# Category Archives: NCERT

Question 1. Determine which of the following polynomials has (x + 1) as a factor: (i) x3+x2+x+1 Solution: p(x) = x3 + x2 + x… Read More
Question 1. Show that the sum of (m + n)th and (m  –  n)th terms of an A.P. is equal to twice the mth term.… Read More
Question 11. If a + ib =  , prove that a2 + b2 =  Solution: Given: a + ib =  On comparing the real and… Read More
Question 17.  If a, b, c, d are in G.P, prove that (an + bn), (bn + cn), (cn + dn) are in G.P. Solution: … Read More
Question 1. Evaluate  Solution: = [-1 – i]3 = (-1)3 [1 + i]3 = -[13 + i3 + 3 × 1 × i (1 +… Read More
Differentiate the following w.r.t x Question 1. y =  Solution:        () Question 2.  Solution: Question 3.  Solution: Question 4. y=sin(tan-1e-x) Solution: Question 5. y = log(cos… Read More
Prove That: Question 1. 2cos(π/13)cos(9π/13) + cos(3π/13) + cos(5π/13) = 0  Solution:  Let’s take L.H.S = 2cos(π/13)cos(9π/13) + cos(3π/13) + cos(5π/13) Rearranging terms, we get … Read More
Question 11. If the sum of the first n terms of an AP is 4n − n2, what is the first term (that is S1)?… Read More
Question 1. Find the sum of the following APs. (i) 2, 7, 12,…., to 10 terms. (ii) − 37, − 33, − 29,…, to 12… Read More
Question 14:  = (n+1) Solution: We have, P(n) =  = (n+1) For n=1, we get P(1) = (1+ ) = 2 = (1+1) = 2 So, P(1) is… Read More
Prove the following by using the principle of mathematical induction for all n ∈ N: Question 1: 1 + 3 + 32 + …….. +… Read More
Find adjoint of each of the matrices in Exercises 1 and 2. Question 1.  Solution:  A =  A11 = 4; A12 = -3; A21 =… Read More
Question 1. Verify Rolle’s theorem for the function f(x) = x2+ 2x – 8, x ∈ [– 4, 2]. Solution: Now f(x) = x² +… Read More
Question 11. In the following figure, E is a point on side CB produced of an isosceles triangle ABC with AB = AC. If AD… Read More
Question 1. State which pairs of triangles in Figure, are similar. Write the similarity criterion used by you for answering the question and also write… Read More