4.08 g of a mixture of BaO and an unknown carbonate MCO3 was heated strongly. The residue weighed 3.64 g. This was disso

Complete and balance the following equation: $$Cr_2O_7^{2-}$$ + C2H4O $$\to$$ C2H4O2 + Cr3+

Complete and balance the following equation: Ce3+ + $$S_2O_8^{-2} \to $$ $$SO_4^{-2}$$ + Ce4+

The density of a 3 M Sodium thiosulphate solution (Na2S2O3) is 1.25 g per ml. Calculate (i) the percentage by weight of

3 g of a salt of molecular weight 30 is dissolved in 250 g of water. The molality if the solution is _____.

Complete and balance the following equation: Zn + $$NO_3^- \to$$ Zn2+ + $$NH_4^+$$

Linear overlap of two atomic p-orbitals leads to a sigma bond.

An organic compound CxH2yOy was burnt with twice the amount of oxygen needed for complete combustion of CO2 and H2O. The

Heavy water is

The absorption of hydrogen by palladium is commonly known as ______.

Which one among the following does not have the hydrogen bond?

The types of bonds present in CuSO4.5H2O are only

Carbon tetrachloride has no net dipole moment because of

Rutherford's scattering experiment is related to the size of the

Any p-orbital can accommodate upto

The principal quantum number of an atom is related to the

The energy of the electron in the 3d-orbital is less than that in the 4s-orbital in the hydrogen atom.

Gamma rays are electromagnetic radiations of wavelengths of 10-6 to 10-5 cm

Elements of the same mass number but of different atomic numbers are known as ____.

Complete and balance the following equations: Cl2 + OH- $$\to$$ Cl- + ClO-

Complete and balance the following equation: HNO3 + HCl $$\to$$ NO + Cl2

The unit vector perpendicular to the plane determined by $$P\left( {1, - 1,2} \right),\,Q\left( {2,0, - 1} \right)$$ and

A vector $$\overrightarrow A $$ has components $${A_1},{A_2},{A_3}$$ in a right -handed rectangular Cartesian coordinate

The volume of the parallelopiped whose sides are given by $$\overrightarrow {OA} = 2i - 2j,\,\overrightarrow {OB} = i

The points with position vectors $$60i+3j,$$ $$40i-8j,$$ $$ai-52j$$ are collinear if

If $$X.A=0, X.B=0, X.C=0$$ for some non-zero vector $$X,$$ then $$\left[ {A\,B\,C} \right] = 0$$

The area of the triangle whose vertices are $$A(1, -1, 2), B(2, 1, -1), C(3, -1, 2)$$ is ..........

$$A, B, C$$ are events such that $$P\left( A \right) = 0.3,P\left( B \right) = 0.4,P\left( C \right) = 0.8$$ $$P\left( {

Cards are drawn one by one at random from a well - shuffled full pack of $$52$$ playing cards until $$2$$ aces are obtai

Fifteen coupons are numbered $$1, 2 ........15,$$ respectively. Seven coupons are selected at random one at a time with

If the letters of the word "Assassin" are written down at random in a row, the probability that no two S's occur togethe

If $$\left( {a + bx} \right){e^{y/x}} = x,$$ then prove that $${x^3}{{{d^2}y} \over {d{x^2}}} = {\left( {x{{dy} \over {d

Find the area bounded by the $$x$$-axis, part of the curve $$y = \left( {1 + {8 \over {{x^2}}}} \right)$$ and the ordin

Evaluate : $$\int\limits_0^{\pi /4} {{{\sin x + \cos x} \over {9 + 16\sin 2x}}dx} $$

The value of the integral $$\int\limits_0^{\pi /2} {{{\sqrt {\cot x} } \over {\sqrt {\cot x} + \sqrt {\tan x} }}dx} $$

Evaluate : $$\int {{{\left( {x - 1} \right){e^x}} \over {{{\left( {x + 1} \right)}^3}}}dx} $$

Find the coordinates of the point on the curve $$y = {x \over {1 + {x^2}}}$$ where the tangent to the curve has the gre

Given positive integers $$r > 1,\,n > 2$$ and that the coefficient of $$\left( {3r} \right)$$th and $$\left( {r +

The straight lines $$x + y = 0,\,3x + y - 4 = 0,\,x + 3y - 4 = 0$$ form a triangle which is

The straight line $$5x + 4y = 0$$ passes through the point of intersection of the straight lines $$x + 2y - 10 = 0$$ and

Given the points $$A\left( {0,4} \right)$$ and $$B\left( {0, - 4} \right)$$, the equation of the locus of the point $$P\

Find three numbers $$a,b,c$$ between $$2$$ and $$18$$ such that (i) their sum is $$25$$ (ii) the numbers $$2,$$ $$a, b$

The rational number, which equals the number $$2\overline {357} $$ with recurring decimal is

m men and n women are to be seated in a row so that no two women sit together. If $$m > n$$, then show that the numbe

