\mathrm{pK_a}$$ for the following phenols is (A) 2, 4 - Dinitrophenol (B) 4 - Nitrophenol (C)

Chiral complex from the following is : Here en = ethylene diamine

The standard electrode potential $$\mathrm{(M^{3+}/M^{2+})}$$ for V, Cr, Mn & Co are $$-$$0.26 V, $$-$$0.41 V, + 1.57 V

Following chromatogram was developed by adsorption of compound 'A' on a 6 cm TLC glass plate. Retardation factor of the

Millimoles of calcium hydroxide required to produce 100 mL of the aqueous solution of pH 12 is $$x\times10^{-1}$$. The v

For certain chemical reaction $$X\to Y$$, the rate of formation of product is plotted against the time as shown in the f

The number of molecules or ions from the following, which do not have odd number of electrons are _________. (A) NO$$_2$

Following figure shows dependence of molar conductance of two electrolytes on concentration. $$\Lambda \mathop m\limits^

Solid Lead nitrate is dissolved in 1 litre of water. The solution was found to boil at 100.15$$^\circ$$C. When 0.2 mol o

Water decomposes at 2300 K $$\mathrm{H_2O(g)\to H_2(g)+\frac{1}{2}O_2(g)}$$ The percent of water decomposing at 2300 K a

Consider the following reaction approaching equilibrium at 27$$^\circ$$C and 1 atm pressure $$\mathrm{A+B}$$ $$\mathrel{

The sum of bridging carbonyls in $$\mathrm{W(CO)_6}$$ and $$\mathrm{Mn_2(CO)_{10}}$$ is ____________.

17 mg of a hydrocarbon (M.F. $$\mathrm{C_{10}H_{16}}$$) takes up 8.40 mL of the H$$_2$$ gas measured at 0$$^\circ$$C and

Let $$\lambda \ne 0$$ be a real number. Let $$\alpha,\beta$$ be the roots of the equation $$14{x^2} - 31x + 3\lambda =

Let $$B$$ and $$C$$ be the two points on the line $$y+x=0$$ such that $$B$$ and $$C$$ are symmetric with respect to the

Three rotten apples are mixed accidently with seven good apples and four apples are drawn one by one without replacement

Let $$f(\theta ) = 3\left( {{{\sin }^4}\left( {{{3\pi } \over 2} - \theta } \right) + {{\sin }^4}(3\pi + \theta )} \rig

Fifteen football players of a club-team are given 15 T-shirts with their names written on the backside. If the players p

Let the tangents at the points $$A(4,-11)$$ and $$B(8,-5)$$ on the circle $$x^{2}+y^{2}-3 x+10 y-15=0$$, intersect at th

Let $$f(x) = x + {a \over {{\pi ^2} - 4}}\sin x + {b \over {{\pi ^2} - 4}}\cos x,x \in R$$ be a function which satisfies

Let $$\alpha$$ and $$\beta$$ be real numbers. Consider a 3 $$\times$$ 3 matrix A such that $$A^2=3A+\alpha I$$. If $$A^4

A light ray emits from the origin making an angle 30$$^\circ$$ with the positive $$x$$-axis. After getting reflected by

For two non-zero complex numbers $$z_{1}$$ and $$z_{2}$$, if $$\operatorname{Re}\left(z_{1} z_{2}\right)=0$$ and $$\oper

Let $$y=f(x)$$ be the solution of the differential equation $$y(x+1)dx-x^2dy=0,y(1)=e$$. Then $$\mathop {\lim }\limits_{

Let $$\Delta$$ be the area of the region $$\left\{ {(x,y) \in {R^2}:{x^2} + {y^2} \le 21,{y^2} \le 4x,x \ge 1} \right\}$

The domain of $$f(x) = {{{{\log }_{(x + 1)}}(x - 2)} \over {{e^{2{{\log }_e}x}} - (2x + 3)}},x \in \mathbb{R}$$ is

Let $$f:R \to R$$ be a function such that $$f(x) = {{{x^2} + 2x + 1} \over {{x^2} + 1}}$$. Then

Let $$[x]$$ denote the greatest integer $$\le x$$. Consider the function $$f(x) = \max \left\{ {{x^2},1 + [x]} \right\}$

Let $$A=\left\{(x, y) \in \mathbb{R}^{2}: y \geq 0,2 x \leq y \leq \sqrt{4-(x-1)^{2}}\right\}$$ and $$ B=\left\{(x, y) \

