STATEMENT - 1 : The plot of atomic number (y-axis) versus number of neutrons (x-axis) for stable nuclei shows a curvatur

Hyperconjugation involves overlapping of the following orbitals:

The major product of the following reaction is:

Aqueous solutions of Na$$_2$$S$$_2$$O$$_3$$ on reaction with Cl$$_2$$ gives:

Native silver metal forms a water soluble complex with a dilute aqueous solution of NaCN in the presence of:

Under the same reaction conditions, initial concentration of 1.386 mol dm$$^{-3}$$ of a substance becomes half in 40 sec

2.5 mL of $$\frac{2}{5}$$M weak monoacidic base (K$$_b$$ = 1 $$\times$$ 10$$^{-12}$$ at 25$$^\circ$$C) is titrated with

The correct statement(s) about the compound given below is(are):

The correct statement(s) concerning the structures E, F and G is(are) :

A solution of colourless salt H on boiling with excess NaOH produces a non-flammable gas. The gas evolution ceases after

A gas described by van Der Waals equation

Statement 1 : Bromobenzene upon reaction with Br$$_2$$/Fe gives 1, 4-dibromobenzene as the major product. and Statement

Statement 1 : Pb$$^{4+}$$ compounds are stronger oxidising agents than Sn$$^{4+}$$ compounds. and Statement 2 : The high

Statement 1 : For every chemical reaction at equilibrium, standard Gibbs energy of reaction is zero. and Statement 2 : A

The structure of the product I is :

The structure of compounds J and K, respectively, are:

The structure of product L is :

Among the following, the correct statement is:

Among the following, the correct statement is :

White phosphorus on reaction with NaOH gives PH$$_3$$ as one of the products. This is a:

The freezing point of the solution M is :

The vapour pressure of the solution M is :

Water is added to the solution M such that the fraction of water in the solution becomes 0.9 mole. The boiling point of

The number of elements in the set $$A \cap B \cap C$$ is

Let z be any point in $$A \cap B \cap C$$ Then, $${\left| {z + 1 - i} \right|^2} + {\left| {z - 5 - i} \right|^2}$$ li

Let z be any point $$A \cap B \cap C$$ and let w be any point satisfying $$\left| {w - 2 - i} \right| < 3\,$$. Then,

Let $${S_n} = \sum\limits_{k = 1}^n {{n \over {{n^2} + kn + {k^2}}}} $$ and $${T_n} = \sum\limits_{k = 0}^{n - 1} {{n \o

A straight line through the vertex p of a triangle PQR intersects the side QR at the point S and the circumcircle of the

The equation of circle C is

Points E and F are given by

Equations of the sides QR, RP are

Let $$P\left( {{x_1},{y_1}} \right)$$ and $$Q\left( {{x_2},{y_2}} \right),{y_1} < 0,{y_2} < 0,$$ be the end points

Let $$f$$ and $$g$$ be real valued functions defined on interval $$(-1, 1)$$ such that $$g''(x)$$ is continuous, $$g\lef

If $$0 < x < 1$$, then $$\sqrt {1 + {x^2}} {\left[ {{{\left\{ {x\cos \left( {{{\cot }^{ - 1}}x} \right) + \sin \l

Consider the two curves $${C_1}:{y^2} = 4x,\,{C_2}:{x^2} + {y^2} - 6x + 1 = 0$$. Then,

Let $$f(x)$$ be a non-constant twice differentiable function defined on $$\left( { - \infty ,\infty } \right)$$ such th

If $$f\left( { - 10\sqrt 2 } \right) = 2\sqrt 2 ,$$ then $$f''\left( { - 10\sqrt 2 } \right) = $$

The area of the region bounded by the curve $$y=f(x),$$ the $$x$$-axis, and the lines $$x=a$$ and $$x=b$$, where $$ - \i

$$\int\limits_{ - 1}^1 {g'\left( x \right)dx = } $$

Consider the system of equations $$ax+by=0; cx+dy=0,$$ where $$a,b,c,d$$ $$ \in \left\{ {0,1} \right\}$$ STATEMENT - 1

The edges of a parallelopiped are of unit length and are parallel to non-coplanar unit vectors $$\overrightarrow a \,,\,

Consider three planes $$${P_1}:x - y + z = 1$$$ $$${P_2}:x + y - z = 1$$$ $$${P_3}:x - 3y + 3z = 2$$$ Let $${L_1},$$ $$

Let a and b be non-zero real numbers. Then, the equation $$(a{x^2} + b{y^2} + c)({x^2} - 5xy + 6{y^2}) = 0$$ represents

Let $$g(x) = {{{{(x - 1)}^n}} \over {\log {{\cos }^m}(x - 1)}};0 0$$, and let $$p$$ be the left hand derivative of $$|x

The total number of local maxima and local minima of the function $$f(x) = \left\{ {\matrix{ {{{(2 + x)}^3},} & { - 3

Consider the system of equations: $$x-2y+3z=-1$$ $$-x+y-2z=k$$ $$x-3y+4z=1$$ Statement - 1 : The system of equations has

Student I, II and III perform an experiment for measuring the acceleration due to gravity (g) using a simple pendulum. T

Figure shows three resistor configurations R1, R2 and R3 connected to 3 V battery. If the power dissipated by the config

Which one of the following statements is WRONG in the context of X-rays generated from a X-ray tube?

Two beams of red and violet colours are made to pass separately through a prism (angle of the prism is 60$$^\circ$$). In

An ideal gas is expanding such that PT$$^2$$ = constant. The coefficient of volume expansion of the gas is

A spherically symmetric gravitational system of particles has a mass density $$\rho = \left\{ {\matrix{ {{\rho _0}}

Two balls, having linear momenta $${\overrightarrow p _1} = p\widehat i$$ and $${\overrightarrow p _2} = - p\widehat i$

Assume that the nuclear binding energy per nucleon (B/A) versus mass number (A) is as shown in the figure. Use this plot

A particle of mass m and charge q, moving with velocity v enters Region II normal to the boundary as shown in the figure

In a Young's double slit experiment, the separation between the two slits is d and the wavelength of the light is $$\lam

STATEMENT - 1 In a Meter Bridge experiment, null point for an unknown resistance is measured. Now, the unknown resistanc

STATEMENT - 1 An astronaut in an orbiting space station above the Earth experiences weightlessness. and STATEMENT - 2 An

STATEMENT - 1 : Two cylinders, one hollow (metal) and the other solid (wood) with the same mass and identical dimensions

STATEMENT - 1 : The stream of water flowing at high speed from a garden hose pipe tends to spread line a fountain when h

As the bubble moves upwards, besides the buoyancy force the following forces are acting on it

When the gas bubble is at a height y from the bottom, its temperature is :

The buoyancy force acting on the gas bubble is (Assume R is the universal gas constant)

The quantum number n of the state finally populated in He$$^+$$ ions is :

The wavelength of light emitted in the visible region by He$$^+$$ ions after collisions with H atoms is

The ratio of the kinetic energy of the $$n=2$$ electron for the H atom to that of He$$^+$$ ion is

The speed of the block at point B immediately after it strikes the second incline is

The speed of the block at point C, immediately before it leaves the second incline is

If collision between the block and the incline is completely elastic, then the vertical (upward) component of the veloci