PUC II Year Mathematics Mid-Term Exam 2023-2024 (PDF)

AS PER NEW PATTERN 2023-2024 PUC II YEAR MATHEMATICS COLLECTION OF DIFFERENT DISTRICT MID TERM EXAMINATION 2023-2024 QUESTION PAPERS By : NAME ; ANAND KABBUR MOBILE...

AS PER NEW PATTERN 2023-2024 PUC II YEAR MATHEMATICS COLLECTION OF DIFFERENT DISTRICT MID TERM EXAMINATION 2023-2024 QUESTION PAPERS By : NAME ; ANAND KABBUR MOBILE : 9738237960 KABBUR PUBLICATIONS SAVADATTI 9738237960  - ಅ಩ಪಣೆ - ವಿವಿಧ ಜಿಲ್ೆೆಯ ವಿದ್಺ಾರ್ಥಪಗಳು ಅವರ ಜಿಲ್ೆೆಯಲ್ಲೆ ಩ರೀಕ್ಷೆಗಳು ಮುಗಿದ ತಕ್ಷಣ, ಩ರಶ್ೆೆ ಩ತ್ರರಕೆಗಳನೆ photo ಅಥವ಺ pdf ಮ಺ಡಿ ನನಗೆ ಕಳುಹಿಸುತ್ರದದರು, ಅವೆಲ್ೆವುಗಳನೆ ಒಂದ್ೆೀ ಕಡೆ Collect ಮ಺ಡಿಕೆ ಂಡು ನ಺ನು ನಿಮಗೆ ಈ QUESTION PAPER MATERIAL ನ ತಲ್ುಪಿಸುತ್ರಿದ್ೆದೀನೆ, ಆದಕ಺ರಣ ಈ COLLECTION OF DIFFERENT DISTRICT QUESTION PAPERS MATERIAL ನ ನ಺ನು ವಿದ್಺ಾರ್ಥಪಗಳಿಗೆ ಅಪಿಪಸುತ್ರಿದ್ೆದೀನೆ. ಈ Material ವಿದ್಺ಾರ್ಥಪಗಳಿಗ ಮತುಿ ಉ಩ನ಺ಾಸಕರಗ ಸಹ಺ಯ ಆಗಬಹುದು. ಯ಺ವುದ್಺ದರ ಜಿಲ್ೆೆಯ ಩ರಶ್ೆೆ ಩ತ್ರರಕೆ ಇದರಲ್ಲೆ ಇರಲ್ಲಲ್ೆ ಅಂದ್ೆರ, ನನೆ WhatsApp number 9738237960 ಆ ಜಿಲ್ೆೆಯ ಩ರಶ್ೆೆ ಩ತ್ರರಕೆಗೆ ಕಳುಹಿಸಿ, ಅದನೆ ಈ pdf ಗೆ ಸೆೀರಸೆ ೀಣ. ಯ಺ವುದ್಺ದರ ಅನಿಸಿಕೆಗಳನೆ ಅಥವ಺ ಸಲ್ಹೆಗಳನೆ ನನಗೆ ನಿೀಡಬೆೀಕು ಎನಿಸಿದರೆ ನನೆ phone number 9738237960 ಗೆ ತ್ರಳುಹಿಸಬಹುದು. KA BB U R PU BL I C AT IO N S Yo uT ub e C ha nn el ,C on ta ct9 73 82 37 96 0 KA BB U R PU BL I C AT IO N S Yo uT ub e C ha nn el ,C on ta ct9 73 82 37 96 0 KA BB U R PU BL I C AT IO N S Yo uT ub e C ha nn el ,C on ta ct9 73 82 37 96 0 KA BB U R PU BL I C AT IO N S Yo uT ub e C ha nn el ,C on ta ct9 73 82 37 96 0 KA BB U R PU BL I C AT IO N S Yo uT ub e C ha nn el ,C on ta ct9 73 82 37 96 0 KA BB U R PU BL I C AT IO N S Yo uT ub e C ha nn el ,C on ta ct9 73 82 37 96 0 KA BB U R PU BL I C AT IO N S Yo uT ub e C ha nn el ,C on ta ct9 73 82 37 96 0 KA BB U R PU BL I C AT IO N S Yo uT ub e C ha nn el ,C on ta ct9 73 82 37 96 0  MIDTERM EXAMINATION OCTOBER 2023 II PUC MATHEMATICS TIME; 3HOURS 15 MINUTES MAX. MARKS;80 Instructions; 1) The question paper has five parts namely A,B,C,D and E. answer all the parts 2) Part A has 15 multiple choice questions, 5 fill in the blanks questions. 3) Use the graph sheet for the question on linear 0 programming problem. 96 37 PART -A 82 IAnswer all the multiple choice questions 73 15 x 1 = 15 9 ct 1) Let A={1,2, 3 ).then number of relations containing (1,2) and (1,3) which are ta reflexive and symmetric but not transitive is on a) 1 b) 2 ,C c) 3 d) 4 2) Letf;R’Rbe defined by f(x) = x*.choose correct answer. el nn a) t is one- one on to b) f is many one on to ha c) f is one- one but not on to d) f is neither one- one nor on to C 3) cos(cos)is equal to e ub a) b) 6 c) uT 4) The number of all possible matrices of order 3x3 with each entry 0 or 1 is; Yo a) 27 b) 18 c) 81 d) 512 S N IO 5)The matrix which is both symmetric and skew- symmetric is AT a) Zero matrix b) unit matrix IC c) scalar matrix d) square matrix BL 6)Let Abe anon singular square matrix of order 3x3. Then |adjA| isequal to PU a) |A| b) |A|' c) |A|? d) 3|A| R 1 U 7) The point of discontinuity of the function f(x) = , Vx ER is BB a) x = 1 b) x = 0 c) x = 2 d) None of these KA 8)If y=log(logx), x>1then dy dx is 1 1 1 a) b) c) log(logx) d) None of these xlogx logx 9) The rate of change of the area of of a circle with respect to its radius r at r= 6 cm is a) 10r cm' b) 12r cm' c) 8n cm? d)11n cm? 10) Inlinear programming problem, the objective function is always a) a constant function b) alinear function c) a quadratic function d) a cubic function 11)The value of i.j xk) +j(i xk) +k.