CBSE Mathematics 2016 Solved paper for Class XII(10+2) Section - A. Q. 1 For what value of k, the system of linear equations.
|
|
- Austen Walker
- 5 years ago
- Views:
Transcription
1 A ONE INSTITUTE A SYNONYM TO SUCCESS, OFFICE SCO, SECTOR 40 D, CHANDIGARH CBSE Mathematics 06 Solved paper for Class XII(0+) Section - A Q. For what value of k, the system of linear equations. y z y z y kz 4 has aunique solution? Ans. For any System of equations to have unique solution. A 0 0 k (k+)-(k+) + (4-) 0 k+-k-+ 0 -k 0 k 0 Q.. If a 4i ˆj kˆ and b i ˆj kˆ, parallel to the vector a b then find a unit vector Ans. a b 4iˆ Jˆ k ˆ iˆ ˆj k ˆ a b = 6iˆ ˆj kˆ a b = Sol : (6iˆ ˆj kˆ ) 7 A ONE INSTITUTE OF COMPETITIONS, PH , Page
2 A ONE INSTITUTE A SYNONYM TO SUCCESS, OFFICE SCO, SECTOR 40 D, CHANDIGARH Q. Find and if i ˆ ˆj kˆ X iˆ ˆj kˆ 9 0. X iˆ ˆj kˆ Ans. iˆ ˆj 9kˆ iˆ ˆj kˆ 9 0 iˆ 9 ˆj 7 kˆ 9 i.e iˆ 0 ˆj 0kˆ Q. 4. Write the sum of intercepts cut off by the plane rˆ. iˆ ˆj kˆ 5 0 on the three aes. Ans. 4 z 5 4 y z Sum of intercepts cut offby plane on three aes = = 5 cos sin Q. 5 If. A=, find satisfying o< < when A+A T = sin cos I where A T is transpose of A. A ONE INSTITUTE OF COMPETITIONS, PH , Page
3 A ONE INSTITUTE A SYNONYM TO SUCCESS, OFFICE SCO, SECTOR 40 D, CHANDIGARH cos sin Ans. A sin cos Condition given to us, T A A I cos asin a cos d sin a 0 sin a cos a sin a cos a 0 cos cos 4 0 Q. 6 if A is a X matri and A =k A, then write the value of K. Ans. A = k A n Using KA = k A, Whereistheorder of square Matine A A k=7 7 A k A A ONE INSTITUTE OF COMPETITIONS, PH , Page
4 A ONE INSTITUTE A SYNONYM TO SUCCESS, OFFICE SCO, SECTOR 40 D, CHANDIGARH SECTION B Q. 7. Find ( ) 4 d. Ans. f 4 d d 4 4 Comparing coefficients of & constants 4,i.e. ( 4 ) 4 d t dt ( 7) ( ) d, Where t sin c 7 Q. 8 Evaluate: d. 5 Sol. f ( ) 5 d A ONE INSTITUTE OF COMPETITIONS, PH , Page 4
5 A ONE INSTITUTE A SYNONYM TO SUCCESS, OFFICE SCO, SECTOR 40 D, CHANDIGARH f ( ) Using property a a a f d f f d 0 5 o 5 5 d d ] 0 0 = 8. Ans Q. 9. Find the equation of tangents to the curve y= + -4, which are perpendicular to line + 4y +=0. Ans.Let coordinates of point of contact be, y as it lies on y 4 A y 4 B Differentiating A w.r.t. dy d dy d, y Since the tangent at, y is perpendicular to line 4y 0 slope of tangentat, y X Slope of line =- A ONE INSTITUTE OF COMPETITIONS, PH , Page 5
6 A ONE INSTITUTE A SYNONYM TO SUCCESS, OFFICE SCO, SECTOR 40 D, CHANDIGARH X 4 X = Now = y 4 8 y ( ) ( ) Coordinates of point of contact are (,8) & (, 6) dy d,8 () 4 dy d, 6 ( ) 4 Equationof tangent at (,8) y-8= 4 (-) y =4 +6 Equiv of tangent at (-,-6) y+6 =4 (+) y+6=4 +8 y =4+ sin ( ) sin Q. 0 If f()={ a,<0,=0 A ONE INSTITUTE OF COMPETITIONS, PH , Page 6
7 A ONE INSTITUTE A SYNONYM TO SUCCESS, OFFICE SCO, SECTOR 40 D, CHANDIGARH b,>0 is Continuous at =0, then find the values of a and b Since f () is continuous at =0 Ans. lim f lim f f sin ( a ) sin lim ( a ) lim 0 ( a ) 0 a++= a=- b b lim 0 b b lim b 0 b b=4 Q..Solve for X: tan - (-)+ tan - + tan - (+) = tan -. Ans. tan tan tan tan tan tan tan A ONE INSTITUTE OF COMPETITIONS, PH , Page 7
8 A ONE INSTITUTE A SYNONYM TO SUCCESS, OFFICE SCO, SECTOR 40 D, CHANDIGARH OR Prove that tan tan tan ; tan tan tan 4 tan tan tan tan Q. if cos (a+y) = cosy then prove that Hence show that sina d y dy sin ( a y) 0. d d dy dy sin( a y) cos( a y) sin y Sol. d d dy a y. d sin a cos ( ) cos ( a y) dy d sin y sin( a y) A ONE INSTITUTE OF COMPETITIONS, PH , Page 8
9 A ONE INSTITUTE A SYNONYM TO SUCCESS, OFFICE SCO, SECTOR 40 D, CHANDIGARH dy cos ( a y) d cos y sin y sin( a y) cos( a y) dy d a y y a y y a y cos sin cos( ) cos sin( ) a y cos ( a y) dy cos sin( a y y ) d sin a Find dy if y sin d 5 Or Sol. Put = sin sin 4cos Sin- 5 4 sin sin cos 5 5 sin cos d sin sin d cos consider sin d 5 sin sin( d) y d y sin sin dy d 4 Q. A bag X contains 4 white balls and black balls, while another bag y contains white balls and black balls. Two balls are drawn (Without replacement) at random from of the bags A ONE INSTITUTE OF COMPETITIONS, PH , Page 9
10 A ONE INSTITUTE A SYNONYM TO SUCCESS, OFFICE SCO, SECTOR 40 D, CHANDIGARH and were found to be one white and one black. Find the probability that the balls were drawn from bag y. Ans. E =Select Bag X E= Select Bag Y A= Selecting white & black P( E ) P( E) A c X c 8 P( ) E c A c X c P( ) E 5 6 c E P(Balls drawn are from bag Y)= P( ) A A p( E) P ( ) E A A p( E ) P ( ) p( E ) P ( ) E E * / 5 8 ( * * ) = 9 ans. 7 7 Or A and B throw a pair of dice alternately, till one of them gets a total of 0 and wins the game. Find their respective probabilities of winning. If A starts first Sol. E person Agets a 0 F person B gets a0 A ONE INSTITUTE OF COMPETITIONS, PH , Page 0
11 A ONE INSTITUTE A SYNONYM TO SUCCESS, OFFICE SCO, SECTOR 40 D, CHANDIGARH P( E) 6 p( E) P( F) p( F) A wins if he throws0 in st, rd &5 th throws. a. '0' in st throw b. 0 in rd throw = P E F E P( E) P( F) P( E) * * ( ) * c. 0 in 5 th throw = P E F E F E * * * * 4 = * And so on. (Probability of A wins)= ( )... P E E F E E F E F E 4 * * X A ONE INSTITUTE OF COMPETITIONS, PH , Page
