Element X is strongly electropositive and element Y is strongly electronegative. Both are univalent. The compound formed would be

The modern atomic unit is based on the mass of ______.

The total no of electron present in 18 ml of water is ______.

M is molecular weight of KMnO₄. The equivalent wight of KMnO₄ when it is converted into K₂MnO₄ is

A hydrocarbon contains 10.5 g of carbon per gram of hydrogen. 1 litre of the hydrocarbon at 127^oC and 1 atmosphere weighs 2.8 g. Find the molecular formula.

A mixture contains NaCl and unknown chloride MCl.

(i) 1g of this is dissolved in water. Excess of acidified AgNO₃ solution is added to it. 2.567 g of white ppt is formed.

(ii) 1 g of original mixture is heated to 300^oC. Some vapours come out which are absorbed in acidified AgNO₃ solution, 1.341 g of white precipitate was obtained.

Find the molecular weight of unknown chloride.

Find
(i) The total number of neutrons and
(ii) The total mass of neutron in 7 mg of ¹⁴C
(Assume that mass of neutron = mass of hydrogen atom)

(a) 1 litre of a mixture of CO and CO₂ is taken. This mixture is passed through a tube containing red hot charcoal. The volume now becomes 1.6 litre. The volumes are measured under the same conditions. Find the composition of the mixture by volume.

(b) A compound contains 28 percent of nitrogen and 72 percent of metal by weight. 3 atoms of metal combine with 2 atoms of N. Find the atomic weight of metal.

(i). A sample of MnSO₄.4H₂O is strongly heated in air. The residue is Mn₃O₄.

(ii). The residue is dissolved in 100 ml of 0.1N FeSO₄ containing dilute H₂SO₄.

(iii). The solution reacts completely with 50 ml of KMnO₄ solution.

(iv). 25 ml of the KMnO₄ solution used in step (iii) requires 30 ml of 0.1 N FeSO₄ solution for complete reaction.

Find the amount of MnSO₄.4H₂O present in the sample.

(a) One litre of a sample of hard water contains 1 mg of CaCl₂ and 1 mg of MgCl₂. Find the total hardness in terms of parts of CaCO₃ per 10⁶ parts of water by weight.

(b) A sample of hard water contains 20 mg of Ca⁺⁺ ions per litre. How many milli-equivalent of Na₂CO₃ would be required to soften 1 litre of the sample?

(c) 1 gm of Mg is burnt in a closed vessel which contains 0.5gm of O₂.
      (i) Which reactant is left in excess?
      (ii) Find the weight of the excess reactants.
      (iii) How many milliliters of 0.5N H₂SO₄ will dissolve the residue in the vessel?

Which of the following compounds are covalent?

The total number of electrons that take part in forming the bond in N₂ is

Which of the following is soluble in water?

Anhydrous MgCl₂ is obtained by hydrated salt with ______.

Calcium is obtained by

HCL is added to the following oxides. Which one would give H₂O₂?

Explain the following in not more than two sentenses.

A solution of FeCl₃ in water gives a brown precipitate on standing.

Compound A is a light green crystalline solid. It gives the following tests :

(i) It dissolves in dilute sulphuric acid. No gas is produced.

(ii) A drop of KMnO₄ is added to the above solution. The pink colour disappears.

(iii) Compound A is heated strongly. Gases B and C, with pungent smell, come out. A brown residue D is left behind.

(iv) The gas mixture (B and C) is passed into a dichromate solution. The solution turns green.

(v) The green solution from step (iv) gives a white precipitate E with a solution of barium nitrate.

(vi) Residue D from step (iii) is heated on charcoal in a reducing flame. It gives a magnetic substance E.

Name the compounds A, B, C, D and E.

The probability that an event $$A$$ happens in one trial of an experiment is $$0.4.$$ Three independent trials of the experiment are performed. The probability that the event $$A$$ happens at least once is

Two events $$A$$ and $$B$$ have probabilities $$0.25$$ and $$0.50$$ respectively. The probability that both $$A$$ and $$B$$ occur simultaneously is $$0.14$$. Then the probability that neither $$A$$ nor $$B$$ occurs is

The equation $$\,2{\cos ^2}{x \over 2}{\sin ^2}x = {x^2} + {x^{ - 2}};\,0 < x \le {\pi \over 2}$$ has

$$ABC$$ is a triangle with $$AB=AC$$. $$D$$ is any point on the side $$BC$$. $$E$$ and $$F$$ are points on the side $$AB$$ and $$AC$$, respectively, such that $$DE$$ is parallel to $$AC$$, and $$DF$$ is parallel to $$AB$$. Prove that $$$DF + FA + AE + ED = AB + AC$$$

Given $$A = {\sin ^2}\theta + {\cos ^4}\theta $$ then for all real values of $$\theta $$

The smallest positive integer n for which $${\left( {{{1 + i} \over {1 - i}}} \right)^n} = 1$$ is

Find the real values of x and y for which the following equation is satisfied $$\,{{(1 + i)x - 2i} \over {3 + i}} + {{(2 + 3i)y + i} \over {3 - i}} = i$$

Given $$\alpha + \beta - \gamma = \pi ,$$ prove that
$$\,{\sin ^2}\alpha + {\sin ^2}\beta - {\sin ^2}\gamma = 2\sin \alpha {\mkern 1mu} \sin \beta {\mkern 1mu} \cos y$$

Given $$A = \left\{ {x:{\pi \over 6} \le x \le {\pi \over 3}} \right\}$$ and
$$f\left( x \right) = \cos x - x\left( {1 + x} \right);$$ find $$f\left( A \right).$$

For all $$\theta $$ in $$\left[ {0,\,\pi /2} \right]$$ show that, $$\cos \left( {\sin \theta } \right) \ge \,\sin \,\left( {\cos \theta } \right).$$

Let $$y = \sqrt {{{\left( {x + 1} \right)\left( {x - 3} \right)} \over {\left( {x - 2} \right)}}} $$

Find all the real values of $$x,$$ for which $$y$$ takes real values.

