What is the molarity and molality of a 13% solution (by weight) of sulphuric acid with a density of 1.02 g/ml? To what v

The substance absorbs CO2 and violently reacts with water. The substance is

Naturally occurring boron consists of two isotopes whose atomic weighs are 10.01 and 11.01. The atomic weight of natural

Igniting MnO2 converts it quantitatively to Mn3O4. A sample of pyrolusite is of the following composition : MnO2 80%, Si

One gram of an alloy of aluminium and magnetism when treated with excess of dil. HCl forms magnesium chloride, aluminiu

What weight of AgCl will be precipitated when a solution containing 4.77 g of NaCl is added to a solution of 5.77g of Ag

A compound was found to contain nitrogen and oxygen in the ratio 28 gm and 80 gm respectively. The formula of compound i

27 g of Al will react completely with how many grams if oxygen?

Find the derivative of $$\sin \left( {{x^2} + 1} \right)$$ with respect to $$x$$ first principle.

From a point $$O$$ inside a triangle $$ABC,$$ perpendiculars $$OD$$, $$OE, OF$$ are drawn to the sides $$BC, CA, AB$$ re

Balls are drawn one-by-one without replacement from a box containing $$2$$ black, $$4$$ white and $$3$$ red balls till a

Evaluate $$\int {{{\sin x} \over {\sin x - \cos x}}dx} $$

A triangle $$ABC$$ has sides $$AB=AC=5$$ cm and $$BC=6$$ cm Triangle $$A'B'C'$$ is the reflection of the triangle $$ABC$

If x = a + b, y = a$$\gamma $$ + b$$\beta $$ and z = a$$\beta $$ +b$$\gamma $$ where $$\gamma $$ and $$\beta $$ are th

Find the equation of the circle whose radius is 5 and which touches the circle $${x^2}\, + \,{y^2}\, - \,2x\,\, - 4y\, -

One side of rectangle lies along the line $$4x + 7y + 5 = 0.$$ Two of its vertices are $$(-3, 1)$$ and $$(1, 1).$$ Find

A straight line segment of length $$\ell $$ moves with its ends on two mutually perpendicular lines. Find the locus of t

The area of a triangle is $$5$$. Two of its vertices are $$A\left( {2,1} \right)$$ and $$B\left( {3, - 2} \right)$$. The

Six X' s have to be placed in the squares of figure below in such a way that each row contains at least one X. In how ma

Sketch the solution set of the following system of inequalities: $$${x^2} + {y^2} - 2x \ge 0;\,\,3x - y - 12 \le 0;\,\,

Find all integers $$x$$ for which $$\left( {5x - 1} \right) < {\left( {x + 1} \right)^2} < \left( {7x - 3} \right)

Show that the square of $$\,{{\sqrt {26 - 15\sqrt 3 } } \over {5\sqrt 2 - \sqrt {38 + 5\sqrt 3 } }}$$ is a rational num

Solve the following equation for $$x:\,\,2\,{\log _x}a + {\log _{ax}}a + 3\,\,{\log _{{a^2}x}}\,a = 0,a > 0$$

Solve for $$x:\,\sqrt {x + 1} - \sqrt {x - 1} = 1.$$

Solve for $$x:{4^x} - {3^{^{x - {1 \over 2}}}}\, = {3^{^{x + {1 \over 2}}}}\, - {2^{2x - 1}}$$

If $$\left( {m\,,\,n} \right) = {{\left( {1 - {x^m}} \right)\left( {1 - {x^{m - 1}}} \right).......\left( {1 - {x^{m - n

If $$\tan \alpha = {m \over {m + 1}}\,$$ and $$\tan \beta = {2 \over {2m + 1}},$$ find the possible values of $$\left

Express $${1 \over {1 - \cos \,\theta + 2i\sin \theta }}$$ in the form x + iy.

A horizontal uniform rope of length L, resting on a frictionless horizontal surface, is pulled at one end by force F. Wh

A car accelerates from rest at a constant rate $$\alpha $$ for some time after which it decelerates at a constant rate $