12 A ONE INSTITUTE A SYNONYM TO SUCCESS, OFFICE SCO, SECTOR 40 D, CHANDIGARH P (B wins) = = Q. 4 Find the coordinates of the foot of perpendicular drawn from the point A (-, 8, 4) to the line joining the points B (0,-, ) and C (, -,-). Hence find the image of A in line BC. Ans. A.(,8.4) B(0,,) y s Equation of BC C(,,) y s 0 y z 0 y z 4 Coordinate of D (,, 4 ) Direction Ratios of AD, 9, 4 S in ce AD is preperdicular tobc ( ) ( 9) 4( 4 ) Coordinates of D(,, 7) Image of A in line BC= A ONE INSTITUTE OF COMPETITIONS, PH , Page
13 A ONE INSTITUTE A SYNONYM TO SUCCESS, OFFICE SCO, SECTOR 40 D, CHANDIGARH 8 y 4 z y 6 7 z 0 Image ofa in line BC is (-,-6,0) Q5.Show that the four points (0,-,-),(-4,4,4), (4,5,) and (, 9, 4)are coplanar. Find the equation of the plane containing them. SOLUTION The equation of plane passing through (0,--) is a( 0) b( y ) c( z ) 0 i If it passesthrough (-4, 4, 4) and (4, 5, ) than a( 4) b(5) c(5) 0 ii and, a(4) b(6) c() 0 or, a() b() c() 0 Solving ii and iii by cross multiplication, we obtain a b c a b c ( say) 5 7 a 5, b 7 and c Substituting the values of a, b and c in i, we get 5 7 ( y ) ( z ) 0 5 7y z 4 0 A ONE INSTITUTE OF COMPETITIONS, PH , Page
14 A ONE INSTITUTE A SYNONYM TO SUCCESS, OFFICE SCO, SECTOR 40 D, CHANDIGARH Q. 6. A typist charges Rs 45 for typing 0 English and Hindi pages, while charges for typing English and 0 Hindi pages are Rs. 80. Using matrices, find the charges of typing one English and one Hindi page separately. However typist charged only Rs. per from a poor student shyam for 5 Hindi pages. How much less was charged from this poor boy? Which values are reflected in this problem? Sol.Let the charge of typing one englishpage = Rs. the change of typing one hindipage =Rs. y 0+y=45 +0y=80 X B Where y 80 A given system has unique solution given by = A B 0 adj A 0 0 A adja A 9 0 X *45 *80 9 *45 0*80 A ONE INSTITUTE OF COMPETITIONS, PH , Page 4
15 A ONE INSTITUTE A SYNONYM TO SUCCESS, OFFICE SCO, SECTOR 40 D, CHANDIGARH Charge for typing English page = Rs.0 Charge for typing Hindi page = Rs.5 Shyam was charged Rs. less than usual. Q. 7. Find the particular solution of the differential equation. y e /y d+(y- e /y ) dy =0 Given that =0 when y=. Sol.We have, y y ye d ( y e ) dy o d dy e y y e y y Clearly, the given differential equation is a homogeneous differential equation. As the right hand side of as a function of y So, we put =vyand d v y dv to get dy dy v dv ve v y dy e v v dv ve y v v dy e dv y dy e v ye v dv dy v ye dv dy y A ONE INSTITUTE OF COMPETITIONS, PH , Page 5
16 A ONE INSTITUTE A SYNONYM TO SUCCESS, OFFICE SCO, SECTOR 40 D, CHANDIGARH v y e dv f dy v e log y log C v c e log y y c e log y, y c Hence e log given the general solution of the given different y equation. y c e log y =0, y = e 0 c = log =log C y e log y is the particular solution Q. 8. Find the particular solution of differential equation dy y cos given that y = when =0. d sin SOLUTION We have, dy y cos dy cos y d sin d sin sin X This is a linear differential equation with P= cos and Q sin sin X A ONE INSTITUTE OF COMPETITIONS, PH , Page 6
17 A ONE INSTITUTE A SYNONYM TO SUCCESS, OFFICE SCO, SECTOR 40 D, CHANDIGARH I.F.=e cos d sin log(sin ) ( sin ) e e Multiplying both sides of i by I.F. = + sin, we get dy (+ sin ) y cos d Integrating with respect to, we get y( sin ) d C y( sin ) C C y, Which gives the generalsolution. ( sin X ) Put y= and =0, c= y ( sin X ) Q. 9 Find : 5 e d Ans. Put t, d dt t ( t 5) e dt ( t ) t t / e dt ( ) ( ) t t t t e dt e dt ( t ) ( t ) A ONE INSTITUTE OF COMPETITIONS, PH , Page 7
18 A ONE INSTITUTE A SYNONYM TO SUCCESS, OFFICE SCO, SECTOR 40 D, CHANDIGARH t t e e dt et dt dt ( t ) ( t ) ( t ) t e e c c ( t ) ( ) Find : d Or Sol: let A B C ( ) A A B B C C C om paring cofficients of, & cons tan ts = A c A B B c A 5 C 5 B 5 d 5 5 d 5 = log( ) tan log ( ) c A ONE INSTITUTE OF COMPETITIONS, PH , Page 8
19 A ONE INSTITUTE A SYNONYM TO SUCCESS, OFFICE SCO, SECTOR 40 D, CHANDIGARH SECTION-C Q. 0 Prove that F in 0, Solution.we have, 4sin ( ) is an increasing function of cos 4sin f ( ) cos cos cos 4cos sin f '( ) 8cos 4 f '( ) cos 4cos cos f '( ) cos f cos (4 cos ) '( ).0 0,. cos 0,4 cos 0 cos 0 cos for all and Hence, f '( ) is incear sin g on 0,. OR show that the semi- vertical angle of a cone of maimum volume and given slant height is tan or co s. Solution let a be the semi show that the semi- vertical angle of a cone VAB of given slant height t. in AOV, A ONE INSTITUTE OF COMPETITIONS, PH , Page 9
20 A ONE INSTITUTE A SYNONYM TO SUCCESS, OFFICE SCO, SECTOR 40 D, CHANDIGARH VO OA cos a and sin a VA VA VO OA cos a and sin a l l VO l cos a, OA l sin a Let be the volume of the cone, then, ( ) ( ) V OA VO ( sin ) cos V l a l a V l sin a sin a cos a dv The critical points of are given by 0 da Check RD Sharma part XII for further solution. Q. Using properties of determinants, prove that ( ) y z zy z ( z y) y yz y z zy y z y Or b c ba ca ab c a cb abc( a b c) ac bc a b Solution b c ba ca / abc ab c a cb MultiplyingR, R andr bya, b, andc ac bc a b A ONE INSTITUTE OF COMPETITIONS, PH , Page 0
21 A ONE INSTITUTE A SYNONYM TO SUCCESS, OFFICE SCO, SECTOR 40 D, CHANDIGARH Respectively, we get abc a b c ba ca ab c a b cb ac bc a b a b c ba ca abc ab c a b cb Taking a, b and ccommon from c, c andcrespectively abc ac bc a b b c a a b c a b abc( a b c) c c a b b c a a c c a b b c a b AppliyingC C C and C C C we get b c a 0 a 0 c a b b c ( a b) c ( a b) a b b c a 0 a a b c 0 c a b b Taking ( a b c) common From C & C c a b c a b a b b c a 0 a a b c 0 c a b b Appliying R R R R b a ab OR abc( a b c) A ONE INSTITUTE OF COMPETITIONS, PH , Page