Given $${n^4} < {10^n}$$ for a fixed positive integer $$n \ge 2,$$ prove that $${\left( {n + 1} \right)^4} < {10^{n + 1}}.$$

For what values of $$m,$$ does the system of equations $$$\matrix{ {3x + my = m} \cr {2x - 5y = 20} \cr } $$$

has solution satisfying the conditions $$x > 0,\,y > 0.$$

Find the solution set of the system $$$\matrix{ {x + 2y + z = 1;} \cr {2x - 3y - w = 2;} \cr {x \ge 0;\,y \ge 0;\,z \ge 0;\,w \ge 0.} \cr } $$$

Both the roots of the equation (x - b) (x - c) + (x - a) (x - c) + (x - a) (x - b) = 0 are always

The least value of the expression $$2\,\,{\log _{10}}\,x\, - \,{\log _x}(0.01)$$ for x > 1, is

If $$\,({x^2} + px + 1)\,$$ is a factor of $$(a{x^3} + bx + c)$$, then

The interior angles of a polygon are in arithmetic progression. The smallest angle is $${120^ \circ }$$, and the common difference is $${5^ \circ }$$, Find the number of sides of the polygon.

The point $$\,\left( {4,\,1} \right)$$ undergoes the following three transformations successively.
Reflection about the line $$y=x$$.
Translation through a distance 2 units along the positive direction of x-axis.
Rotation through an angle $$p/4$$ about the origin in the counter clockwise direction.
Then the final position of the point is given by the coordinates.

A straight line $$L$$ is perpendicular to the line $$5x - y = 1.$$ The area of the triangle formed by the line $$L$$ and the coordinate axes is $$5$$. Find the equation of the Line $$L$$.

A square is inscribed in the circle $${x^2} + {y^2} - 2x + 4y + 3 = 0$$. Its sides are parallel to the coordinate axes. The one vertex of the square is

Two circles $${x^2} + {y^2} = 6$$ and $${x^2} + {y^2} - 6x + 8 = 0$$ are given. Then the equation of the circle through their points of intersection and the point (1, 1) is

Given $$y = {{5x} \over {3\sqrt {{{\left( {1 - x} \right)}^2}} }} + {\cos ^2}\left( {2x + 1} \right)$$; Find $${{dy} \over {dx}}$$.

$$ABC$$ is a triangle, $$P$$ is a point on $$AB$$, and $$Q$$ is point on $$AC$$ such that $$\angle AQP = \angle ABC$$. Complete the relation $$${{area\,\,of\,\,\Delta APQ} \over {area\,\,of\,\,\Delta ABC}} = {{\left( {...} \right)} \over {A{C^2}}}$$$

$$ABC$$ is a triangle with $$\angle B$$ greater than $$\angle C.\,D$$ and $$E$$ are points on $$BC$$ such that $$AD$$ is perpendicular to $$BC$$ and $$AE$$ is the bisector of angle $$A$$. Complete the relation $$$\angle DAE = {1 \over 2}\left[ {\left( {} \right) - \angle C} \right]$$$

In a $$\Delta ABC,\,\angle A = {90^ \circ }$$ and $$AD$$ is an altitude. Complete the relation $${{BD} \over {BA}} = {{AB} \over {\left( {....} \right)}}$$.

$$ABC$$ is a triangle. $$D$$ is the middle point of $$BC$$. If $$AD$$ is perpendicular to $$AC$$, then prove that $$$\cos A\,\cos C = {{2\left( {{c^2} - {a^2}} \right)} \over {3ac}}$$$

(i) $$PQ$$ is a vertical tower. $$P$$ is the foot and $$Q$$ is the top of the tower. $$A, B, C$$ are three points in the horizontal plane through $$P$$. The angles of elevation of $$Q$$ from $$A$$, $$B$$, $$C$$ are equal, and each is equal to $$\theta $$. The sides of the triangle $$ABC$$ are $$a, b, c$$; and the area of the triangle $$ABC$$ is $$\Delta $$. Show that the height of the tower is $${{abc\tan \theta } \over {4\Delta }}$$.

(ii) $$AB$$ is vertical pole. The end $$A$$ is on the level ground. $$C$$ is the middle point of $$AB$$. $$P$$ is a point on the level ground. The portion $$CB$$ subtends an angle $$\beta $$ at $$P$$. If $$AP = n\,AB,$$ then show that tan$$\beta $$ $$ = {n \over {2{n^2} + 1}}$$

Give the MKS units for each of the following quantities.

(i) Young's modulus

(ii) Magnetic Induction

(iii) Power of a lens

A rocket moves forward by pushing the surrounding air backwards.

A block of mass 2 kg rests on a rough inclined plane making an angle of $$30^\circ $$ with the horizontal. The coefficient of static friction between the block and the plane is 0.7. The frictional force on the block is

A ship of mass 3 $$ \times $$ 10⁷ kg initially at rest, is pulled by a force of 5 $$ \times $$ 10⁴ N through a distance of 3 m. Assuming that the resistance due to water is negligible, the speed of the ship is

Two masses of 1gm and 4 gm are moving with equal kinetic energies. The ratio of the magnitude of their linear momentum is

If a machine is lubricated with oil