(ixj) is a) 0 b) -1 c) 1 d) 3 12)Let åand bbe two unit vectors and Ois the angle between them. thenå + bis a unit vector if a) =:4 b) 8 = c) 0 =:2 d) e = 3 13)The domain of cosx is a) x¬ [1,1] b) xE [-1,1] c) x¬ [0,n] d) (-oo,co ) 1 14) sin'xcos²x equals a) tanX+cotx +C b)tanx-cotx +c c) tanxcotx +c d) tanx-cot2x +c 0 96 15) f d) 37 dx is equal to dx 82 73 a) b) 2x c)x² d) None of these 9 ct I|Fill in the blanks by choosing the appropriate answer given in the bracket ta on (6, 2, 0,1,;) ,C 5x1 = 5 el nn 16) The value of sin[-sin(-)] is ha C 17) If Ais a singular matrix then |A| = - e ub 18) The number of all one-one functions from set A={1,2,3 ) to it self is = uT Yo 19) The critical point of the function f(x) = 2x'-8x +6 is S N 20) If |a: b< = |xb| then the angle between ä and b is equal to IO AT IC PART -B BL PU Answer any six questions 6x2 = 12 R 21) Prove that 2 sin()= tan () U BB 22) Provethat sin(2xV1-*)= 2sin''xsxs KA 23) Find Xand YIf X+Y= and X - Y 24) Find the area of the triangle whose vertices are (1,0), (6,0) and (4,3) using Determinants. 25) Check the continuity of the function f given by f(x) = 2x -1,at x=3 26) If y=x, then find dy dx 27) Prove that the logarithmic function is increasing on (0, o)  cos2x-cos2 a 28) find the dx COSX- cOsa 29) Find the integral of (+-1 dx x-1 30) Find the projection of the vector î+3 +7k on the vector 7-‘ +8 k. 31) Find the area of the parallelogram whose adjacent sides are determined by the vectors å=i-j+3k and b= 2i-7j +k. 0 96 37 82 PART -C 73 9 ct IV Answer any six questions 6x3 = 18 ta on 32) Showthat the relation Rin the set A={1,2,3,4,5 } given by ,C R={(a,b);|a -b| is even) is an equivalence relation. el nn 33) Write tan-1cosx-sinx );0 0 and x,y >0 by graphical method. 6 OR Maximize and minimize ;Z = 3x + 9y subject tothe constraints x+3y < 60, x+ y> 10, x0 by graphical method 52) Find the value of k so that the function f(x) = fkx + 1,if x 5 OR 4 2 3 -2 IfA=i -4 and B=_ 3 then verify that (AB)= B'A KA BB U R PU BL I C AT IO N S Yo uT ub e C ha nn el ,C on ta ct9 73 82 37 96 0 KA BB U R PU BL I C AT IO N S Yo uT ub e C ha nn el ,C on ta ct9 73 82 37 96 0  MIDTERM EXAMINATION OCTOBER 2023 II PUC MATHEMATICS TIME; 3HOURS 15 MINUTES MAX. MARKS;80 Instructions; 1) The question paper has five parts namely A,B,C,D and E. answer all the parts 2) Part A has 15 multiple choice questions, 5 fill in the blanks questions. 3) Use the graph sheet for the question on linear 0 programming problem. 