22 A ONE INSTITUTE A SYNONYM TO SUCCESS, OFFICE SCO, SECTOR 40 D, CHANDIGARH 0 If A = 0 and A 6A 7A KI 0 Find k. 0 Sol. A A K= Q.. Using the method of integration, find the area of the triangular region whose vertices are A(, -), B(4,) and C(,) Ans.Equation of AB Y ( ) 4 5 Y ( ) 5 Y 7 ( y 7) 5 eqn of BC y 4 4 y 4 A ONE INSTITUTE OF COMPETITIONS, PH , Page
23 A ONE INSTITUTE A SYNONYM TO SUCCESS, OFFICE SCO, SECTOR 40 D, CHANDIGARH 5 5 y y equl of AC Y 4 Y y 6 y BC AC d BC AB d d 5 d d d * * squnits Q.. Let A =R R and * be a binary operation on A defined by (a, b) * (c, d) = (a + c, b + d) A ONE INSTITUTE OF COMPETITIONS, PH , Page
24 A ONE INSTITUTE A SYNONYM TO SUCCESS, OFFICE SCO, SECTOR 40 D, CHANDIGARH Show that * is commutative and associative. Find the identify element for* on A. Also find the inverse of every element (a, b) E A. Eample Let A N 0 N 0 and let '*' be binary operation on A defined by a, b * c, d a c, b d For all( a, b),( c, b) A. Show that (i) * is commutative on A. (ii) * is associative on A. Also find the identity element, if any, in A. SOLUTION (i) Commutativity: Let (a,b), (c,d)a. Then, ( a, b) * ( c, d) ( a c, d b) and ( c, d) * ( a, b) ( c a, d b) a c c a and b d d b for all a, b, c, d N ( a, c) * ( c, d) ( c, d) * ( a, b) for all ( a, b),( c, d) NN A '* ' is Commutative ona. Please Refer RD Sharma page.0 Eample 9 Q. 4. Three numbers are select at random (Without replacement) from first si positive integers. Let X denotes the largest of the three numbers obtained. Find the probability distribution of X. Also. Find the mean and variance of the distribution. Ans. we observe that X on take value, 4, 5 6. A ONE INSTITUTE OF COMPETITIONS, PH , Page 4
25 A ONE INSTITUTE A SYNONYM TO SUCCESS, OFFICE SCO, SECTOR 40 D, CHANDIGARH P (X=)=Probability that largest of three number is. X X * P (=4)= Probability that largest of no. is 4 4 * X X c P( 5) Pr obalitity that l arg est of three no is * * * c P ( 6) c X P(X) To Be solved later.. Q. 5. A retired person wants to invest an amount of Rs. 50,000 his broker recommends investing in two types of bonds. A and B yielding 0% and 9% return respectively on the invested amount. He decides to invest at least Rs. 0, 000 in bond A and at least R.s 0, 000 in bond B. he also wants to invest at least as much in bond A as in bond B solve this linear programming problem graphically to maimize his returns. Q.5. Let his investment on Bond ' A' Rs. Bond ' B ' Rs. Y A ONE INSTITUTE OF COMPETITIONS, PH , Page 5
26 A ONE INSTITUTE A SYNONYM TO SUCCESS, OFFICE SCO, SECTOR 40 D, CHANDIGARH y 50, 000 0, 000 y 0, z y Q. 6. Find the equation of the plane which contains the line of intersection of the planes. r. (i-j+k) -4= and r. (-i +j+k)+5=0 And whose intercept on - ais is equal to that of on Y-ais. y z 4 Sol. 6 y z 5 equation of intersection of planes y z 4 ( y z 5) 0 y z 4 5 y z A ONE INSTITUTE OF COMPETITIONS, PH , Page 6
SOLUTION CLASS-XII / (CBSE)
CBSE XII EXAMINATION-6 SOLUTION--6 CBSE th Board MATHEMATICS SET- CLASS-XII / CBSE Corporate Office : CG Tower, A-6 &, IPIA, Near Cit Mall, Jhalawar Road, Kota Raj.- PCCP Head Office: J-, Jawahar Nagar,
More informationRao IIT Academy/ ISC - Board 2018_Std XII_Mathematics_QP + Solutions JEE MEDICAL-UG BOARDS KVPY NTSE OLYMPIADS. XII - ISC Board
Rao IIT Academy/ ISC - Board 8_Std XII_Mathematics_QP + Solutions JEE MEDICAL-UG BOARDS KVPY NTSE OLYMPIADS XII - ISC Board MATHEMATICS - QP + SOLUTIONS Date: 6..8 Ma. Marks : Question SECTION - A (8 Marks)
More informationCBSE Board Paper Class-XII. Time allowed : 3 hours Maximum Marks : 100
L.K.Gupta (Mathematic Classes) www.poineermathematics.com. MOBILE: 98155771, 461771 CBSE Board Paper -011 Class-XII (SET-1) Time allowed : hours Maimum Marks : 100 General Instructions: (i) All questions
More informationMarking Scheme (Mathematics XII )
Sr. No. Marking Scheme (Mathematics XII 07-8) Answer Section A., (, ) A A: (, ) A A: (,),(,) Mark(s). -5. a iˆ, b ˆj. (or an other correct answer). 6 6 ( ), () ( ) ( ). Hence, is not associative. Section
More informationSAMPLE QUESTION PAPER MATHEMATICS CLASS XII:
SAMPLE QUESTION PAPER MATHEMATICS CLASS XII: 05-6 Question numbers to 6 carry mark each. SAMPLE PAPER II Section A Q. Evaluate: - 3 sin(cos (- )). 5 Q. State the reason for the following Binary Operation
More information1 are perpendicular to each other then, find. Q06. If the lines x 1 z 3 and x 2 y 5 z
Useful for CBSE Board Examination of Math (XII) for 6 For more stuffs on Maths, please visit : www.theopgupta.com Time Allowed : 8 Minutes Max. Marks : SECTION A 3 Q. Evaluate : sin cos 5. Q. State the
More informationEINSTEIN CLASSES. C B S E XIIth Board PRACTICE ASSIGNMENT
EINSTEIN CLASSES P R E S E N T S C B S E XIIth Board PRACTICE ASSIGNMENT MATHEMATICS NOTE THE FOLLOWING POINTS : Einstein Classes is primarily concerned with the preparation of JEE-ADVANCE /JEE-MAIN/BITS/PMT/AIIMS
More informationCBSE Examination Papers
