cbse class 12 maths sample papers model 5 - http://cbse.edurite.com/cbse-maths/cbse-class-12-maths.html

1. MATHEMATICS
SAMPLE TEST PAPER
CLASS XII
Class:12
Max Mks:100
Time 3hrs
No of pages: 4
Ò
General Instructions:
Ò All questions are compulsory.
Ò The question paper consists of 29 questions divided into three sections - A, B and C.
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Ò Section - A comprises of 10 questions of one mark each, Section B is of 12 questions of four
marks each, Section C comprises of 7 questions of six marks each.
Ò Internal choice has been provided in four marks question and six marks question. You have to
attempt any one of the alternatives in all such questions
Ò use of calculator not permitted..
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SECTION A
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Question number 1 to 10 carry 1 mark each
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1. Show that the functions f:R→R given by f(x) = x3 is injective.
2. Find the value of sin-1x = y when 0<y<π
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3. Find the value of x,y an d z in from the following equations.
4. Find the derivative with respect to x sec(tan√x)
5. The radius of an air bubble increasing at the rate of 5cm/s. At what rate is the volume of the
bubble increasing when the radius is 2cm.
6.
Find the area between the curve y=x and y = x2
7. Find the direction cosine of the ides of the triangle whose vertices are (3,5,-4) ,(-1,1,2) and (-5,5,-2)
8. Evaluate sin-1(sin1000)+cos-1(cos1000)
9. f(x) = e2log(sinx) then find f' (π/4)

2. 10. Find the amplitude of the number (1+cos Ө+isin Ө)
SECTION B
Question numbers 11 to 22 carry 4 marks each.
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11. show that the function f:R→{xέ R:-1<X<1} defined by f(x) = (1+∣ x∣) , x belongs to R is one
and onto function
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12. Simplify
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13. Write the Minors and Co factors of the determinant
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or
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Given A , show that A2-5A+7I = 0. Hence find A-1
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14. Without eliminating the parameter find dx x = cos θ -cos2θ , y= sin θ -sin2θ
or
x = 5at3, y = 2at2+6t
15. Find the equation of the tangent and normal to the hyperbola
16. Evaluate: limit 0-π/2
or
√
sinx
√
dx
cosx
√sinx + √
x
2
a
2
-
y
2
b
2
=1 at the point (x0,y0)

3. Evaluate: limit a-0
√
√x
dx
a−
√x + √ x
17. Find the area enclosed between the parabola y2 = 4ax and the line y = mx
dy x + 1
18. Find the differential solution of the differential equation dx = 2− y ,y# 2
or
dy
Find the general solution of: dx =(1+x)2 (1+y)2
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19. Two adjacent sides of a parallelogram are 2 ⃗ -4 ⃗j +4 ⃗ and ⃗ -2 ⃗j -3 ⃗ , find the unit vector
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20. Find the shortest distance between the lines whose vector equation are ⃗ = (1-t) ⃗ +(t-2) ⃗j +(3-
parallel to its diagonal. Also find its area.
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r
i
k
k
2t) ⃗ and re ⃗ = (s+1) ⃗ +(2s-1) ⃗j -(2s+1) ⃗
21. A company manufactures two types of novelly souvenirs made of plywood. Souvenirs of type
A require 5 mint each for cutting and 10 mint each for assembling. Souvenirs of type B
requires 8 mint each for cutting 8 mint and 8 mint for assembling. The profit is Rs 5 each for
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type A and Rs 6 each for type B souvenirs. How many souvenirs of each type should the
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company manufactures in order to maximize the profit ?
22. A and b throw a die alternately till one of them gets a '6' and wins the game . Find their
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SECTION C
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respective probability of winning , if A starts first.
Question numbers 23 to 29 carry 6 marks each.
1+
√ x 2− 1
23. Write the function in simplest form tan-1
x
or
√
1− cosx
Write the function in simplest form tan-1 1+ cosx ,x<π
,x#0

4. 24. If A = , prove that A3-6A2+7A+2I = 0
25. Solve system of linear equations, using matrix method
2x+3y+3z = 5
x-2y+z = - 4
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3x-y-2z = 3
sinx
26. Differentiate with respect to x tan-1 1+ cosx
27. Find
tanx
∫ ( √cotx+ √ dx)
28. 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.
29. A dietician wishes to mix together two kinds of food X and Y in such a way that the mixture
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contains at least 10 units of vitamins A,12 units of vitamin B and 8 units of vitamin C. The
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vitamin content of 1 kg food is below. 1 kg of food X costs Rs 16 and 1 kg of food Y costs Rs
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20.Find the least cost of mixture which will produce the required diet?