Use mathematical Induction to prove : If $$n$$ is any odd positive integer, then $$n\left( {{n^2} - 1} \right)$$ is divi

If $${\left( {1 + x} \right)^n} = {C_0} + {C_1}x + {C_2}{x^2} + ..... + {C_n}{x^n}$$ then show that the sum of the produ

The coefficient of $${x^4}$$ in $${\left( {{x \over 2} - {3 \over {{x^2}}}} \right)^{10}}$$ is

The vertices of a triangle are $$\left[ {a{t_1}{t_2},\,\,a\left( {{t_1} + {t_2}} \right)} \right],\,\,\left[ {a{t_2}{t_3

If $${\left( {1 + ax} \right)^n} = 1 + 8x + 24{x^2} + .....$$ then $$a=..........$$ and $$n =............$$

The equation $$2{x^2} + 3x + 1 = 0$$ has an irrational root.

Find all real values of $$x$$ which satisfy $${x^2} - 3x + 2 > 0$$ and $${x^2} - 2x - 4 \le 0$$

If one root of the quadratic equation $$a{x^2} + bx + c = 0$$ is equal to the $$n$$-th power of the other, then show tha

Show that $$$16\cos \left( {{{2\pi } \over {15}}} \right)\cos \left( {{{4\pi } \over {15}}} \right)\cos \left( {{{8\pi }

Find all solutions of $$4{\cos ^2}\,x\sin x - 2{\sin ^2}x = 3\sin x$$

Prove that the complex numbers $${{z_1}}$$, $${{z_2}}$$ and the origin form an equilateral triangle only if $$z_1^2 + z_

The points z1, z2, z3, z4 in the complex plane are the vertices of a parallelogram taken in order if and only if

If $$z = x + iy$$ and $$\omega = \left( {1 - iz} \right)/\left( {z - i} \right),$$ then $$\,\left| \omega \right| = 1

The value of $$\tan \left[ {{{\cos }^{ - 1}}\left( {{4 \over 5}} \right) + {{\tan }^{ - 1}}\left( {{2 \over 3}} \right)}

Show that $$1+x$$ $$In\left( {x + \sqrt {{x^2} + 1} } \right) \ge \sqrt {1 + {x^2}} $$ for all $$x \ge 0$$

If $$y = a\,\,In\,x + b{x^2} + x$$ has its extreamum values at $$x=-1$$ and $$x=2$$, then

The normal to the curve $$\,x = a\left( {\cos \theta + \theta \sin \theta } \right)$$, $$y = a\left( {\sin \theta - \t

$$AB$$ is a diameter of a circle and $$C$$ is any point on the circumference of the circle. Then

If $$x-r$$ is a factor of the polynomial $$f\left( x \right) = {a_n}{x^4} + ..... + {a_0},$$ repeated $$m$$ times $$\lef

If $$a+b+c=0$$, then the quadratic equation $$3a{x^2} + 2bx + c = 0$$ has

The function $$y = 2{x^2} - In\,\left| x \right|$$ is monotonically increasing for values of $$x\left( {x \ne 0} \right)

The larger of $$\cos \left( {In\,\,\theta } \right)$$ and $$In $$ $$\left( {\cos \,\,\theta } \right)$$ If $${e^{ - \pi

Find all the solution of $$4$$ $${\cos ^2}x\sin x - 2{\sin ^2}x = 3\sin x$$

If $$\tan \,A = \left( {1 - \cos B} \right)/\sin B,$$ then $$tan2A = tan\,B$$.

The ex-radii $${r_1},{r_2},{r_3}$$ of $$\Delta $$$$ABC$$ are H.P. Show that its sides $$a, b, c$$ are in A.P.

From the top of a light-house 60 metres high with its base at the sea-level, the angle of depression of a boat is $${15^

The derivative of an even function is always an odd function.

Through a fixed point (h, k) secants are drawn to the circle $$\,{x^2}\, + \,{y^2} = \,{r^2}$$. Show that the locus of t

The equation of the circle passing through (1, 1) and the points of intersection of $${x^2} + {y^2} + 13x - 3y = 0$$ an

The centre of the circle passing through the point (0, 1) and touching the curve $$\,y = {x^2}$$ at (2, 4) is

The point of intersection of the line 4x - 3y - 10 = 0 and the circle $${x^2} + {y^2} - 2x + 4y - 20 = 0$$ are .........

The end $$A, B$$ of a straight line segment of constant length $$c$$ slide upon the fixed rectangular axes $$OX, OY$$ re

The coordinates of $$A, B, C$$ are $$(6, 3), (-3, 5), (4, -2)$$ respectively, and $$P$$ is any point $$(x, y)$$. Show

A river is flowing from west to east at a speed of 5 meters per minute. A man on the south bank of the river, capable of

Two balls of different masses are thrown vertically upwards with the same speed. They pass through the point of projecti

A particle moves in a circle of radius R. In half the period of revolution its displacement is ________ and distance cov

Match the physical quantities given in column I with dimension expressed in terms of mass (M), length (L), time (T), and