Consider the following system of equations $$\alpha x+2y+z=1$$ $$2\alpha x+3y+z=1$$ $$3x+\alpha y+2z=\beta$$ for some $$

If the vectors $$\overrightarrow a = \lambda \widehat i + \mu \widehat j + 4\widehat k$$, $$\overrightarrow b = - 2\w

Let $$x=2$$ be a root of the equation $$x^2+px+q=0$$ and $$f(x) = \left\{ {\matrix{ {{{1 - \cos ({x^2} - 4px + {q^2}

Let $$a_1,a_2,a_3,...$$ be a $$GP$$ of increasing positive numbers. If the product of fourth and sixth terms is 9 and th

Suppose $$f$$ is a function satisfying $$f(x + y) = f(x) + f(y)$$ for all $$x,y \in N$$ and $$f(1) = {1 \over 5}$$. If $

Let the coefficients of three consecutive terms in the binomial expansion of $$(1+2x)^n$$ be in the ratio 2 : 5 : 8. The

If the co-efficient of $$x^9$$ in $${\left( {\alpha {x^3} + {1 \over {\beta x}}} \right)^{11}}$$ and the co-efficient of

If all the six digit numbers $$x_1\,x_2\,x_3\,x_4\,x_5\,x_6$$ with $$0

Let $$f:\mathbb{R}\to\mathbb{R}$$ be a differentiable function that satisfies the relation $$f(x+y)=f(x)+f(y)-1,\forall

Five digit numbers are formed using the digits 1, 2, 3, 5, 7 with repetitions and are written in descending order with s

Let the co-ordinates of one vertex of $$\Delta ABC$$ be $$A(0,2,\alpha)$$ and the other two vertices lie on the line $${

Two particles of equal mass '$$m$$' move in a circle of radius '$$r$$' under the action of their mutual gravitational at

Find the mutual inductance in the arrangement, when a small circular loop of wire of radius '$$R$$' is placed inside a l

In a cuboid of dimension $$2 \mathrm{~L} \times 2 \mathrm{~L} \times \mathrm{L}$$, a charge $$q$$ is placed at the cente

Surface tension of a soap bubble is $$2.0 \times 10^{-2} \mathrm{Nm}^{-1}$$. Work done to increase the radius of soap bu

Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R. Assertion A: If $$

The magnitude of magnetic induction at mid point $$\mathrm{O}$$ due to current arrangement as shown in Fig will be

A stone is projected at angle $$30^{\circ}$$ to the horizontal. The ratio of kinetic energy of the stone at point of pro

A block of mass $m$ slides down the plane inclined at angle $$30^{\circ}$$ with an acceleration $$\frac{g}{4}$$. The val

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A car is moving on a horizontal curved road with radius 50 m. The approximate maximum speed of car will be, if friction

Which of the following are true? A. Speed of light in vacuum is dependent on the direction of propagation. B. Speed of l

In a Young's double slit experiment, two slits are illuminated with a light of wavelength $$800 \mathrm{~nm}$$. The line

A single current carrying loop of wire carrying current I flowing in anticlockwise direction seen from +ve $$\mathrm{z}$

Which one of the following statement is not correct in the case of light emitting diodes? A. It is a heavily doped p-n j

A bicycle tyre is filled with air having pressure of $$270 ~\mathrm{kPa}$$ at $$27^{\circ} \mathrm{C}$$. The approximate

The threshold wavelength for photoelectric emission from a material is 5500 $$\mathop A\limits^o $$. Photoelectrons will

Ratio of thermal energy released in two resistors R and 3R connected in parallel in an electric circuit is :

Two simple harmonic waves having equal amplitudes of 8 cm and equal frequency of 10 Hz are moving along the same directi

A solid sphere of mass 2 kg is making pure rolling on a horizontal surface with kinetic energy 2240 J. The velocity of c

In a metre bridge experiment the balance point is obtained if the gaps are closed by 2$$\Omega$$ and 3$$\Omega$$. A shun

A point charge $$q_1=4q_0$$ is placed at origin. Another point charge $$q_2=-q_0$$ is placed at $$x=12$$ cm. Charge of p

As shown in the figure, three identical polaroids P$$_1$$, P$$_2$$ and P$$_3$$ are placed one after another. The pass ax

A 0.4 kg mass takes 8s to reach ground when dropped from a certain height 'P' above surface of earth. The loss of potent

A certain elastic conducting material is stretched into a circular loop. It is placed with its plane perpendicular to a

A tennis ball is dropped on to the floor from a height of 9.8 m. It rebounds to a height 5.0 m. Ball comes in contact wi