2012 Model test for mathematics for std xii as per cbse syllabus Question paper
Are you looking for self assessment tests CBSE Plus II, the model question paper for Mathematics is given below as per the latest pattern and syllabus laid down by the Board for the forthcoming exams. Assuming that this is a real exam, write the answers for this practice question paper in three hours and see how much you know about Mathematics.
MODEL TEST FOR MATHEMATICS
Time Allowed : 3 Hrs Maximum Marks: 100
1. All questions are compulsory.
2. The question paper consist of 29 questions divided into three sections A, B and C. Section A comprises of 10 questions of one mark each, section B comprises of 12 questions of four marks each and section C comprises of
7 questions of six marks each.
3. All questions in Section A are to be answered in one word, one sentence or as per the exact requirement of the question.
4. There is no overall choice. However, internal choice has been provided in 04 questions of four marks each and 02 questions of six marks each. You have to attempt only one of the alternatives in all such questions.
5. Use of calculators is not permitted.
SECTION – A
1.Without expanding the determinant prove that it equals zero.
1 a b ? c
??? 1 b c ? a
1 c a ? b
2.In the given mapping , is f a bijection? Give reason for your answer.
f:N?N defined by f(x)=2x ?x?N
3. Let A be a diagonal A = (d1, d2, ……………, dn ) write the value of | A |.
4. If a matrix A = ? ? and , its square A2 = I, find the value of ?2 + ??.
1 ?3 ?
5.If sin ? ? ? x, find cos x
? 5 ?
6.Find the angle between the curves y2 = x and x2 = y at (1, 1). 7. Integrate x.5x dx
8. Find angle ? between the vectors a ? (i? ? ?j ? k)? andb ? (i? ? ?j ? k)?.
9. Find the scalar component and the magnitude of a vector joining the point (a, b, c) and ( u, v , w)
10. If a is a unit vector and (x ? a).(x ? a) ? 15 then find x .
SECTION – B
x+4 2x 2x ? ?5x ? 4??4 ? x ?2
11.Prove that 2x x+4 2x
2x 2x x+4
x x 2 1+x3
If x,y,z are different and y y2 1+y3 ? 0show that xyz = -1
z z2 1+z3
12. Find the probability distribution of the number of kings drawn when two cards are drawn one by one , without replacement , from a pack of 52 playing cards .
13. Examine the continuity of the given function at x = / 2
? cos x , x ? ?
? ? ? x 2
f(x) ??? 2
?1 , x=
14. Differentiate log10 (sin x)
-1 ? 1 ?
Differentiate sec ? ?, w . r. t x
? 2x ?1 ?
15.Find p, if the points (1,1,p) and (-3, 0 , 1) are equidistant from the plane whose equation is
r. ? 3i? ? 4j? ?12k? ??13 ? 0
16. Evaluate as Limit of Sum ?x 2 ? x ?1?dx
/2 cos2 x
2 2 dx
0 cos x ? 4sin x
sin3 x sin( x ? )
20. Show that the function f : R R defined by f ( x ) ? 2 x 1 , x ? R is one-one
3 and onto function. Also find the inverse of the function f.
For the Power set of all subsets of a non empty set, a relation ARB is defined if and only if A ?B .Is R an equivalence relation on the Power set?
21. Two bags I and II contain 4 red , 3 black balls 2 red and 4 black balls respectively. One bag is selected at random and from the bag selected, a ball is drawn. Find the probability that the ball is red.
A company has two factories to manufacture machinery . The factory I manufacture 70% of the machinery and the factory II manufactures 30% of the machinery. At Factory I , 80% of the machinery are rated to be of a standard quality and at Factory II 90% of the machinery are rated to be of a standard quality. A machinery is chosen at random and is found to be of a standard quality. What is the probability that it came from Factory II
22.Evaluate ? 1+x2 dx
SECTION – C
23. Show that the semi vertical angle of the right circular cone of maximum volume and the given slant height is tan?2.
ABC is a right triangle , right angled at C . P is a point on AB at a distance of a and b from sides
AC and BC respectively.. Show that the minimum length of the hypotenuse AB is given by:
3 ? 3 2 ?
? 2 ?a2 ? b3 ?
24 A pharmaceutical company manufactures two types of drugs, A and B. The combined production of the packets of the two drugs should not exceed900 per week and the demand for packets of drug of type B is at most half of that for packets of drug of type A. Further, the production level of drugs of type A can exceed three times the production of drugs of other
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