CBSE Eamination Papers (Foreign 0) Time allowed: hours Maimum marks: 00 General Instructions: As given in CBSE Sample Question Paper. Set I SECTION A Question numbers to 0 carry mark each.. Write the principal
More informationCBSE 2018 ANNUAL EXAMINATION DELHI
CBSE 08 ANNUAL EXAMINATION DELHI (Series SGN Code No 65/ : Delhi Region) Ma Marks : 00 Time Allowed : Hours SECTION A Q0 Find the value of tan cot ( ) Sol 5 5 tan cot ( ) tan tan cot cot 6 6 6 0 a Q0 If
More informationSAMPLE QUESTION PAPER MATHEMATICS (041) CLASS XII
SAMPLE QUESTION PAPER MATHEMATICS (01) CLASS XII 017-18 Time allowed: hours Maimum Marks: 100 General Instructions: (i) All questions are compulsory. (ii) This question paper contains 9 questions. (iii)
More informationMATHEMATICS. Time allowed : 3 hours Maximum Marks: 100
MATHEMATICS Time allowed : 3 hours Maimum Marks: 00 General Instructions:. All questions are compulsory.. This question paper contains 9 questions. 3. Questions 4 in Section A are very short-answer type
More informationSAMPLE QUESTION PAPER MATHEMATICS CLASS XII :
SAMPLE QUESTION PAPER MATHEMATICS CLASS XII : 05-6 TYPOLOGY VSA ( M) L A I (4M) L A II (6M) MARKS %WEIGHTAGE Remembering 3, 6, 8, 9, 5 0 0% Understanding, 9, 0 4, 6 % Applications 4 3, 5, 6, 7, 0 9 9%
More informationAll Rights Reserved Wiley India Pvt. Ltd. 1
Question numbers to carry mark each. CBSE MATHEMATICS SECTION A. If R = {(, y) : + y = 8} is a relation of N, write the range of R. R = {(, y)! + y = 8} a relation of N. y = 8 y must be Integer So Can
More information02. If (x, y) is equidistant from (a + b, b a) and (a b, a + b), then (A) x + y = 0 (B) bx ay = 0 (C) ax by = 0 (D) bx + ay = 0 (E) ax + by =
0. π/ sin d 0 sin + cos (A) 0 (B) π (C) 3 π / (D) π / (E) π /4 0. If (, y) is equidistant from (a + b, b a) and (a b, a + b), then (A) + y = 0 (B) b ay = 0 (C) a by = 0 (D) b + ay = 0 (E) a + by = 0 03.
More informationTime allowed : 3 hours Maximum Marks : 100
CBSE XII EXAMINATION-8 Series SGN SET- Roll No. Candiates must write code on the title page of the answer book Please check that this question paper contains printed pages. Code number given on the right
More informationHSC - BOARD MATHEMATICS (40) - SOLUTIONS
Date: 8..5 Q. (A) SECTION - I (i) (d) A () (ii) (c) A A I 6 6 6 A I 64 I I A A 6 (iii) (a) fg cos A cos HSC - BOARD - 5 MATHEMATICS (4) - SOLUTIONS cos cos ch () hy g fy c...(i) Comparing with A Hy By
More informationMATHEMATICS. Time allowed : 3 hours Maximum Marks : 100
MATHEMATICS Time allowed : hours Maimum Marks : General Instructions:. All questions are compulsory.. The question paper consists of 9 questions divided into three sections, A, B and C. Section A comprises
More informationMINIMUM PROGRAMME FOR AISSCE
KENDRIYA VIDYALAYA DANAPUR CANTT MINIMUM PROGRAMME FOR AISSCE 8 SUBJECT : MATHEMATICS (CLASS XII) Prepared By : K. N. P. Singh Vice-Principal K.V. Danapur Cantt () MATRIX. Find X and Y if 7 y & y 7 8 X,,
More informationOperating C 1 C 1 C 2 and C 2 C 2 C 3, we get = 0, as R 1 and R 3 are identical. Ans: 0
Q. Write the value of MATHEMATICS y y z z z y y y z z z y Operating R R + R, we get y z y z z y z y ( y z) z y Operating C C C and C C C, we get 0 0 0 0 ( y z) z y y ( y z)( ) z y y 0 0 0 0 = 0, as R and
More informationC.B.S.E Class XII Delhi & Outside Delhi Sets
SOLVED PAPER With CBSE Marking Scheme C.B.S.E. 8 Class XII Delhi & Outside Delhi Sets Mathematics Time : Hours Ma. Marks : General Instructions : (i) All questions are compulsory. (ii) The question paper
More informationWBJEEM Answer Keys by Aakash Institute, Kolkata Centre MATHEMATICS
WBJEEM - 05 Answer Keys by, Kolkata Centre MATHEMATICS Q.No. μ β γ δ 0 B A A D 0 B A C A 0 B C A * 04 C B B C 05 D D B A 06 A A B C 07 A * C A 08 D C D A 09 C C A * 0 C B D D B C A A D A A B A C A B 4
More informationRao IIT Academy/ 2015/ XII - CBSE - Board Mathematics Code(65 /2 /MT) Set-2 / Solutions XII - CBSE BOARD CODE (65/2/MT) SET - 2
Rao IIT Academ/ 5/ XII - CBSE - Board Mathematics Code(65 / /MT) Set- / Solutions XII - CBSE BOARD CODE (65//MT) SET - Date: 8.3.5 MATHEMATICS - SOLUTIONS. Let a iˆ 3iˆ kˆ b iˆ ˆj and a b 3 5, b a b Projection
More information12 th Class Mathematics Paper
th Class Mathematics Paper Maimum Time: hours Maimum Marks: 00 General Instructions: (i) All questions are compulsory. (ii) The question paper consists of 9 questions divided into four sections A, B, C
More informationMATHEMATICS. r Statement I Statement II p q ~p ~q ~p q q p ~(p ~q) F F T T F F T F T T F T T F T F F T T T F T T F F F T T
MATHEMATICS Directions : Questions number to 5 are Assertion-Reason type questions. Each of these questions contains two statements : Statement- (Assertion) and Statement- (Reason). Each of these questions
More informationIIT-JEE (2012) (Vector+3D+Probability) Solutions
L.K. Gupta (Mathematic Classes) www.pioneermathematics.com MOBILE: 985577, 4677 PAPER -A IIT-JEE (0) (Vector+D+Probability) Solutions TOWARDS IIT- JEE IS NOT A JOURNEY, IT S A BATTLE, ONLY THE TOUGHEST
More informationSeries SC/SP Code No. SP-16. Mathematics. Time Allowed: 3 hours Maximum : 100
Sample Paper (CBSE) Series SC/SP Code No. SP-16 Mathematics Time Allowed: 3 hours Maximum : 100 General Instructions: (i) (ii) (iii) (iv) (v) (vi) There are 26 questions in all. All questions are compulsory.
