
	Trending ▼ ICSE CBSE 10th ISC CBSE 12th CTET GATE UGC NET Vestibulares ResFinder

CBSE XII Pre Boards 2015 : MATHEMATICS with Answers (KV Kolkata)

9 pages, 32 questions, 22 questions with responses, 59 total responses,

Kendriya Vidyalaya No.1 Salt Lake
Kendriya Vidyalaya (KV) No. 1, Salt Lake

+Fave Message

Profile Timeline Uploads

Home > kv_kendriya_vidyalaya_salt_lake > F Also featured on: souvikp

Formatting page ...

KENDRIYA VIDYALAYA SANGATHAN-KOLKATA REGION 3rd PRE-BOARD EXAMINATION: 2014-15 SUB: MATHEMATICS TIME ALLOWED: 3 HOURS M.M :100 General Instructions: 1. All questions are compulsory. 2. The question paper consists of 26 questions divided into three sections-A, B and C. Section A comprises of 6 questions of one mark each, Section B comprises of 13 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 4 questions of four marks each and 2 questions of six mark each. You have to attempt only one of the alternatives in all such questions. 5. Use of calculators is not permitted. Section A Q1. Evaluate: tan 1 3 sec 1 ( 2) Q2 Find gof if f(x) =8 x3 , g(x)= Q3. If = . , find the value of y . Q4. Evaluate: Q5. Find p such that x y z y z x and are perpendicular to each other. 1 2 3p 2 4 1 Q6. If determinant of a square matrix of order 3 is 4,find the determinant of its adjoint. Section B Q7. Show that is commutative and associative. Find the identity element for on A, if any. Q8. Prove = , x OR Solve for x Q9. By using properties of determinants, show that: 1 = Q10. If cos y = x cos(a + y) with cos a 1, prove that OR Find of the function , show that Q11. If Q12 Find the equation of plane passing through the line of intersection of the planes x + 2y + 3z = 4 and 2 x + y z + 5 = 0 and perpendicular to the plane 5 x + 3y 6 z + 8 = 0 Q13.Find the intervals in which the function f given by f(x) = 2x3 3x2 36x + 7 is (a) strictly increasing (b) strictly decreasing Q14.Show that [ + + + ] =2[ ] OR Find a unit vector perpendicular to each of the vectors + - ) where and . Q15.Evaluate: Q16. Evaluate: dx dx Q17.If sum of two unit vectors is a unit vector ,then show that the magnitude of their difference is Q18.. A man is known to speak truth 3 out of four times .He throws a die and report that it is a six. Find the probability that it is actually six. Which value is discussed in this question? Q19.Find the shortest distance between the lines ) and j (2i r i j k (3 ) r 2 i j- k i - 5 j 2k Section C Q20.Two institutions decided to award their employees for the three values of resourcefulness, competence and determination in the form of prizes at the rate of Rs. x ,Rs.y and Rs.z respectively per person. The first Institute decided to award respectively 4,3 and 2 employees with a total prize money of Rs.37000 and the second Institute decided to award respectively 5, 3 and 4 employees with a total prize money of Rs.47000.If all the three prizes per person together amount to Rs.12000, using matrix method find the value of x, y and z. Write the values described in the question. Q21.Solve the differential equation 2 , given that y = 0 where x = Q22..Using properties of definite integrals, evaluate: OR Using properties of definite integrals, evaluate: Q23. The sum of the perimeter of a circle and square is k, where k is some constant. Prove that the sum of their areas is least when the side of square is double the radius of the circle. OR Show that the volume of greatest cylinder that can be inscribed in a cone of height h and semi vertical angle is, 4 h 3 tan 2 . 27 Q.24 There are a group of 50 people who are patriotic, out of which 20 believe in non-violence. Two persons are selected at random out of them, write the probability distribution for the selected persons who are nonviolent. Also find the mean of the distribution. Explain the importance of non- violence in patriotism. Q25. Using integration Find the area lying above x-axis and included between the circle parabola + = 8 x and =4x OR Using the method of integration, find the area of the region bounded by the following lines 5x - 2y = 10, x + y 9 =0 , 2x 5y 4 =0 Q26. Reshma wishes to mix two types of food P and Q in such a way that the vitamin contents of the mixture contain at least 8 units of vitamin A and 11 units of vitamin B. Food P costs Rs 60/kg and Food Q costs Rs 80/kg. Food P contains 3 units /kg of vitamin A and 5 units /kg of vitamin B while food Q contains 4 units /kg of vitamin A and 2 units /kg of vitamin B. Determine the minimum cost of the mixture? What is the importance of Vitamins in our body? 3 Marking Scheme Second Pre Board Examination Mathematics-2014 Kolkata Region Q1. - Q2.2xQ3. y = -6 Q4. 1 Q5. p = - 2 Q6. 16 Q7. 1X6 for commutativity. 1 1 for associativity. No identity element. 1 2 1 2 1 ______________________________________________________________________ Q8. 1 1 1 2 1 1/2 1 2 _______________________________________________________________________ OR 1 1 1 1 2 1/2 _________________________________________________________________________________________ Ans 9. Applying R1 R1 + bR3 and R2 R2 aR3, we have: 1 1 Expanding along R1, we have: 1 1 Answer 1 ____________________________________________________________________________________ Q10. 