Integrate cos2x cos4x cos6x dx
Given: ∫cos2x cos4x cos6x dx We know that cos A cos B = ½ [ cos (A+B) + cos (A-B)]... View Article
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The line x+y=1 meets the lines represented by the equation y3−xy2−14x2y+24x3=0 at the points A,B,C. If O is the origin, then OA2+OB2+OC2 is equal to
Given equation: y3−xy2−14x2y+24x3=0 y3-xy2-14x2y+24x3=0 y3-2xy2 + xy2-2x2y-12x2y+24x3=0 y2(y-2x) +xy(y-2x) -12x2(y-2x)=0 (y-2x)(y2 +xy -12x2)=0 (y-2x)(y-3x)(y+4x)=0 Hence, the three lines are: y=... View Article
What is the factorial of a number?
Factorial of a number, say k is equal to the product of all numbers such as 1 × 2 ×... View Article
What are decimal numbers?
Decimal numbers are one of the types of numbers, which has a whole number and the fractional part separated by... View Article
What is the inverse of a matrix?
If A and B are two square matrices such that AB = BA = I, then B is the inverse... View Article
Find the area of the parallelogram formed by vectors A = [3, 2] and B = [-3, 7].
Given, \(\begin{array}{l}\vec{A}=3\hat{i}+2\hat{j}\end{array} \) and \(\begin{array}{l}\vec{B}=-3\hat{i}+7\hat{j}\end{array} \) Area of the parallelogram formed by the vectors \(\begin{array}{l}\vec{A}\end{array} \) and \(\begin{array}{l}\vec{B}\end{array} \) =... View Article
Two statements, s1 and s2, are given below, followed by a question. s1: 114 < x < 126, where x is a natural number. s2: x is a factor of 169. Question: Is x a prime number?
From the first statement:s1: 114 < x < 126, where x is a natural number. x = {115, 116, 117,... View Article
Which of the following is not an irrational number? (a) 7√5 (b) √2 + 2√2 (c) (√7 – 3) – √7 (d) √3 + 2
We know that,The sum or difference between rational and irrational numbers is always irrational.Also, the product of rational and irrational... View Article
What are composite numbers?
Numbers having more than two factors are called Composite numbers. The smallest composite number is 4 and the smallest odd... View Article
What is the standard deviation?
Standard deviation is a measure that shows how much variation (such as spread, dispersion, spread) from the mean. It is... View Article
What is a linear equation?
A linear equation is an equation with the highest variable power as 1. If a linear equation contains only one... View Article
What are irrational numbers?
A number is called irrational if it cannot be written in the form p/q, where p and q are integers... View Article
o2 and so2 gases are filled in the ratio of 1:3 by mass in a closed container of 3L at temp of 27 degree celsius . the partial pressure of O2 is 0.60atm , the concentration of SO2 would be
Solution: Let the mass of O2 is x and the mass of SO2 is 3x Partial pressure of O2 is ... View Article
1.2 g of organic compound on kjeldahl method liberates ammonia which consumes 30 cm3 of 1 N HCl. The percentage of nitrogen in the organic compound is
The organic compound (w) = 1.2 g Ammonia consume = 30 cm3 = 30 ml Normality of HCl = 1N... View Article
which of the following is correct for reaction of chiral substrate ?
(A) A reaction in which different stereoisomers produce different products or act at different rates is called stereospecific reaction. (correct)... View Article
In the standardisation of Na2S2O3 using K2Cr2O7. The equivalent weight of K2Cr2O7is:
Solution An equivalent weight of a solution is defined as the molecular weight of the solute divided by the valence... View Article
which one of the following has the lowest boiling point? a)H2O b) H2Te c) H2Se d) H2S.
Answer: (d) H2S. Explanation The boiling point of a liquid is the temperature at which the vapour pressure of the liquid... View Article
mercury boils at 356 degrees celsius However, mercury thermometers are made such that they can measure temperatures up to 500 degree celsius. This is done by
The boiling point of mercury is 356°C. By filling nitrogen gas at high pressure, the boiling point of mercury is... View Article
unknown gas diffuses with co2 Rate of diffusion of unknown gas is double than that of CO2. The molecular weight of the unknown gas is
Let M1 is the mass of CO2 = 44 gm M2 is the mass of unknown gas r1 is the... View Article
in the reaction VO + Fe2O3 →FeO+V2O5, the eq.wt.of V2O5 is equal to its
Solution: VO + Fe2O3 ⟶ FeO + V2O5 Oxidation number of V in VO=+2 Oxidation number of V in V2O5... View Article