More informationMarking Scheme. Section A 3. 2 [1] l m n 1 n 1 cos [1] Direction ratios of the given line are 2, 1, 2.
Marking Scheme Section A. B. AB 6 A B 6. sin( ) cos( ) or sin( ). 4. l m n n cos 45 or 6 4 OR Direction ratios of the given line are,,. [/] Hence, direction cosines of the line are:,, or,, [/] Section
More informationJEE MAIN 2013 Mathematics
JEE MAIN 01 Mathematics 1. The circle passing through (1, ) and touching the axis of x at (, 0) also passes through the point (1) (, 5) () (5, ) () (, 5) (4) ( 5, ) The equation of the circle due to point
More informationMATHEMATICS (SET -3) Labour cost Z 300x 400y (to be minimized) The constraints are: SECTION - A 1. f (x) is continuous at x 3 f (3) lim f (x)
8 Class th (SET -) BD PPER -7 M T H E M T I C S () SECTION -. f () is continuous at f () lim f () ( ) 6 k lim ( )( 6) k lim ( ) k. adj I 8 I 8 I 8I 8. P : z 5 5 P : 5 5z z 8 Distance between P & P sin
More informationQUESTION PAPER CODE 65/2/2/F EXPECTED ANSWER/VALUE POINTS
QUESTION PAPER CODE EXPECTED ANSWER/VALUE POINTS SECTION A. P 6 (A A ) P 6 9. (a b c) (a b c) 0 a b c (a b b c c a) 0 a b b c c a. a b sin θ a b cos θ 400 b 4 4. x z 5 or x z 5 mark for dc's of normal
More informationDesign of Question Paper Mathematics - Class XII
Design of Question Paper Mathematics - Class XII Time : 3 hours Max. Marks : 100 Weightage of marks over different dimensions of the question paper shall be as follows : A. Weightage to different topics/content
More informationTransweb Educational Services Pvt. Ltd Tel:
. An aeroplane flying at a constant speed, parallel to the horizontal ground, km above it, is observed at an elevation of 6º from a point on the ground. If, after five seconds, its elevation from the same
More informationSECTION A 1. Find the vector equation of a plane which is at a distance of 5 units from the origin and its normal vector is 2iˆ
Session: 01-17 Subject: Mathematics Class XII Duration: 3 hr. M.M: 100 General Instructions: (i) All questions are compulsor. (ii) This question paper contains 9 questions. (iii) Question 1 in Section
More informationMath Bank - 6. What is the area of the triangle on the Argand diagram formed by the complex number z, -iz, z iz? (a) z 2 (b) 2 z 2
Math Bank - 6 Q.) Suppose A represents the symbol, B represents the symbol 0, C represents the symbol, D represents the symbol 0 and so on. If we divide INDIA by AGRA, then which one of the following is
More informationMathematics. Guess Paper: 2014 Class: XII. Time Allowed: 3Hours Maximum Marks: 70. Section A
Mathematics Guess Paper: 04 Class: XII Time llowed: Hours Maimum Marks: 70 General Instructions:. The question paper consists of 9 questions divided into three sections, B and C.. Section comprises of
More informationGOVERNMENT OF KARNATAKA KARNATAKA STATE PRE-UNIVERSITY EDUCATION EXAMINATION BOARD SCHEME OF VALUATION. Subject : MATHEMATICS Subject Code : 35
GOVERNMENT OF KARNATAKA KARNATAKA STATE PRE-UNIVERSITY EDUCATION EXAMINATION BOARD II YEAR PUC EXAMINATION MARCH APRIL 0 SCHEME OF VALUATION Subject : MATHEMATICS Subject Code : 5 PART A Write the prime
More informationMODEL PAPER - I MATHEMATICS. Time allowed : 3 hours Maximum marks : 100
MODEL PAPER - I MATHEMATICS Time allowed : 3 hours Maimum marks : General Instructions. All questions are compulsy.. The question paper consists of 9 questions divided into three sections A, B and C. Section
More informationCLASS XII MATHEMATICS. Weightage (Marks) (i) Relations and Functions 10. Type of Questions Weightage of Number of Total Marks each question questions
CLASS XII MATHEMATICS Units Weightage (Marks) (i) Relations and Functions 0 (ii) Algebra (Matrices and Determinants) (iii) Calculus 44 (iv) Vector and Three dimensional Geometry 7 (v) Linear Programming
More information3. Total number of functions from the set A to set B is n. 4. Total number of one-one functions from the set A to set B is n Pm
ASSIGNMENT CLASS XII RELATIONS AND FUNCTIONS Important Formulas If A and B are finite sets containing m and n elements, then Total number of relations from the set A to set B is mn Total number of relations
More informationMATHEMATICS (SET -1)
8 Class th (SET ) BD PPER -7 M T H E M T I C S (). adj 8 I 8 I 8I 8 SECTION - I. f () is continuous at f () lim f () ( ) 6 k lim ( )( 6) k lim ( ) k sin cos d tan cot d sin cos ln sec ln sin C.. P : z
More informationBLUE PRINT: CLASS XII MATHS
BLUE PRINT: CLASS XII MATHS CHAPTER S NAME MARK 4 MARKS 6 MARKS TOTAL. RELATIONS AND FUNCTIONS 5. INVERSE TRIGONOMETRIC 5 FUNCTIONS 3. MATRICES 7 4. DETERMINANTS 6 5. 8 DIFFERENTIATION 6 APPLICATION OF
More informationFILL THE ANSWER HERE
HOM ASSIGNMNT # 0 STRAIGHT OBJCTIV TYP. If A, B & C are matrices of order such that A =, B = 9, C =, then (AC) is equal to - (A) 8 6. The length of the sub-tangent to the curve y = (A) 8 0 0 8 ( ) 5 5
More information38. The total number of carboxylic acid groups in the product P is 38. [2] O C HO 3 O C C O C O C O. Total no. of carboxylic group = 2
(6) Vidyalankar : IIT JEE 0 Advanced : Question Paper & Solution 8. The total number of carboxylic acid groups in the product P is 8. [] C.... + H Heat C Total no. of carboxylic group = C C H 9. A tetrapeptide
More informationSample Paper-05 Mathematics Class XII. Time allowed: 3 hours Answers Maximum Marks: 100. Section A. Section B
Sample Paper-05 Mathematics Class XII Time allowed: hours Answers Maimum Marks: 00. No. (, ) R but (, ) R r. a () + ( ) + ( 5) 8 5 l, m, n 8 8 8. [0, ]. A A ( 8) 8 ( 6) A 8 Hence Prove tan cos sin sin
More informationMemory Based Questions & Solutions
PAPER- (B.E./B. TECH.) JEE (Main) 09 COMPUTER BASED TEST (CBT) Memory Based Questions & Solutions Date: 09 April, 09 (SHIFT-) TIME : (9.0 a.m. to.0 p.m) Duration: Hours Ma. Marks: 60 SUBJECT : MATHEMATICS
More informationSOLUTIONS TO CONCEPTS CHAPTER 2
SOLUTIONS TO CONCPTS CHAPTR 1. As shown in the figure, The angle between A and B = 11 = 9 A = and B = 4m Resultant R = A B ABcos = 5 m Let be the angle between R and A 4 sin9 = tan 1 = tan 1 (4/) = 5 4cos9
More informationSAMPLE QUESTION PAPER
SAMPLE QUESTION PAPER CLASS-XII (201-17) MATHEMATICS (01) Time allowed: 3 hours Maximum Marks: 100 General Instructions: (i) All questions are compulsory. (ii) This question paper contains 29 questions.