1 1+1 = = 1 ________________________________________________________________________________________________ OR Taking logarithm on both the sides, 1 Differentiating both sides 2 1 _______________________________________________________________________ Q11. 1 1 1 1 _____________________________________________________________________________ Q12 Sol: The required plane is (x + 2y + 3z ) + k (2x + y z +5 )= 0 Or (1 + 2k)x +(2 + k)y +(3 - k)z-4 + 5k = 0 5(1+2k) +3 (2+k) -6 (3-k)=0 Solving k= 7/19 The equation of the plane is : 33x+45y +50z = 41 . 1 1 1 1 ______________________________________________________________________ Q13. 1 x = 2, 3 1/2 Intervals: (- ,-2),( -2,3) and (3, ) 1 (f) is strictly increasing in (- ,-2) and (3, ) and strictly decreasing in interval ),( -2,3) 1 ___________________________________________________________________________ = Q14. =( + ). +( ). +( +( }.( + ). +( 1 ). +( 2 = ]+ =2[ 1 2 ] ] 1 2 _________________________________________________________________________ OR + . + | - ) = - ) = + . 1 . - 1 1 2 1 _________________________________________________________________________ Q15. Let x2 = t 2x dx = dt 1/2 1 A=1/2, B=-1/2 1/2 2 _____________________________________________________________________________________________________ Q16. 1 1 2 1 +1 _____________________________________________________________________ Q17 To find the dot product ; 2 To find the value : 2 ______________________________________________________________ Q18.P(T) =3/4, P(F) =1/4 E: getting a six,F: he is not getting a six 1 P(E/T)= 1/6, P(E/F)=5/6 By Bay,s Theorem P(T/E)= Truthfulness 1 =3/8 1 1 2 , k a 2 a1 i Q19. b1 b2 3i j 7k b1 b 2 59 (b1 b2 ).(a 2 a 2 ) b1 b2 shortest distance = 1+1+1 = 10 1 59 _____________________________________________________________________ Q20.4 x + 3 y + 2z = 37000, 5 x + 3 y + 4z = 47000,x+ y + z =12001 A-1 exists. X = A-1 B1/2 |A| = - 3 Cofactors of A 2 AdjointA 1/2 1 X = 4000 ,y = 5000, z = 3000 Values _______________________________________________________________ Q21.P = 2tan x, Q = sin x I.F = 1 y 1 y = sec x + C y= + 1 = cos x + C -------------------(1) 1 putting x = and y = 0 in eqn (1) C = -2 1 __________________________________________________________________________ Y= cos x - 2 Q22. Use of property ,I= 2I = 1/2 1/2 Use of property 2I = 1 tanx = t, sec2xdx =dt & Correct result I = 1 1 _________________________________________________________________ OR 1 2 1 ____________________________________________________________________________________ Q23. Let r be the radius of the circle and a be the side 1+1 1/2 2 1/2 a =2 r 1 ___________________________________________________________________ OR fixed height (h) and semi-vertical angle ( ) relation of h and H 1+1/2 ( figure) 1 1 + 1 Result _________________________________________________________________ 24. Let X = The number of non -violent persons out of selected two. So, X = 0, 1, 2 C2 87 P(X = 1) = C2 245 30 P(X = 0) = 50 C1 C1 120 P(X = 0) = 50 245 C2 20 30 1 1/2 C2 38 C2 245 20 50 3 X 0 1 2 P(X) 87 245 120 245 38 245 Mean = X P (X) = 0 245 1 245 2 245 245 87 120 38 196 2 Importance of non- violence ______________________________________________________________ 25. (1) + = 8x + = 16 represents a circle with centre (4,0) and radius 4 units 1/2 (2) =4 x represents parabola with vertex at origin and axis as x-axis. + ( figure) Point of intersection of the curves are (0,0) and (4,4) = dx + dx 1+1/2 =2 =2 1/2 dx + dx + = _______________________________________ 2 1 OR Solving (1) and (2) point of intersection is C(4,5) Solving (2) and (3) point of intersection is B(7,2) 1 2 Area of triangle ABC= area of triangle ACD + area of CDEB + area of triangle ABE 1 = 1 2 1 = [ 1 2 1 = 1 2 ______________________________________________________________ Q26.Let the mixture contain x kg of food P and y kg of food Q. Minimise Z = 60x + 80y 1/2 subject to the constraints, 3x + 4y 5x + 2y 1 x, y 1 2 1 Figure and shading 2 2 The corner points of the feasible region are .A(8/3,0),B(2,1/2),C(0,11/2) 1 minimum cost Rs 160 at the line segment A(8/3,0) & B(2,1/2) 1 2 Marking scheme can be for any alternative method by the evaluator. Solving (1) and (3) point of intersection is A(2,0) 1

Formatting page ...

Top Contributors
to this ResPaper
(answers/comments)

Karthik Shivkumar
(13)

Ram S Kaushik
(10)

Rupal Gupta
(8)

Akhil Samson
(8)

Formatting page ...

Additional Info : KV Sangathan, Kolkata Region MATHEMATICS Pre-Board Examination 2014-15 with Marking Scheme of Class XII PB-III MATHEMATICS Question Paper
Tags : kendriya vidyalaya kv no. 1 salt lake, kendriya vidyalaya sangathan, kolkata region, west bengal, cbse pre boards, prelims preliminary exams, cbse specimen / guess / mock papers / books, cbse india portal, central board for secondary education, answer keys, top schools, cbse question bank, cbse model test papers with answers, solved question papers of cbse last year, previous years papers with solutions, free download pdf online cbse paper, cbse syllabus, pattern, dates notification, application forms, india cbse board sample last 10 years, how to prepare, 2015, 2014.

kv_kendriya_vidyalaya_salt_lake chat

Horizontal lines at:
Guest Horizontal lines at:
AutoRM Data:
Box geometries: