The energy released when an electron is added to a neutral gaseous atom is called ______ of the atom.

The oxidation number of carbon in CH2O is

Hydroxylamine reduces iron (III) according to the equation: 2NH2OH + 4Fe3+ $$\to$$ N2O(g) $$ \uparrow $$ + H2O + 4Fe2+

The mass of a hydrogen atom is ______ kg.

Isotopes of an element differ in the number of ______ in their nuclei.

When there are two electrons in the same orbital, they have _____ spins.

The outer electronic configuration of the ground state chromium atom is 3d4 4s2

Calculate the wavelength in Angstrom of the photon that is emitted when an electron in the Bohr orbit, n = 2 returns to

The element with the highest first ionization potential is

There are ______ $$\pi$$ bonds in a nitrogen molecule.

____ hybrid orbitals of nitrogen atom are involved in the formation of ammonium ion.

The ion that is isoelectronic with CO is

Among the following, the molecule that is linear is

The compound with no dipole moment is

Helium atom is two times heavier than a hydrogen molecule. At 298 K, the average kinetic energy of a helium atom is

At room temparature, ammonia gas at 1 atm pressure and hydrogen chloride gas at P atm pressure are allowed to effuse thr

MgCl2.6H2O on heating give anhydrous MgCl2

How will you prepare bleaching powder from slaked lime.

Write down the balanced equations for the reaction when: An alkaline solution of potassium ferricyanide is reacted with

Find the value of $$\int\limits_{ - 1}^{3/2} {\left| {x\sin \,\pi \,x} \right|\,dx} $$

Show that $$\int\limits_0^\pi {xf\left( {\sin x} \right)dx} = {\pi \over 2}\int\limits_0^\pi {f\left( {\sin x} \righ

For any real $$t,\,x = {{{e^t} + {e^{ - t}}} \over 2},\,\,y = {{{e^t} - {e^{ - t}}} \over 2}$$ is a point on the hyperb

If $$A$$ and $$B$$ are two events such that $$P\left( A \right) > 0,$$ and $$P\left( B \right) \ne 1,$$ then $$P\left

$$A$$ and $$B$$ are two candidates seeking admission in $$IIT.$$ The probability that $$A$$ is selected is $$0.5$$ and t

For non-zero vectors $${\overrightarrow a ,\,\overrightarrow b ,\overrightarrow c },$$ $$\left| {\left( {\overrightarrow

$${A_1},{A_2},.................{A_n}$$ are the vertices of a regular plane polygon with $$n$$ sides and $$O$$ is its cen

Find all values of $$\lambda $$ such that $$x, y, z,$$$$\, \ne $$$$(0,0,0)$$ and $$\left( {\overrightarrow i + \overri

The area bounded by the curves $$y=f(x)$$, the $$x$$-axis and the ordinates $$x=1$$ and $$x=b$$ is $$(b-1)$$ sin $$(3b+4

Ten different letters of an alphabet are given. Words with five letters are formed from these given letters. Then the nu

The inequality |z-4| < |z-2| represents the region given by

Without using tables, prove that $$\left( {\sin \,{{12}^ \circ }} \right)\left( {\sin \,{{48}^ \circ }} \right)\left( {

$$mn$$ squares of equal size are arranged to from a rectangle of dimension $$m$$ by $$n$$, where $$m$$ and $$n$$ are nat

Show that the equation $${e^{\sin x}} - {e^{ - \sin x}} - 4 = 0$$ has no real solution.

The coeffcient of $${x^{99}}$$ in the polynomial (x -1) (x - 2)...(x - 100) is ..............

If $$2 + i\sqrt 3 $$ is root of the equation $${x^2} + px + q = 0$$, where p and q are real, then (p, q) = (..........,.

The number of real solutions of the equation $${\left| x \right|^2} - 3\left| x \right| + 2 = 0$$ is

Two towns A and B are 60 km apart. A school is to be built to serve 150 students in town A and 50 students in town B. If

If p, q, r are any real numbers, then

The largest interval for which $${x^{12}} - {x^9} + {x^4} - x + 1 > 0$$ is

The larger of $${99^{50}} + {100^{50}}$$ and $${101^{50}}$$ is ..............

The sum of the coefficients of the plynomial $${\left( {1 + x - 3{x^2}} \right)^{2163}}$$ is ...............

Prove that $${7^{2n}} + \left( {{2^{3n - 3}}} \right)\left( {3n - 1} \right)$$ is divisible by 25 for any natural number

In a certain test, $${a_i}$$ students gave wrong answers to atleast i questions, where i = 1, 2,..., k. No student gave

If $$z = {\left( {{{\sqrt 3 } \over 2} + {i \over 2}} \right)^5} + {\left( {{{\sqrt 3 } \over 2} - {i \over 2}} \right)^

Eight chairs are numbered 1 to 8. Two women and three men wish to occupy one chair each. First the women choose the chai

The value of the expression $$\,{}^{47}{C_4} + \sum\limits_{j = 1}^5 {^{52 - j}\,{C_3}} $$ is equal to

The third term of a geometric progression is 4. The product of the first five terms is

If $$x,\,y$$ and $$z$$ are $$pth$$, $$qth$$ and $$rth$$ terms respectively of an A.P. and also of a G.P., then $${x^{y -

Does there exist a geometric progression containing $$27, 8$$ and $$12$$ as three of its terms? If it exits, how many su

$$y = {10^x}$$ is the reflection of $${\log _{10}}\,x$$ in the line whose equation is ...........

The set of lines $$ax + by + c = 0,$$ where $$3a + 2b + 4c = 0$$ is concurrent at the point ..........

If A and B are points in the plane such that PA/PB = k (constant) for all P on a given circle, then the value of k canno

$$A$$ is point on the parabola $${y^2} = 4ax$$. The normal at $$A$$ cuts the parabola again at point $$B$$. If $$AB$$ su

If $$y = f\left( {{{2x - 1} \over {{x^2} + 1}}} \right)$$ and $$f'\left( x \right) = \sin {x^2}$$, then $${{dy} \over

Let $$f$$ be a twice differentiable function such that $$f''\left( x \right) = - f\left( x \right),$$ and $$f'\left( x

A vertical pole stands at a point $$Q$$ on a horizontal ground. $$A$$ and $$B$$ are points on the ground, $$d$$ meters a

If $$f(x)$$ and $$g(x)$$ are differentiable function for $$0 \le x \le 1$$ such that $$f(0)=2$$, $$g(0)=0$$, $$f(1)=6$$;

If $$a{x^2} + {b \over x} \ge c$$ for all positive $$x$$ where $$a>0$$ and $$b>0$$ show that $$27a{b^2} \ge 4{c^3}

Write the dimensions of the followings in terms of mass, time, length and charge (i) magnetic flux (ii) rigidity modulus

A particle is moving eastwards with a velocity of 5 m/s. In 10s the velocity changes to 5 m/s northwards. The average ac

In the arrangement shown in Fig. the ends P and Q of an unstretchable string move downwards with uniform speed U. Pulley