More informationMATHEMATICS. metres (D) metres (C)
MATHEMATICS. If is the root of the equation + k = 0, then what is the value of k? 9. Two striaght lines y = 0 and 6y 6 = 0 never intersect intersect at a single point intersect at infinite number of points
More informationPART B MATHEMATICS (2) (4) = +
JEE (MAIN)--CMP - PAR B MAHEMAICS. he circle passing through (, ) and touching the axis of x at (, ) also passes through the point () (, ) () (, ) () (, ) (4) (, ) Sol. () (x ) + y + λy = he circle passes
More informationXII HSC - BOARD
Rao IIT Academy/ XII HSC - Board Eam 08 / Mathematics / QP + Solutions JEE MEDICAL-UG BOARDS KVPY NTSE OLYMPIADS Date: 0.0.08 XII HSC - BOARD - 08 MATHEMATICS (40) - SOLUTIONS Q. (A) SECTION - I (i) If
More informationIIT JEE (2012) (Calculus)
L.K. Gupta (Mathematic Classes) www.pioneermathematics.com MOBILE: 985577, 4677 PAPER B IIT JEE (0) (Calculus) TOWARDS IIT JEE IS NOT A JOURNEY, IT S A BATTLE, ONLY THE TOUGHEST WILL SURVIVE TIME: 60 MINS
More informationSET-I SECTION A SECTION B. General Instructions. Time : 3 hours Max. Marks : 100
General Instructions. All questions are compulsor.. This question paper contains 9 questions.. Questions - in Section A are ver short answer tpe questions carring mark each.. Questions 5- in Section B
More informationBasic Mathematics - XII (Mgmt.) SET 1
Basic Mathematics - XII (Mgmt.) SET Grade: XII Subject: Basic Mathematics F.M.:00 Time: hrs. P.M.: 40 Model Candidates are required to give their answers in their own words as far as practicable. The figures
More informationBoard Answer Paper: MARCH 2014
Board Answer Paper: MARCH 04 and Statistics SECTION I Q.. (A) Select and write the correct answer from the given alternatives in each of the following: i. (C) Let l 0, m 3, n be the direction cosines of
More informationANNUAL EXAMINATION - ANSWER KEY II PUC - MATHEMATICS PART - A
. LCM of and 6 8. -cosec ( ) -. π a a A a a. A A A A 8 8 6 5. 6. sin d ANNUAL EXAMINATION - ANSWER KEY -7 + d + + C II PUC - MATHEMATICS PART - A 7. or more vectors are said to be collinear vectors if
More informationSUBJECT : PAPER I MATHEMATICS
Question Booklet Version SUBJECT : PAPER I MATHEMATICS Instruction to Candidates. This question booklet contains 50 Objective Type Questions (Single Best Response Type) in the subject of Mathematics..
More informationSTD. XII ISC - BOARD MATHEMATICS - SOLUTIONS
Rao IIT Academ/XII-ISC-Board -05_Mathematics_SOLUTIONS Date: 6.0.05 Question STD. XII ISC - BOARD MATHEMATICS - SOLUTIONS SECTION A (i) 4 6 M 6 4 9 5 8 M 8 km k k k k M km I 0 5 8 k k 0 0 0 8 k k 0 0 0
More informationCHAPTER 10 VECTORS POINTS TO REMEMBER
For more important questions visit : www4onocom CHAPTER 10 VECTORS POINTS TO REMEMBER A quantity that has magnitude as well as direction is called a vector It is denoted by a directed line segment Two
More information22 (Write this number on your Answer Sheet)
Question Booklet Version (Write this number on your Answer Sheet) Day and Date : Thursday, 0th May, 08 QUESTION BOOKLET (MHT-CET - 08) Subjects : Paper I : Mathematics MH-CET 08 Roll No. Question Booklet
More informationDIRECTORATE OF EDUCATION GOVT. OF NCT OF DELHI
456789045678904567890456789045678904567890456789045678904567890456789045678904567890 456789045678904567890456789045678904567890456789045678904567890456789045678904567890 QUESTION BANK 456789045678904567890456789045678904567890456789045678904567890456789045678904567890
More informationObjective Mathematics
Chapter No - ( Area Bounded by Curves ). Normal at (, ) is given by : y y. f ( ) or f ( ). Area d ()() 7 Square units. Area (8)() 6 dy. ( ) d y c or f ( ) c f () c f ( ) As shown in figure, point P is
More informationADDITIONAL MATHEMATICS
005-CE A MATH HONG KONG CERTIFICATE OF EDUCATION EXAMINATION 005 ADDITIONAL MATHEMATICS :00 pm 5:0 pm (½ hours) This paper must be answered in English 1. Answer ALL questions in Section A and any FOUR
More informationANSWER KEY 1. [A] 2. [C] 3. [B] 4. [B] 5. [C] 6. [A] 7. [B] 8. [C] 9. [A] 10. [A] 11. [D] 12. [A] 13. [D] 14. [C] 15. [B] 16. [C] 17. [D] 18.
