SAMPLE TEST PAPER
No of pages: 4
Ò All questions are compulsory.
Ò The question paper consists of 29 questions divided into three sections - A, B and C.
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..
Question number 1 to 10 carry 1 mark each
1. If f: R→R is defined by f(x) =x2-3x+2, find (f(x))
2. Find the value of cos-1 2 +sin-1 2
a ij = j
3. construct a 2X2 matrix A =a ij whose element are given by
4. Find dx for x3+x2y+xy2+y3 = 81
6. Find a vector in the direction of vector ⃗ = ⃗ -2 ⃗j that has a magnitude of 9 units.
Find the approximate value o the number (54)1/2
7. Cartesian equation of a line is
3 = 7 = 2 write its vector form.
9. compute P( ∣A∣ B), if P(B) = 0.5 and P(AnB) = 0.32
8. Find the distance of the plane 3x-4y+12z = 3 from the origin
10. Find the scalar components of the vector AB with initial point A(4,2) and terminal point B(-6,5)
Question numbers 11 to 22 carry 4 marks each.
11. Show that sin-1(2x √ x ) = 2sin-1x
12. compute the following :
compute the following
13. By using the property of determinant show that
= 0, if 0≤x≤1
= 4x, if x>1
f(x) =2x, if x<0
14. Find the continuity of the function f, where f is defined by
Explain the continuity of the functions f(x) = sin x + cos x
15. Differentiate with respect to x
( x− 3)( x 2 + 4)
3x2+ 4x+ 5
16. Find the equation of all lines having slope 2 and begins tangent to the curve y+ ( x − 4)2 = 0
The radius of a circle is increasing uniformly at the rate of 5 cm/s. Find the rate at which the area of the
circle is increasing when the radius is 20cm.
sin (x− a) dx
1+ x dx
18. Find the area of region enclosed by the parabola x2=y, the line y = x+2 and the x – axis.
19. Find the general solution of equation (x+3y)2 dx = y (y>0)
20. Show that the points A,B and C with position vectors, ⃗ =3 ⃗ -4 ⃗j -4 ⃗ , ⃗ =3 ⃗ -4 ⃗j -4 ⃗ and
⃗ = ⃗ -3 ⃗j +5 ⃗ respectively from the vertices of a right angled triangle.
21. Find the angle between the following pair of lines
= 5 = − 3 and − 1 = 8 = 4
22. Find the coordinates of the point where the line through the points A (3,4,1) and B(5,1,6)
crosses the XY-plane.
Question numbers 23 to 29 carry 6 marks each.
23. Express tan-1 1− sinx , 2 <x< 2 in the simplest form.
show that sin-1 5 -sin-1 17 = cos-1 85
24. Find the value of x and y from the following equation
25. Examine the consistency of the system of equation
5x-y+4z = 5
2x+3y+5z = 2
5x-2y+6z = -1
26. a)Prove that the function given by f(x) = log cosx is strictly decreasing on(0,π /2) and strictly
increasing on (π/2,π)
b)Find the equation of the normal to the curve x2 = 4y which passes through the point (1,2)
27. One kind of cake requires 200g of flour and 25g of fat, and another kind of cake required 100g
of flour and 1kg of fat assuming that there is no shortage of the other ingredients used in
making the cakes
28. A die is thrown three times .Events A and B are defined as below A: 4 on third throw
B:6 on the first probability of A given that B has already occurred. Find the probability of A given that
B has already occurred.
29. show that the plane 2x+y+3z-2 – 0 and x-2y+5 = 0 are perpendicular to each other.