96 37 PART -A 82 IAnswer all the multiple choice questions 73 15 x 1 = 15 9 ct 1) Let A={1,2, 3 ).then number of relations containing (1,2) and (1,3) which are ta reflexive and symmetric but not transitive is on a) 1 b) 2 ,C c) 3 d) 4 2) Letf;R’Rbe defined by f(x) = x*.choose correct answer. el nn a) t is one- one on to b) f is many one on to ha c) f is one- one but not on to d) f is neither one- one nor on to C 3) cos(cos)is equal to e ub a) b) 6 c) uT 4) The number of all possible matrices of order 3x3 with each entry 0 or 1 is; Yo a) 27 b) 18 c) 81 d) 512 S N IO 5)The matrix which is both symmetric and skew- symmetric is AT a) Zero matrix b) unit matrix IC c) scalar matrix d) square matrix BL 6)Let Abe anon singular square matrix of order 3x3. Then |adjA| isequal to PU a) |A| b) |A|' c) |A|? d) 3|A| R 1 U 7) The point of discontinuity of the function f(x) = , Vx ER is BB a) x = 1 b) x = 0 c) x = 2 d) None of these KA 8)If y=log(logx), x>1then dy dx is 1 1 1 a) b) c) log(logx) d) None of these xlogx logx 9) The rate of change of the area of of a circle with respect to its radius r at r= 6 cm is a) 10r cm' b) 12r cm' c) 8n cm? d)11n cm? 10) Inlinear programming problem, the objective function is always a) a constant function b) alinear function c) a quadratic function d) a cubic function 11)The value of i.j xk) +j(i xk) +k.(ixj) is a) 0 b) -1 c) 1 d) 3 12)Let åand bbe two unit vectors and Ois the angle between them. thenå + bis a unit vector if a) =:4 b) 8 = c) 0 =:2 d) e = 3 13)The domain of cosx is a) x¬ [1,1] b) xE [-1,1] c) x¬ [0,n] d) (-oo,co ) 1 14) sin'xcos²x equals a) tanX+cotx +C b)tanx-cotx +c c) tanxcotx +c d) tanx-cot2x +c 0 96 15) f d) 37 dx is equal to dx 82 73 a) b) 2x c)x² d) None of these 9 ct I|Fill in the blanks by choosing the appropriate answer given in the bracket ta on (6, 2, 0,1,;) ,C 5x1 = 5 el nn 16) The value of sin[-sin(-)] is ha C 17) If Ais a singular matrix then |A| = - e ub 18) The number of all one-one functions from set A={1,2,3 ) to it self is = uT Yo 19) The critical point of the function f(x) = 2x'-8x +6 is S N 20) If |a: b< = |xb| then the angle between ä and b is equal to IO AT IC PART -B BL PU Answer any six questions 6x2 = 12 R 21) Prove that 2 sin()= tan () U BB 22) Provethat sin(2xV1-*)= 2sin''xsxs KA 23) Find Xand YIf X+Y= and X - Y 24) Find the area of the triangle whose vertices are (1,0), (6,0) and (4,3) using Determinants. 25) Check the continuity of the function f given by f(x) = 2x -1,at x=3 26) If y=x, then find dy dx 27) Prove that the logarithmic function is increasing on (0, o)  cos2x-cos2 a 28) find the dx COSX- cOsa 29) Find the integral of (+-1 dx x-1 30) Find the projection of the vector î+3 +7k on the vector 7-‘ +8 k. 31) Find the area of the parallelogram whose adjacent sides are determined by the vectors å=i-j+3k and b= 2i-7j +k. 0 96 37 82 PART -C 73 9 ct IV Answer any six questions 6x3 = 18 ta on 32) Showthat the relation Rin the set A={1,2,3,4,5 } given by ,C R={(a,b);|a -b| is even) is an equivalence relation. el nn 33) Write tan-1cosx-sinx );0 0 and x,y >0 by graphical method. 