Download - Modern Indian School

MODERN INDIAN SCHOOL
CHOBHAR, KATHMANDU
CLASS : XI
SUBJECT:MATHEMATICS
FINAL EXAM
M.M. 100
TIME:3HRS
GENERAL INSTRUCTIONS:
I. All questions are compulsory.
II. The question paper consists of 26 questions divided into three Sections A, B, and C. Section A comprises of 6 questions of
one mark each. Section B comprises of 13 questions of four marks each. Section C comprises of 7 questions of six marks
each.
III. All questions in Section A are to be answered in one word, one sentence or as per the exact requirement of the question.
IV. There is no overall choice. However internal choice has been provided in 4 questions of 4 marks each and 2 questions of six
marks each. You have to attempt only one of the alternatives in all such questions.
V. Use of calculator is not permitted. You may ask for logarithmic tables if required.
SECTION A
1+𝑖
1. Find the modulus of z if z=
1−𝑖
2.
3.
4.
5.
6.
How many chords can be drawn through 21 points on a circle.
Write out the expansion of (x+y)5.
Write the negation of the given statement, P: intersection of two disjoint sets is not an empty set.
Write the contrapositive of the statement, P: if a number is divisible by 6 then it is divisible by 3.
A coin is tossed thrice. Write the sample space.
SECTION B
7. A market research group conducted a survey of 1000 consumers & reported that 720 consumers like
product A & 450 consumers like product B, what is the least number that must have liked both
products?
8. Find the domain of the function f(x)=√𝑥 − 1
OR
Find the domain of the function f(x)=
3
9. If Tanx=4 , 𝜋 < 𝑥 <
3𝜋
2
x 2  2x  1
x 2  8 x  12
𝑥
𝑥
𝑥
find the value of 𝑠𝑖𝑛 2 , 𝑐𝑜𝑠 2 , 𝑡𝑎𝑛 2
10. Represent the complex number z=1-i√3 in the polar form
11. In how many ways can the letters of the "MISSISSIPPI" be arranged so that all the S'S not come
together.
12. Find the equation of the circle with radius 5 whose center lies on x-axis and passes through the point
(2,3)
OR
Find the equation of the ellipse whose vertices are(±5,0)and foci are (±4,0)
13. Find the equation of the hyperbola whose foci are(0, ±12) and length of latus rectum is 36.
14. Using section formula prove that the points(3,2,-4), (5,4,-6)& (9,8,-10)are collinear.
OR
Find the ratio in which the line segment joining the points (4,8,10) & (6,10,-8)is divided by the YZplane.
15. Evaluate lim
𝑥→0
1−𝑐𝑜𝑠𝑥
𝑥
4𝑥+5𝑠𝑖𝑛𝑥
16. Find the derivative of the given function f(x) = 3𝑥+7𝑐𝑜𝑠𝑥
17. Fine the derivative of y = xsinx using first principle
18. Find the probability that when 7 cards are drawn from a well shuffled deck of 52 cards, all the black
card are obtained.
19. Solve 2cos2x+3sinx=0
SECTION C
20. In a class of 60 students, 30 opted for NCC, 32 opted for both NCC & NSS.If one of these student is
selected at random. Find the probability that (a) the student opted for NCC or NSS (b) neither NCC (c)
NCC but not NSS.
n(4n  6n  1)
3
21. Use mathematical induction for the series to prove that1.3+3.5+5.7+……+(2n-1)(2n+1)=
22. Solve the following system of inequalities graphically x+2y≤ 10, 𝑥 + 𝑦 ≥ 1, 𝑥 − 𝑦 ≤ 0, 𝑥 ≥ 0 𝑦 ≥ 0
th
23. The coefficient of r  1 , r , r  1 terms in the expansion of x  1 are in the ratio1:3:5 find n and r.
th
th
n
24. If p is the length of perpendicular from the origin to the line whose intercept in the axes are a and b
1
1
1
 2 2
2
a
b
then show that p
OR
Find the equation of the line passing through (-3,5) and perpendicular to the line through the point (2,5),
(-3,6)
25. Find the mean and standard deviation of
x
f
60 61
2
1
62
12
63
29
64
25
65 66 67 68
12 10 4 5

 

2
2
2
2
2
2
26. Find the 𝑛𝑡ℎ term and sum to n terms of 1  1  2  1  2  3  .................
****************