XI Mathematics - II
CLASS XI
MATHEMATICS
F.M. 60
Time 2 hrs
Part àI
Question 1 [3 x 10]
a) Find the sum (√2 + 1) + 1 + (√2 – 1 )……ᾱ
b) Find two numbers whose AM is 25 and GM 20
c) If 16Cr = 16Cr + 2 find rC 4
d) Find the value of “a” if 17th and 18th terms in the expansion of (2 + a)50 are equal
e) Prove that tan 4Ө = {4 tan Ө(1 – tan2 Ө)}/(1 – 6tan2 Ө + tan4 Ө)
f) Solve 2sin2x + sin22x = 2
g) Using first principle find dy/dx of sin x
h) Evaluate ∫(x4 + x2 + 1)/(x2 – x + 1)dx
i) Find the equation of the circle whose centre is (2, -3) and passes through the point of intersection of the lines 3x – 2y – 1 = 0 and 4x – y – 27 = 0
j) Prove that sin A sin (60o – A) sin (60o + A)= ¼ sin 3A
Part à II
Question 2 [ 5 + 5]
a) Find the term independent of x in the expansion of (3x2 –1/2x3)10
b) Find the sum 0.7 + 0.77 + 0.777 +…….to n terms
Question 3 [ 5 + 5]
a) Find the equation of the circle whose centre lies on the line 3x + 4y = 7 and passes through the points (1, –2) and ( 4 ,–3)
b) Find dy/dx if y = log{( a + bsinx)/(a – b sinx)}
Question 4 [ 5 + 5]
a) Hemant borrowed ` 10,000 from Mahesh, He paid back `3,000 after 2 months, `3,200 after 6 months, `4,800 after 8 months and `1,000 after 10 months. Find the rate of interest.
b) Evaluate ∫(sin 4x/sin x) dx
Answers
Q1a)(4 + 3√2)/2, b)40&10, c) 35,d)1, f)nπ +/- π/2, mπ +/- π/4,h) x3/3 +x2/2 + x + c, i) x2 + y2 – 4x + 6y – 96 = 0
Q2a)5th term = 76545/8 ,b) 7/81(9n – 1 + 1/10n), Q3a) (x – 47/15)2 + (y + 3/5)2 = 1465/225, b) 2ab cosx/(a2 – b2sin2x) Q4a) r = 24%, b) 2 { sin 3x/3 + sin x} + C