Mathematics – Important Question Bank for Madhya Pradesh HSSC 12th (HSC) Board Exam 2018

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After the tremendous success of our last year Important Question Bank for Madhya Pradesh HSSC (HSC) Board Exam 2016 and Important Question Bank for Madhya Pradesh HSSC 12th (HSC) Board Exam 2017 we have also created a list of Most Important Question Bank for Madhya Pradesh HSSC 12th (HSC) Board Exam 2018  which are likely to appear in HSC Board Exams this year.

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1.Prove that: ʃ sec x dx = log (sec x + tan x) +c
2. Evaluate: dx
3. Evaluate:
a. dx
b. dx
4. Find the value of :
a. ʃ x e x dx
b. ʃ sec 2 x tan 3 x dx
c. ʃ x sin x dx
d. ʃ x tan 2 x dx
e. ʃ sec 3 x dx
5. Find the value of :
6. If y = then prove that (1-2y)dy/dx = sin x
7. If y = then prove that (1-2y)dy/dx = cos x
8. Prove that cos -1 4/5 +tan -1 3/5 = tan -1 27/11.
9. Find the differential coefficient of
10. Differentiate (cos x) cos x with respect to x.
11. If y = then prove that
dy/ dx = y 2
x (2-ylogx)

12. Calculate correlation coefficient between x and y for the following data:
X 65 66 67 67 68 69 70 72
Y 67 68 65 68 72 72 69 71
13. Prove that correlation coefficient is the geometric mean of the regression coefficient.
14. Prove that the correlation coefficient lies between -1 to +1.
15. The following data are given:

X Y
Arithmetic mean 36 85
Standard deviation 11 8
Correlation coefficient = 0.66
Find the two regression equations for X and Y on the basis of the above data.
16. Calculate regression coefficient b yx and b xy for the variable x and y for the following data:
∑x=24, ∑y=44, xy=306, ∑x 2 =164, ∑y 2 =574, n=4.
17. Find the covariance for the pair of values:
(1,6), (2,9), (3,6), (4,7), (5,8), (6,5), (7,12), (8,3), (9,17), (10,1).
18. Given two lines of regression x+3y =11 and 2x+y =7. Find the coefficient of correlation between x
and y. Also estimate the value of x when y=4.

19. Find the equation of the plane passing through the point (4, 5, 1), (0,-1,- 1) and (-4, 4, 4).
20. Find the value of: ʃ dx
5+ 4sinx

21. Solve the differential equations: (x-1) dy/dx = 2x 3 y.
22. Solve the differential equations: dy/dx = x 2 +5xy+4y 2
x 2

23. Solve the differential equation:
a. (e x + e -x ) dy/dx = e x – e -x
b. dy/dx =
24. A card is drawn at random from well shuffled pack of 52 cards. Find the probability that it is
neither an ace nor a king.
25. A fair coin tossed six times. What is the probability of getting at least three heads.
26. Find the probability distribution of the number 6 in the three throw of a dice.
27. Tickets are marked from 1 to 12 and mixed up. One ticket is taken out at random. Find the
probability of its being a multiple of 2 or 3.
28. In single throw of two dice, what is probability of not obtaining a total of 9 or 11?
29. Differentiate √sin x from first principle.
30. Differentiate √ x from first principle.
31. Find the differential coefficients of e x (using first principle)
32. Express into partial fraction: x and 2x-3 .
1-x 3 (x-1)(x 2 +1) 2
33. Express into partial fraction: 1 and x 3 .
(x+3)(x+1)(x-2) (1-x) 4

34. Prove by vector method:
Cos (a+b) =cos a. cos b – sin a. sin b.
35. Prove by vector method:
Sin (a+b) =sin a. cos b + cos a. sin b.
36. Find the angle between those lines whose direction cosines are recognized by the following
equations:
2l + 2m – n = 0 and mn + nl + lm = 0.
37. Evaluate:
38. Evaluate the limit:


39.
 Find domain and range of the function
 If f(x) =; x = 0
Find whether function f(x) is continuous at x=0.
40. Find the area bound by the curve x 2 = 4y and the line x= 4y-2.
41. Find the equation of a plane through the points (-1, 3, 2) and perpendicular to the plane
x+2y+2z = 5 and 3x+3y+2z = 8.

42. Find the equation of the sphere passing through the points (1, -3, 4), (1, -5, 2), (1, -3, 0) and
its center lying on the plane x + y + z = 0.
43. If the profit is given by p(x) = 41+ 24x -18x 2 , find maximum profit.
44. A ball is thrown
45. Find the shortest distance between the lines:
X+3 = Y-6 = Z and X+2 = Y = Z-7
-4 3 2 -4 1 1
46. If = +4-3 and =2-2- , then find the modulus of .
47. a. Prove that vectors 2-3+5 and -2+2+2 are mutually perpendicular.
c. If = 2-3+ and = 3+2, then find x .
48. Find the shortest distance between two lines, whose vector equations are:
= (3-t)+(4+2t)+(t- 2)
= (1+s)+(3s-7)+(2s- 2)
Where, s and t are scalar.
49. Find the equation of the plane which passes through the intersecting line of the planes
x+ 2y+3z=5 and
2x-4y+z- 3=0
And also passes through the point (0, 1, 0).
50. By vector method show that the points A(2,3,6), B(-1,- 1,2) and C(5,7,10) are collinear.
51. Show that the angle between any two diagonals of the cube is.
52. A variable plane is at a constant distance p from the origin and meets the axis at A,B and C.
show that the locus of the centroid of tetrahedron OABC is x -2 +y -2 +z -2 =16p -2.

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