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Class XI I Chhorepatan Scondary School
Second Term Exam2078
F M: 75
Subject: Mathematics Time: 3hrs
PM: 30
Candidates are required to give their answers in their own words as
practicable.
Group A 11×1 =11
Tick the appropriate option of multiple choice question.
1. In how many ways can the letters of the word “ELEMENT” be
arranged ?.
a. 840 b . 480 c. 840ways
d.720ways.
2. The sum of the series x x2 x3 x4 .............. to is ……..
234
…
a. ln(1+x) b.ln (1-x) c. –ln (1+x) d. – ln(1-
x)
3. The value of 2 cos15o i sin 15o 6 is ……………
a. 64i b . 64 c. . -64 d.-64i
4. The nature of the roots of the equation x2 + x+1 = 0 are
…………..
a. real and equal b. rational and
unequal
c. irrational and unequal d. imaginary and
unequal
5. If the roots of the equation ax2 + bx+ c = 0 be in the ratio of 3:4
then the required condition is …………….
a.12b2 = 49ac b. 12 = 49ac c. 12b2=49ac d.b2
=ac
6. The system of equation 3x-y =5 and 6x-2y =10 are …………….
a. consistent and dependent b. inconsistent and
independent
c.consistent and independent d. non of the above
7. The area of triangle of a i j k and b 2 i 3 j k is ...
a. 38sq.unit b . 38 sq.unit . c. 6 d. 38sq.unit
2
8. In the equation of ellipse x h2 y k 2 1 a b 0 foci of
a2 b2
the ellipse is …………..
a. h ae,k b . h ae, k . c. h ae,0. d.
ae,0
9. The derivative of y = log(tanh x) is ……………..
a. 1 sinh x b . 2cosech2x . c. 1 sinh x d. 1 cosechx
2 22
10. The limit of correlation coefficient are ………..
a. 1, 1 b . [1, 1) c. 1, 1 d. (1, 1]
11. Suppose 4 cards are drawn at random from a well shuffled deck
of 52 cards .
The probability that all 4 are black is …………..
a. 11 b . 46 . c. 208 d.non of the above.
4165 833 833
Group –B 8×5 =40
12 . A committee of 5 is to be formed out of 6 gentlemen and 4
ladies .
In how many ways this can be done when at least one
lady included?
13. If the three consecutive coefficients in the expansion of
(1+x)n be 165, 330,462, Find n ?
14. a. USe De- Moivre’s theorem and find the
square root of 1 i 3 .
22
b.If one root of the equation ax2+bx+c = 0 be
the square of the other , then show that:
b3+a2c+ac2=3abc
15. a.Solve by row equivalent or Matrice inverse method:
x+y+z =1,x+2y+3z = 4, x+3y +7z = 13. 3+2
b. Solve by Cramer’s Rule : x-2y =-7, 3x+7y=5.
16. Find the coordinates of the vertices , foci, the eccentricity ,length
of major axis and equation of directix of ellipse
25x2 +4y2 = 100 .
17. Define vector Product .
Prove that Sin(A-B) =SinACosB - cosAsinB
18. The following table gives marks of mathematics and
physics obtained by 10 students in the test .Find the
rank coefficient of correlation :
Marks of 8 3 9 2 7 10 4 6 1 5
Mathematics
Marks of 9 5 10 1 8 7 3 4 2 6
physics
19 .Suppose that in a certain city 60% of all recorded births are
males .If we select 5 births from the population ,what will be
the probability that : a. none of them are male.
b.exactly three of them are male.
c. at least one of them are male .
Group C
3×8 = 24
.20. a.Find the derivative from first principle of : log( tanx)
Or State Rolle’s Theorem and verified it of
f(x) = 3x2 - 4 in [-1,1]
b.Evaluate : lim ex x 1 . 5+3
x0
x2
21.a. Prove that :
1 1 2 1 2 3 1 2 3 4 ................ 3e
2! 3! 4! 2
b.Prove that by Mathematical induction Method:
12 22 32 42.........................n2 n(n 1)(2n 1) 4+4
6
22. a. Solve by Simplex Method :
Maximize :P = 5x - 3y subject to the
constraints 3x+ 2y 6 ,x - 3y 4 , x ,y 0 .
b. Solve by Gauss elimination Method: 2x + y -3z = 5 ,
x + y - z =1, x - 3y + 3z = -6 5 +3
The end