Class XI Mathematics
MATHEMATICS
F.M. 100
Time 3 hours
Question1 3 X 10
a) Which term of 4, 9, 14……is 254?
b) If √3 + 3 + 3√3………..=39 + 13√3, find the number of terms.
c) Find dy/dx of √x using first principle
d) Evaluate ∫(x3 + 5x2 + 4x + 1)/x2 dx
e) Find the sum 5 + 55 + 555 + …….to n terms
f) Differentiate w r t x à (x2 – 3x + 2)(x + 2)
g) Evaluate ∫(1 + √x)2/√x dx
h) Prove that (cos 8o - sin 8o )/ (cos 8o + sin 8o ) = tan 37o
i) Prove that sin(x + y)/ sin(x – y) = (tanx + tan y)/(tanx - tany)
j) Find dy/dx if y = sin2{log(2x – 3)}
Question2 [ 5 + 5 ]
a) Show that the sum of (m + n)th term and (m – n)th term of an AP is equal to twice the mth term.
b) Prove that nCr/ NCr – 1 = (n – r + 1)/r
Question3 [ 5 + 5 ]
a) The first term of an AP is 2 and the last term is 50. If the sum of all these terms is 442, find the common difference.
b) Find the value of 2.4.6 + 3.5.7 + 4.6.8……..to n terms.
Question3 [ 5 + 5 ]
a) How many different products can be obtained by multiplying two or more of the numbers 3,5,7& 11 without repetition?
b) Prove that tan3A tan2A tan A = tan 3A – tan2A – tanA
Question4 [ 5 + 5 ]
a) Prove that cosA.cos2A.cos22A.cos23A……cos2n – 1A = sin2nA/2nsin A
b) Find the value of A if sinA + sin 3A + sin 5A = 0
Question5 [ 5 + 5 ]
a) Find the equation of the circle whose radius id 5 and cuts off intercepts 4 and 6 from the axes.
b) The volume of a cube is increasing @ 7cm3/sec. how fast is the surface area increasing when the length of the edge is 12 cm?
Question6 [ 5 + 5 ]
a) Find the equation of the tangent to the curve y2 – 2x3 – 4y + 8 = 0 at (1,2)
b) Evaluate ∫(3x + 1)/(3x2 + 2x + 1) dx
Question7 [ 5 + 5 ]
a) Evaluate ∫sin(logx)/x dx
b) Consider the following bills à `10,000 payable on 1st January 2013, `30,000 payable on 18thJanuary 2013, `22,000 payable on 3rd May 2013, `36,000 payable on 30th June 2013 if a fifth bill of `14,000 was drawn on a certain date such that the average due date for the five bills is 6th April 2013. Find the due date of the fifth bill.