3
CBSE CBSC_2015_SET_2 SECTION – A 1. If A is a square matrix such that A 2 =A, then write the value of 7A − (I + A) 3 , where I is an identity matrix. 2. If , 4 5 1 0 z w 7 2 y x x find the value of x + y. 3. If tan -1 + tan -1 y = , 4 xy <1, then write the value of x + y + xy. 4. , 7 4 8 6 7 4 3x 2 - If find the value of x. 5. If f(x) = x 0 t sin t dt, write the value of f’(x). 6. Find the value of 'p' for which the vectors k ˆ 9 j ˆ 2 i ˆ 3 and k ˆ 3 j ˆ 2p i ˆ are parallel. 7. If R = {(x, y): x + 2y = 8} is a relation on N, write the range of R. 8. If the cartesian equations of a line are , 4 6 - 2z 7 4 y 5 x - 3 write the vector equation for the line. 9. a 0 2 a. of value the find 8 π dx x 4 1 If 10. a and 13 a s, lar vector perpendicu are b and a If b 5 and find the value of . b SECTION – B 11. Solve the differential equation x e y 1 tan dx dy x 1 2 . 12. Show that the four points A, B, C and D with position vectors k ˆ j ˆ i ˆ - 4 and k ˆ 4 j ˆ 9 i ˆ ,3 k ˆ - j ˆ ,- k ˆ j ˆ 5 i ˆ 4 respectively coplanar. OR The scalar product of the vector k ˆ j ˆ i ˆ a with a unit vector along the sum of vectors k ˆ 3 j ˆ 2 i ˆ c and k ˆ 5 - j ˆ 4 i ˆ 2 b is equal to one. Find the value of l and hence find the unit vector along c ˆ b ˆ . 13. Evaluate: π 0 2 x cos 1 sin x 4x OR Evaluate: dx 6 5 2 x 2 x x 14. Find the value(s) of x for which y = [x (x − 2)] 2 is an increasing function. OR CBSE SAMPLE PAPER CLASS-XII MATHS SET-1 2014

CBSE SAMPLE PAPER CLASS-XII MATHS SET-1 CBSE 2014 · CLASS-XII MATHS SET-1 2014. CBSE Find the equations of the tangent and normal to the curve . y 1 at the point 2 a, b. b - a x

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Page 1: CBSE SAMPLE PAPER CLASS-XII MATHS SET-1 CBSE 2014 · CLASS-XII MATHS SET-1 2014. CBSE Find the equations of the tangent and normal to the curve . y 1 at the point 2 a, b. b - a x

CBSE

CBSC_2015_SET_2 SECTION – A

1. If A is a square matrix such that A2 =A, then write the value of 7A − (I + A)3, where I is an identitymatrix.

2. If ,45

10

zw 72

yx

xfind the value of x + y.

3. If tan-1 + tan-1 y = ,4

xy <1, then write the value of x + y + xy.

4. ,74

86

74

3x2-

If find the value of x.

5. If f(x) = x

0

t sin t dt, write the value of f’(x).

6. Find the value of 'p' for which the vectors k9j2i3 and k3j2p i are parallel.

7. If R = {(x, y): x + 2y = 8} is a relation on N, write the range of R.

8. If the cartesian equations of a line are ,4

6-2z

7

4y

5

x-3

write the vector equation for the

line.

9.

a

0

2a. of value thefind

8

π dx

x4

1If

10. a and 13 a s,lar vectorperpendicu are b and a If

b 5 and find the value of .b

SECTION – B

11. Solve the differential equation xey

1tan

dx

dyx1 2

.

12. Show that the four points A, B, C and D with position vectors

kji-4 and k4j9i,3k- j ,-kj5i4 respectively coplanar.

