Practice Paper -6
Class XII
Mathematics
Max.Marks-100 Time-3Hours
Blue Print
S.N. / Topics / VSA / SA / LA / Total1(a)
(b) / Relations &Functions
Inverse Trigonometric functions / 1(1)
1(1) / 4(1)
4(1) / 10(4)
2(a)
(b) / Matrices
Determinants / 2(2)
1(1) / -
4(1) / 6(1)
- / 13(5)
3(a)
(b)
(c)
(d)
(e) / Continuity Differentiability
Application of derivatives
Integration
Applications of Integrals
Differential Equations / -
-
2(2)
-
- / 8(2)
4(1)
4(1)
-
8(2) / -
6(1)
6(1)
6(1)
- / 44(11)
4(a)
(b) / Vector Algebra
3-Dimensional geometry / 2(2)
1(1) / 4(1)
4(1) / 6(1) / 17(6)
5 / Linear Programming / - / - / 6(1) / 6(1)
6 / Probability / - / 4(1) / 6(1) / 10(2)
Total / 10(10) / 48(12) / 42(7) / 100(29)
Practice Paper-6
Mathematics
Class –XII
Max Marks-100 Time-3 Hours
General Instructions
1.All questions are compulsory.
2.The question paper consists of 29 questions divided into three sections A,B and C.Section A comprises 10 questions of 1 mark each, section B comprises of 12 questions of 04 marks each and section C comprise 07 questions of 06 marks each. 3. All questions in section A are to be answered in one word or one sentence or as per the exact requirement of the questions.
4. There is no overall choice. However, internal choice has been provided in 04 questions of 04 marks each and 02 questions of 06 markeach. You have to attempt only one of alternatives in all such questions.
5. Use of calculator is not permitted. You may ask for logarithmic tables, if required.
(SECTION-A)
1. If f(x)= x+ 7 and g(x) = x-7, xR find (fog) (7).
2.Evaluate Sin/3 –Sin-1(-1/2)].
3 If B is skew symmetric matrix, write whether (AB'A) is skew symmetric or symmetric matrix.
4. If A is asquare matrix order 3 such that │adj A│= 64, find |A|.
6. Write the value of ∫ 1/(x +x log x) dx
7. Write the value of ∫1 Sin5x Cos4x dx.
-1
8. Find position vector of a point R which divides the line joining two points P and Q whose position vectors are and respectively in ratio 2:1 internally.
9.Find the value of x for which is a unit vector.
10. If a line has direction ratio as 2, -1,-2, determine its direction cosines.
(Section B)
11.Show that f: R-R - given by f(x) = is invertible. Also find.
OR
Show that the relation R on set A = given by R=R= {(a, b):|a-b| is even}is an equivalence relation.
12. using the property of determinant show that
=23
13. If tan-1 + tan -1 = /4 then find the value of x.
14. Find the value of a and b such that the function defined by
f(x) = 5 if x2
= ax +b if 2<x 10
= 21 if x10
is continuous at x =2and x = 10
15. Differentiate the function + xwith respect to x.
OR
If y = (tan -1x) 2show that (x 2+1)2 y2+ 2x (x2 +1) y1 = 2.
16. Find the interval in which the function f is given by f(x) =,0≤ x ≤2 is strictly increasing or decreasing.
OR
Find the equation of normal to the curve y = x3 +2x+6 which are parallel to the line x+14y +4 = 0.
17. Evaluate ∫ (+) dx
OR
Evaluate dx
18. Form differential equation representing the family of curves by eliminating the arbitrary constants a and b.
Y = a + b.
19. Solve the differential equation
(1+) dx + (1-x/y) dy = 0
20. If, and are unit vectors such that ++=,find the value of.+ . +.
21. Find the shortest distance between the lines
= i + j + k + λ (2i – j + k)
= 2i + j –k + μ (3i -5j +2k)
22. Three balls are drawn one by one without replacement from a bag containing 5 white and 4 green balls .Find the probability distribution of number green balls drawn.
SECTION C
23. Solve following system of equation by matrix method
3x -2y +3z =8
2x + y – z =1
4x -3y +2z =4
OR
Using elementary operation find inverse of
24. Prove that the volume of the largest cone that can be inscribed in a sphere of radius R is 8/27 of the volume of sphere.
OR
Show that semi vertical angle of the cone of the maximum volume and of given slant height is tan -1.
25. Using the method of integration find area of the region bounded by lines 2x +y = 4 ,3x -2y = 6 and x -3y +5 = 0
26.Evaluate (x2 +x +2 ) dx as the limit of sum.
27. Find the coordinates of foot of the perpendicular and perpendicular distance of point(1, 2, 3)from a plane x + 2y +4z = 38. Find also image of the point in the plane.
28. A dealer wishes to purchase a number of fans and sewing machines .He has only Rs 5760 to invest and has space for at most 20 items. A fan cost him Rs 360 and a sewing machine Rs 240. He expect to sell a fan at profit of Rs 22 and sewing machine for a profit of Rs 18.Assuming that he can sell all the items he buys, how should he invest his money to maximize his profit .Solve it graphically.
29. An insurance company insured 2000 scooter drivers, 4000 car drivers and 6000 truck drivers. The probability of an accident involving a scooter driver, a car driver and a truck driver is 0.01, 0 .03 and 0.15 respectively. One of the insured person meets with an accident .What is the probability that he a scooter driver.