ANSWER KEY. [A]. [C]. [B] 4. [B] 5. [C] 6. [A] 7. [B] 8. [C] 9. [A]. [A]. [D]. [A]. [D] 4. [C] 5. [B] 6. [C] 7. [D] 8. [B] 9. [C]. [C]. [D]. [A]. [B] 4. [D] 5. [A] 6. [D] 7. [B] 8. [D] 9. [D]. [B]. [A].
More informationMathematics. Section B. CBSE XII Mathematics 2012 Solution (SET 2) General Instructions:
CBSE XII Mathematics 0 Solution (SET ) General Instructions: Mathematics (i) (ii) (iii) (iv) (v) All questions are compulsor. The question paper consists of 9 questions divided into three Sections A, B
More informationKEAM (ENGINEERING) ANSWER KEY 2017
MTHMTICS KM KY 07 PG: KM (NGINRING) KY 07 PPR II MTHMTICS QUSTIONS & S. p q r p q r + is equal to () q p () q + p (C) q () p () 0 5 0. Let = 0 5 5 () 0 and () 0 = 0. If + 5 C = 0, then C is 0 5 5 5 5 0
More informationMATHEMATICS Paper & Solutions
CBSE-XII-8 EXAMINATION Series SGN MATHEMATICS Paper & Solutions SET- Code : 6/ Time : Hrs. Ma. Marks : General Instruction : (i) All questions are compulsor. (ii) The question paper consists of 9 questions
More informationClass XII_All India_Mathematics_Set-2 SECTION C. Question numbers 23 to 29 carry 6 marks each.
SECTION C Question numbers 3 to 9 carr 6 marks each. 3. Find the equation of the plane passing through the line of intersection of the planes r ˆi 3j ˆ 6 0 r 3i ˆ ˆ j k ˆ 0, whose perpendicular distance
More informationMATHEMATICS SOLUTION
MATHEMATICS SOLUTION MHT-CET 6 (MATHEMATICS). (A) 5 0 55 5 9 6 5 9. (A) If the school bus does not come) (I will not go to school) ( I shall meet my friend) (I shall go out for a movie) ~ p ~ q r s ~ p
More informationBLUE PRINT - III MATHEMATICS - XII. (b) Applications of Derivatives (1) 44 (11) (b) 3 - dimensional geometry - 4 (1) 6 (1) 17 (6)
BLUE PRINT - III MATHEMATICS - XII S.No. Topic VSA SA LA TOTAL 1. (a) Relations and Functions 1 (1) 4 (1) - 10 (4) (b) Inverse trigonometric 1 (1) 4 (1) - Functions. (a) Matrices () - 6 (1) - (b) Determinants
More informationBASIC MATHEMATICS - XII SET - I
BASIC MATHEMATICS - XII Grade: XII Subject: Basic Mathematics F.M.:00 Time: hrs. P.M.: 40 Candidates are required to give their answers in their own words as far as practicable. The figures in the margin
More informationPre-Regional Mathematical Olympiad Solution 2017
Pre-Regional Mathematical Olympiad Solution 07 Time:.5 hours. Maximum Marks: 50 [Each Question carries 5 marks]. How many positive integers less than 000 have the property that the sum of the digits of
More informationSAMPLE QUESTION PAPER MATHEMATICS (041) CLASS XII Time allowed : 3 Hours MAX.MARKS 100 Blue Print. Applicatoin.
Knowledge Understanding Applicatoin HOTS Evaluation Knowledge Understanding Applicatoin HOTS Evaluation Knowledge Understanding Applicatoin HOTS Evaluation Knowledge Understanding Applicatoin HOTS Evaluation
More informationCLASS XII MATHEMATICS. Weightage (Marks) (i) Relations and Functions 10. (ii) Algebra 13. (iii) Calculus 44
CLASS XII MATHEMATICS Units Weightage (Marks) (i) Relations and Functions 0 (ii) Algebra (iii) Calculus 44 (iv) Vector and Three Dimensional Geometry 7 (v) Linear Programming 06 (vi) Probability 0 Total
More informationNATIONAL QUALIFICATIONS
Mathematics Higher Prelim Eamination 04/05 Paper Assessing Units & + Vectors NATIONAL QUALIFICATIONS Time allowed - hour 0 minutes Read carefully Calculators may NOT be used in this paper. Section A -
More informationHALF SYLLABUS TEST. Topics : Ch 01 to Ch 08
Ma Marks : Topics : Ch to Ch 8 HALF SYLLABUS TEST Time : Minutes General instructions : (i) All questions are compulsory (ii) Please check that this question paper contains 9 questions (iii) Questions
More informationJEE(Advanced) 2015 TEST PAPER WITH ANSWER. (HELD ON SUNDAY 24 th MAY, 2015) PART - III : MATHEMATICS
PART - III : JEE(Advanced) 5 Final Eam/Paper-/Code- JEE(Advanced) 5 TEST PAPER WITH ANSWER (HELD ON SUNDAY 4 th MAY, 5) SECTION : (Maimum Marks : ) This section contains EIGHT questions. The answer to
More informationMATHEMATICS Class: XII Mock Paper 1 Solutions
MATHEMATICS Class: XII Mock Paper Solutions Section A. If A { a, b, c } and B {,, } and a function f : A B is given by f { (a, ), ( b, ), ( c, ) } Every element of set A is mapped to the unique element
More informationMockTime.com. (b) (c) (d)
373 NDA Mathematics Practice Set 1. If A, B and C are any three arbitrary events then which one of the following expressions shows that both A and B occur but not C? 2. Which one of the following is an
More informationTEST PAPER 6. dx is equal to Q.1) 1 log 1 + (a) 1. (d) ( ) (c) Q.2) e cos x dx is equal to. (a) e + 1 (b) e 1
TEST PAPER 6 Total Questions: 60 Time allotted 75 minutes Q.) d equal to + e (a) log + + c log + e + c + e + c (b) ( e ) (c) log ( + e ) + c (d) ( ) Q.) π / sin e cos d equal to 0 (a) e + (b) e (c) e +
More informationPAPER ¼isij½- 1. SECTION-1 (Maximum Marks : 24)
JEE (Advanced) (ADVANCED) 06 08 PAPER ¼isij½- -05-06 DATE: 0-05-08 This question paper has three (0) parts: PART-I: Physics, PART-II: Chemistry and PART-III: Mathematics. Each part has total of eighteen
More informationRegn. No. North Delhi : 33-35, Mall Road, G.T.B. Nagar (Opp. Metro Gate No. 3), Delhi-09, Ph: ,
1. Section-A contains 0 Multiple Choice Questions (MCQ). Each question has 4 choices (a), (b), (c) and (d), for its answer, out of which ONLY ONE is correct. From Q.1 to Q.10 carries 1 Marks and Q.11 to
