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_×_= 29

Since 29 is a prime number, it has only two factors such as 1 and 29. Hence, the positive and negative pair factors of 29 are (1, 29) and (-1,... View Article

What acts as a boundary for all the other parts of abacus?

The frame acts as a boundary for all the other parts of the abacus. The abacus has 17 rods, and each rod has 5 beads. The upper and lower part of... View Article

What is divisibility rule in Math?

A divisibility rule is a type of shortcut that allows us to determine whether a given number is divisible by a divisor by looking at its digits... View Article

What is 3 to the power of -1?

3 to the power of -1 means 3-1. 3-1 is written as ⅓ Hence, ⅓ = 0.333. Therefore, 3 to the power of -1 is 0.333.... View Article

If the curves y=2e^x and y=ae^−x intersect orthogonally, then a=?

Given: y = 2ex Hence, dy/dx = 2ex = m1 Also, given that y= ae-x dy/dx = -ae-x = m2 Two curves intersect orthogonally when m1. m2 = -1... View Article

The graph of the function y=f(x) passing through the point (0, 1) and satisfying the differential equation (dx/dy)+ycosx=cosx is such that

(a) It is a constant function (b) It is periodic (c) It is neither an even nor an odd function (d) It is continuous and differentiable for all... View Article

Integrate cos2x cos4x cos6x dx

Given: ∫cos2x cos4x cos6x dx We know that cos A cos B = ½ [ cos (A+B) + cos (A-B)] Thus, ∫cos2x cos4x cos6x dx = ∫cos2x .... View Article

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... 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 × 3 × 4 . . . × (k – 1) ×... 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 a decimal point. For example,... 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 matrix of A and is denoted by A-1, and A is the inverse of B. In... View Article

Find the area of the parallelogram formed by vectors A = [3, 2] and B = [-3, 7].

Given, Therefore, the area of parallelogram is 27 sq.units.... 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, 118, 119, 120, 121, 122, 123, 124, 125}From... 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 composite number is 9.... 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 a popular measure of... 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 variable, we call it a linear... 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 and q ≠ 0. Also, the decimal expansion of an... 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 pO2 = XO2 x Ptotal Partial pressure of O2 = 0.60 atm... 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 Percentage of Nitrogen = {1.4 x N x V(ml)}/ w(gm) =... View Article