class 12 model question-merged

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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  h2  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
x0
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