More informationDIFFERENTIATION RULES
3 DIFFERENTIATION RULES DIFFERENTIATION RULES Before starting this section, you might need to review the trigonometric functions. DIFFERENTIATION RULES In particular, it is important to remember that,
More informationCLASS 12 SUBJECT: MATHEMATICS CBSE QUESTION PAPER : 2016 (DELHI PAPER)
CLASS 12 SUBJECT: MATHEMATICS CBSE QUESTION PAPER : 2016 (DELHI PAPER) General Instructions: (i) All questions are compulsory. (ii) Questions 1 6 in Section A carrying 1 mark each (iii) Questions 7 19
More informationCBSE Examination Paper, Foreign-2014
CBSE Eamination Paper, Foreign-4 Time allowed: hours Maimum marks: General Instructions: As per given in CBSE Eamination Paper Delhi-4. SET I SECTION A Question numbers to carr mark each.. Let R = {(a,
More informationCHAPTER 4 VECTORS. Before we go any further, we must talk about vectors. They are such a useful tool for
CHAPTER 4 VECTORS Before we go any further, we must talk about vectors. They are such a useful tool for the things to come. The concept of a vector is deeply rooted in the understanding of physical mechanics
More informationRAJASTHAN P.E.T. MATHS 1997
RAJASTHAN P.E.T. MATHS 1997 1. The value of k for which the points (0,0), (2,0), (0,1) and (0,k) lies on a circle is : (1) 1,2 (2) -1,2 (3) 0,2 (4) 0, 1 2. The area of the triangle formed by the tangent
More informationy mx 25m 25 4 circle. Then the perpendicular distance of tangent from the centre (0, 0) is the radius. Since tangent
Mathematics. The sides AB, BC and CA of ABC have, 4 and 5 interior points respectively on them as shown in the figure. The number of triangles that can be formed using these interior points is () 80 ()
More informationMATHEMATICS PAPER IB COORDINATE GEOMETRY(2D &3D) AND CALCULUS. Note: This question paper consists of three sections A,B and C.
MATHEMATICS PAPER IB COORDINATE GEOMETRY(D &3D) AND CALCULUS. TIME : 3hrs Ma. Marks.75 Note: This question paper consists of three sections A,B and C. SECTION A VERY SHORT ANSWER TYPE QUESTIONS. 0X =0.
More informationPhysics 101 Lecture 2 Vectors Dr. Ali ÖVGÜN
Phsics 101 Lecture 2 Vectors Dr. Ali ÖVGÜN EMU Phsics Department www.aovgun.com Coordinate Sstems qcartesian coordinate sstem qpolar coordinate sstem Januar 21, 2015 qfrom Cartesian to Polar coordinate
More informationPRADEEP SHARMA INSTITUTE OF COMPETITIVE STUDIES PRADEEP SHARMA. PRADEEP SHARMA INSTITUTE OF COMPETITIVE STUDIES Page 1
PRADEEP SHARMA PRADEEP SHARMA INSTITUTE OF COMPETITIVE STUDIES Page Chapter Relation and Functions Mark Questions A relation R in a Set A is called..., if each element of A is related to every element
More information1 / 23
CBSE-XII-017 EXAMINATION CBSE-X-008 EXAMINATION MATHEMATICS Series: RLH/ Paper & Solution Code: 30//1 Time: 3 Hrs. Max. Marks: 80 General Instuctions : (i) All questions are compulsory. (ii) The question
More informationMATHEMATICS. IMPORTANT FORMULAE AND CONCEPTS for. Final Revision CLASS XII CHAPTER WISE CONCEPTS, FORMULAS FOR QUICK REVISION.
MATHEMATICS IMPORTANT FORMULAE AND CONCEPTS for Final Revision CLASS XII 2016 17 CHAPTER WISE CONCEPTS, FORMULAS FOR QUICK REVISION Prepared by M. S. KUMARSWAMY, TGT(MATHS) M. Sc. Gold Medallist (Elect.),
More information63487 [Q. Booklet Number]
WBJEE - 0 (Answers & Hints) 687 [Q. Booklet Number] Regd. Office : Aakash Tower, Plot No., Sector-, Dwarka, New Delhi-0075 Ph. : 0-7656 Fa : 0-767 ANSWERS & HINTS for WBJEE - 0 by & Aakash IIT-JEE MULTIPLE
More information1. Matrices and Determinants
Important Questions 1. Matrices and Determinants Ex.1.1 (2) x 3x y Find the values of x, y, z if 2x + z 3y w = 0 7 3 2a Ex 1.1 (3) 2x 3x y If 2x + z 3y w = 3 2 find x, y, z, w 4 7 Ex 1.1 (13) 3 7 3 2 Find
More informationChapter 3 Vectors 3-1
Chapter 3 Vectors Chapter 3 Vectors... 2 3.1 Vector Analysis... 2 3.1.1 Introduction to Vectors... 2 3.1.2 Properties of Vectors... 2 3.2 Cartesian Coordinate System... 6 3.2.1 Cartesian Coordinates...
More informationDIFFERENTIATION RULES
3 DIFFERENTIATION RULES DIFFERENTIATION RULES Before starting this section, you might need to review the trigonometric functions. DIFFERENTIATION RULES In particular, it is important to remember that,
More informationSCIENCE ENTRANCE ACADEMY PREPARATORY EXAMINATION-3 (II P.U.C) SCHEME 0F EVALUATION Marks:150 Date: duration:4hours MATHEMATICS-35
JNANASUDHA SCIENCE ENTRANCE ACADEMY PREPARATORY EXAMINATION- (II P.U.C) SCHEME F EVALUATION Mrks:5 Dte:5-9-8 durtion:4hours MATHEMATICS-5 Q.NO Answer Description Mrk(s)!6 Zero mtri. + sin 4det A, 4 R 4
More informationSYLLABUS. MATHEMATICS (041) CLASS XII One Paper Three Hours Marks: 100
SYLLABUS MATHEMATICS (041) CLASS XII 2012-13 One Paper Three Hours Marks: 100 Units Marks I. RELATIONS AND FUNCTIONS 10 II. ALGEBRA 13 III. CALCULUS 44 IV. VECTS AND THREE - DIMENSIONAL GEOMETRY 17 V.
More informationCBSE MATHS 2010 YEAR PAPER
CBSE MATHS YEAR PAPER Important Instructions: (i) The question papers consists of three sections A B and C. (ii) All questions are compulsory. (iii) Internal choices have been provided in some questions.
More informationPractice Test Material
Directorate of Education Govt. of NCT of Delhi Practice Test Material 015-016 Subject : Mathematics Class : XII Under the guidance of : Addl. DE (School/Eam) Prepared by : 1. Sanjay Lakra Lecturer RPVV,
More information