Find the common factors of 12x, 36. 12x = 2 × 2 × 3 × x 36 = 2 × 2 × 3 × 3 Common factor = 2 × 3 = 6... View Article
Which constant must be added and subtracted to solve the quadratic equation 9x2 + (3 / 4) x + 2 = 0 by the method of completing the square? The given expression is... View Article
Find the perpendicular distance from the origin of the line joining the points (cos θ, sin θ) and (cosφ, sinφ). Let A = (cos θ, sin θ) and B = (cosφ, sinφ) be the given points.... View Article
Define coaxial circles and deduce their equation in the simplest form. A family of circles, out of which every pair have the same radical axis, are called co-axial circles. Equation of coaxial circles in simplest... View Article
Write the following statement in the form of the equation: One-fourth of m is 3 more than 7. One-fourth of m is m / 4.... View Article
Give reason: A square can be thought of as a special rhombus. All sides of a rhombus and a square are the same. A rhombus with each angle as a right angle becomes a square. Hence, a square can be... View Article
Write the following rational numbers in ascending order: (1 / 3), (- 2 / 9), (- 4 / 3). The given rational numbers are... View Article
From a point in the interior of an equilateral triangle, perpendiculars are drawn on From a point in the interior of an equilateral triangle, perpendiculars are drawn on the three sides.... View Article
Find all the solutions of 4 cos2 xsinx – 2 sin2 x = 3 sinx. The given expression can be written as... View Article
A rectangular plot is given for constructing a house, having a measurement of 40m long and 15m in the front. According to the laws, a minimum of 3m wide space should be left in the front and back each and 2m wide space on each of the other sides. Find the largest area where the house can be constructed. Length of rectangular plot = 40m Width = 15m By keeping 3m wide space both in front and back The length becomes = 40 - 3 - 3 =... View Article
A sum of money lent out at simple interest amounts to Rs 720 after 2 years and to Rs 1020 after a further period of 5 years. What is the sum? Simple interest for 2 years = Rs. 720. Simple interest for 7 years = Rs. 1020 Simple interest for 5 years = Rs. 1020 - Rs. 720 = Rs. 300.... View Article
By actual division find the quotient and the remainder when (x4 + 1) is divided by (x – 1). The division is as follows.... View Article
If sin α + sin β = a and cos α + cos β = b, then prove that cos (α − β) = [a2 + b2 – 2] / 2. On squaring sin α + sin β = a and cos α + cos β = b and adding them,... View Article
Find the sum of all natural numbers which are multiples of 7 or 3 or both and lie between 200 and 500. The sum is calculated in the following way.... View Article
Find the reciprocal of 3 / 5, 9 / 10, 3 / 9, 7 / 4 and 9 / 2 also classify them as proper, improper fractions. The given fractions are... View Article