OR The scalar product of the vector kjia

with a unit vector along the sum of vectors

k3j2 ic and k5- j4 i2 b

is equal to one. Find the value of l and hence find the unit

vector along cb . 13. Evaluate:

π

0

2xcos 1

sin x4x

OR Evaluate:

dx 65

2x

2

xx

14. Find the value(s) of x for which y = [x (x − 2)]2 is an increasing function.OR

CBSE SAMPLE PAPER CLASS-XII

MATHS SET-1 2014

Page 2: CBSE SAMPLE PAPER CLASS-XII MATHS SET-1 CBSE 2014 · CLASS-XII MATHS SET-1 2014. CBSE Find the equations of the tangent and normal to the curve . y 1 at the point 2 a, b. b - a x

CBSE

Find the equations of the tangent and normal to the curve .ba, 2point at the 1 b

y -

a

x2

2

2

2

15. If the function f : R ® R be given by f (x) = x2+2 and g: R®R be given by 1,x,1x

xxg

find

fog and gof and hence find fog (2) and gof ( −3).16. Prove that

12

1- ,cos

2

1

4

11

11tan 11-

xxxx

xx

OR

x.of value thefind,2

π

4x

2xtan

4-x

2-x tanIf 11-

17. An experiment succeeds thrice as often as it fails. Find the probability that in the next five trials,there will be at least 3 successes.

18. If y = Peax + Q ehx, show that

0abydx

dyba

2d

ydx

2

19. Using properties of determinants, prove that:

c111

111

11a1

b = abc + bc + ca +ab

20. If x = cost (3 − 2 cos2 t) and y = sin t (3 − 2 sin2 t), find the value of .4

π at t

dx

dy

21. Find the particular solution of the differential equation log

0. when x 0 y given that,43dx

dy

yx

22. Find the value of p, so that the lines

5

z6

1

5y

3p

7x7:l and

2

3-z

p

147y

3

x1:l 21

are perpendicular to each other. Also find the equations of a line passing through a point (3, 2, − 4) and parallel to line l1.

SECTION – C 23. Find the equation of the plane through the line of intersection of the planes x + y + z = 1 and 2x +

3y + 4z = 5 which is perpendicular to the plane x- y + z = 0. Also find the distance of the planeobtained above, from the origin.

OR Find the distance of the point (2, 12, 5) from the point of infersection of the line

.0kj2-i .r plane theand k2j4i3 k2j4-i2r

24. Using integration, find the area of the region bounded by the triangle whose

2014

Page 3: CBSE SAMPLE PAPER CLASS-XII MATHS SET-1 CBSE 2014 · CLASS-XII MATHS SET-1 2014. CBSE Find the equations of the tangent and normal to the curve . y 1 at the point 2 a, b. b - a x

CBSE

vertices are (-1, 2), (1, 5) and (3, 4).

25. A manufacturing company makes two types of teaching aids A and B of Mathematics forclass XII.Each type of A requires 9 labour hours of fabricating and 1 labour hour forfinishing. Each type ofB requires 12 labour hours for fabricating and 3 labour hoursfor finishing. For fabricating andfinishing, the maximum labour hours available per weekare 180 and 30 respectively. Thecompany makes a profit of 80 on each piece of type A and120 on each piece of type B. Howmany pieces of type A and type B should be manufacturedper week to get a maximum profit?Make it as an LPP and solve graphically. What is the maximum profit per week?

26. There are three coins. One is a two-headed coin (having head on both faces),another is abiased coin that comes up heads 75% of the times and third is also abiased coin thatcomes up tails 40% of the times. One of The three coins is chosen atrandom and tossed,and it shows heads. What is the probability that it was the two-headed coin?

OR

Two numbers are selected at random (without replacement) from the first six positive integers. Let X denote the larger of the two numbers obtained. Find the probability distribution of the random variable X, and hence find the mean of the distribution.

27. Two schools A and B want to award their selected students on the values ofsincerity, truthfulness and helpfulness. The school A wants to award x each, y eachand z each for the three respective values to 3, 2 and 1 students respectively with atotal award money of 1,600. School B wants to spend 2,300 to award its 4, 1 and 3students on the respective values (by giving the same award money to the threevalues as before). If the total amount for one prize on each value is 900, usingmatrices, find the award money for each value. Apart from these three values,suggest one more value which should beconsidered for award.

28. If the sum of the lengths of the hypotenuse and a side of a right triangle is given,show that the area of the triangle is maximum, when the angle between them is 60°.

29. Evaluate:

dxxcosxxcossin x sin

14224

s

2014