# Category Archives: NCERT

Question 1. Let f : R → R be defined as f(x) = 10x + 7. Find the function g : R → R such… Read More
Question 1. Prove that the function f(x) = 5x – 3 is continuous at x = 0, at x = – 3 and at x… Read More
Question 17. If the 4th, 10th and 16th terms of a G.P. are x, y, and z, respectively. Prove that x, y, z are in… Read More
Question 1.  Find the 20th and nth terms of the G.P 5/2, 5/4, 5/8, … Solution: According to the question G.P: 5/2, 5/4, 5/8, …… Read More
Question 15: cot 4x (sin 5x + sin 3x) = cot x (sin 5x – sin 3x) Solution:  Taking LHS in consideration, we get =… Read More
Prove that: Question 1: sin2+cos2– tan2= Solution:  Taking LHS in consideration, we get = sin2+cos2– tan2 Substituting the values, = =– 1 = Hence, LHS… Read More
Question 13. Find two numbers whose sum is 24 and whose product is as large as possible. Solution: Let us assume two numbers x and… Read More
Evaluate the following limits in Exercises 1 to 22. Question 1:  Solution: In , as x⇢3  Put x = 3, we get  = 3+3  = 6… Read More
Question 17: Solution: In, as x⇢0 As we know, cos 2θ = 1-2sin2θ Substituting the values, we get = Put x = 0, we get… Read More
Question 1. Find the maximum and minimum values, if any, of the following function given by (i) f(x) = (2x – 1)2 + 3  … Read More
Question 11. Prove that the line through the point (x1, y1) and parallel to the line Ax + By + C = 0 is A… Read More
Question 1. Reduce the following equations into slope – intercept form and find their slopes and the y – intercepts. (i) x + 7y =… Read More
Question 1. Find a, b, and n in the expansion of (a + b)n if the first three terms of the expansion are 729, 7290,… Read More
Question 1. Find the coefficient of x5 in (x+3)8 Solution:  The (r+1)th term of (x+3)8 is given by Tr+1 = 8Cr(x)8-r(3)r (eq1). Therefore for x5… Read More
In each of the following, give the justification of the construction also: Question 1. Draw a line segment of length 7.6 cm and divide it… Read More