6 OR Maximize and minimize ;Z = 3x + 9y subject tothe constraints x+3y < 60, x+ y> 10, x0 by graphical method 52) Find the value of k so that the function f(x) = fkx + 1,if x 5 OR 4 2 3 -2 IfA=i -4 and B=_ 3 then verify that (AB)= B'A  ~hf'- - ( _fl/ DISTRICT LEVEL II PUC MID-TERM EXAM , OCTOBER : 2023 ®@ Time: 3 Hrs. 15 Mi ns. Sub : MAJHEMA!IG§ /35) Max Maass· so Genera l Instructions: 1.. Th e question Part_ A p aper h. as F1ve parts , namely A, B, C, D and E. Answer all the parts. 2 _ Use th Iias 15 Multiple choice questions, 5 Fill in the blanks question s. 3 e graph sheet for question on Linear programmi ng problem In Part E. PART-A I. Answer ALL the questions: 15 x 1 = 15 1 · Le_ t A = {l, 2, 3} and consider the relation R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 3), (1, 3)} then R IS (A) Reflexive but not symmetric (B) Re fl exive bu t not transitive 0 (C) Symmetric and tra ns itive (D ) Neither symmetric nor transitive 96 2. Let N be the set of Natural numbers and the function f :N --+ N defined by 37 f ( n) = 2n + 3 \:/ n E N then f is 82 (A) Surjective (B) Injective (C) Bijective (D) None of these 73 tan-' x t9 3. The principal value branch of is c ta (A) ( - ; , ; ) (B) [ - ; , ; ] (C) [ - ~,;) (D) ( - ; , ; ] on ,C 1 1 4. Thevalueof[cos- ( -1)-sin - (1)] is el 3n 3,r nn ;r (D) - (C)-- (B) 7r 2 ha (A)- 2 l 2 C A=[~ e ub 5. If then A' is equallo uT Yo I (C) [ 0 o] (A)[~ ~] (B) [: ~] 1 S N IO 6. If 'A' is a matrix of order m x n and B is a matrix such that A' B and BA' are both AT defined, then the order of the matrix Bis (A) m x m (B) n x n nxm mxn C (C) (D) I BL 5 2x =6 -2 PU 7. If then the value of x = 8 X 7 3 R (D) 6 (C) ±6 U (A) 3 {B) ±3 BB 8. Let A be a non-singular matrix of order 3 x 3 and ladj Al= 25 then a poss ible value of IAI KA is (C) 125 (D) 6 (A) 625 {B) 25 9. If A = [; ~] and IA' I= 27 , then the value of a is (A) ±1 (B) ±2 (C). _ (D~ 10 The function f(x ) = [x], where [x] the gr~atest integer function 1s continuous at. (A) 4 (B) -2 (C) 1 (D) 1.5 c dy 2 ·15 _1f x = ct and y = ; , then ;;; at t = (D) 4 11 1 (C) 0 (A)~ (B) -:; P.1.0. 4 Page 1  2 12 ·If J -- Iog ( ---i- I- x ) , then -d1 ·- is equal to I +x dx 3 4x 4 - 4x 3 I (A) -I - 4 (B) (C)-~ (D) - - - x l -x4 1-x 4-x4 13. The point of infle ction of the function y =x 3 , is (A) (~. 8). (B) ( 1, 1) (C)(0, 0) (D) (-3, -27) 14.A cylindrical ta nk of radius 10m is being fi ll ed with wheat at the rate of 314 cubic me ters per hour. The depth of the wheat is increasi ng at the rate of (A) 1 m/h (B) 0.1 m/h (C) 1.1 m/h (D) 0.5 m/lt 15. In a linear programm ing prob lem, the objective fu nction is always r:~: :-::~~':~off (A) a cu bic fu nction (B) a quad ratic functi on (C ) a linear fu nction (D) a co nstant fu nction 5x1=5 0 II. FIii !!! tho blanks !,l( choosing tho oso g;v," !!! tho bmkot 96 37 sin(; -sin-'(-~)J ;, ___ 82 73 16.The value of t9 c ta 17.A square matrix A is singular matrix if I A I is _ _ _ __ on 18. lf I A I= 2, then the value of I AA' I is _ __ ,C el nn 19. For the curve + Jy =1 , the dy at (.!_ )-) is _ __ ha dx 4 4 C e ub 20. The maximum value o_f f if f(x) = sinxin [-;,;]is _ _ _ _ __ uT Yo PART-B 2 = 12 S 111. Answer any SIX of the following questions: 6 X N }i IO 21. Prove that sin- 1 ( - x2 ) = 2 cos- I : x 1. AT for I C BL 1- - tan- 1 - -X, O