VIVEKANANDA VIDYALAYA MATRIC HR SEC SCHOOL FIRST MODEL EXAM (A) 10th Standard Reg.No. : MATHEMATICS - MOD EXAM 1(A)

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Time : 0:30:00 Hrs VIVEKANANDA VIDYALAYA MATRIC HR SEC SCHOOL FIRST MODEL EXAM 018-19(A) 10th Stadard Reg.No. : MATHEMATICS - MOD EXAM 1(A) Total Mark : 100 I.

1 Time : 0:30:00 Hrs VIVEKANANDA VIDYALAYA MATRIC HR SEC SCHOOL FIRST MODEL EXAM (A) 10th Stadard Reg.No. : MATHEMATICS - MOD EXAM 1(A) Total Mark : 100 I. CHOOSE THE BEST ANSWER WITH CORRECT OPTION:- 15 x 1 = 15 1) For ay two sets A ad B, (A B) (B A) (A B) is (a) (b) A B (c) A B (d) A B ) If the third term of a G.P is, the the product of first 5 terms is 3) 4) 5) 5 5 (a) (b) (c) 10 (d) 15 th = 3 5, t If the term of a A.P. is the the sum of the first terms is (a) [1 5] (b) (1 5) (c) (1 + 5) (d) (1 + ) The LCM of a k, a k+1, a k+5 where kϵn is (a) a k+9 (b) a k (c) a k+6 (d) a k+5 The square root of x + y + z xy + yz zx x + y z x y + z x + y + z x y z 6) If a matrix is of order x 3, the the umber i the matrix is (a) 5 (b) 6 (c) (d) 3 7) If the lie segmet joiig the poits A(3, 4) ad B(14,-3) meets the x-axis at P,the the ratio i which P divides the segmet AB is (a) 4 :3 (b) 3 : 4 (c) : 3 (d) 4 :1 8) 9) If the poits (, 5), (4, 6) ad (a, a) are colliear, the the value of a is equal to (a) -8 (b) 4 (c) - 4 (d) 8 If a straight lie itersects the sides AB ad AC of a AE ad is parallel to BC, the DB AB AC DE BC = 10) I I EC PQR, RS is the bisector of \( If PQ = 6 cm, QR = 8 cm, ABC at D ad E respectively RP = 4 cm the PS is equal to (a) cm (b) 4 cm (c) 3 cm (d) 6 cm 11) si 1 θ = 1+cosθ (a) cosθ (b) taθ (c) cotθ (d) cosecθ 1) 9ta θ 9sec θ = (a) 1 (b) 0 (c) 9 (d) -9 13) The curved surface area of a right circular cylider of radius 1 cm ad height 1 cm is equal to

2 (a) πcm (b) π cm (c) 3 π cm 3 (d) cm 14) Stadard deviatio of a collectio of data is. If each value is multiplied by 3, the the stadard deviatio of the ew data is ) 4 The probability that a studet will score cetum i mathematics is. The 5 probability that he will ot score cetum is II. ANSWER ANY 10 OF THE FOLLOWING:- Q.NO 30 IS 10 x = 0 COMPULSORY:- 16) Represet the followig usig Ve diagram U = {5,6,7,8,...13}, A = {5,8,10,11}, ad B = {5,6,7,9,10} 17) Let A = {10, 11, 1, 13, 14}; B = {0, 1,, 3, 5} ad fi : A B, i = 1,, 3 State the type of fuctio for the followig (give reaso) : f ={ (10,1), (11,1), (1,1), (13,1), (14,1) } 18) Fid the sum of the first 30 terms of a A.P. whose th term is ) Fid the zeros of the quadratic polyomial x + 9x + 0, ad verify the basic relatioships betwee the zeros ad the coe iciets. 0) Determie the ature of the roots of the equatio. 3 x + 1 = 0 5 x 3 1) Let A = ad B = Fid A+B if it exists ) Fid the product of the matrices,if exists ( 1) ( 5 4 ) 3) Fid the equatio of the straight lie perpedicular to the straight lie x - y + 3 = 0 ad passig through the poit (1, -). 4) Fid the area of the triagle whose vertices are (1, ), (-3, 4), ad (-5,-6). 5) The strig of kite is 100m log ad it makes a agle of 60 with the horizotal. Fid the height of the kite assumig that these is o slack i the strig. 6) If the curved surface area of a solid hemisphere is 77 sq.cm, the fid its total surface area. 7) A coe, a hemisphere ad cylider have equal bases. If the heights of the coe ad a cylider are equal ad are same as the commo radius, the fid the ratio of their respective volumes. 8) The smallest value of a collectio of data is 1 ad the rage is 59. Fid the largest value of the collectio of data. 9) A two digit umber is formed with the digits 3, 5 ad 7. Fid the probability that the umber so formed is greater tha 57 (repetitio of digits is ot allowed).

3 30) a) I P QR, AB QR. If AB is 3 cm, PB is cm ad PR is 6 cm, the fid the legth of QR. b) Prove the idetity (si 6 θ + co s 6 θ) = 1 3si θ cos θ III. ANSWER ANY 9 OF THE FOLLOWING:- Q.NO 45 IS 9 x 5 = 45 COMPULSORY:- 31) Let A = {4, 6, 8, 10 } ad B = { 3, 4, 5, 6, 7 }. If f : A B is defied by 1 f (x) = x + 1 the represet f by (i) a arrow diagram (ii) a set of ordered pairs ad (iii) a table. 3) Give that U = {a, b, c, d, e, f, g, h}, A = {a, b, f, g} ad B = {a, b, c} verify De Morga's law of complemetatio 33) Fid the sum of the first terms of the followig series How may terms of the arithmetic series , be take 34) cotiuously so that their sum is ) Factorize each of the followig polyomials. x x + 3x ) Solve the followig quadratic equatios by completig the square. 4 x + 4bx ( a b ) = 0. 37) Fid the values of k for which the roots are real ad equal i each of the followig equatios x + k(x ) + 5 = 0 38) If A =, B = ad C = fid (A+B)C ad AC+BC.Is (A+B)C=AC+BC? 39) A triagle has vertices at (6, 7), (, -9) ad (-4, 1). Fid the slopes of its medias. 40) 3 Fid the equatio of the lie whose gradiet is ad which passes through P, where P divides the lie segmet joiig A(-, 6) ad B (3, -4) i the ratio : 3 iterally. 41) I the figure, tagets PA ad PB are draw to a circle with cetre O from a exteral poit P. If CD is a taget to the circle at E ad AP = 15 cm, fid the

4 perimeter of P CD. 4) si( 90 Prove the followig idetities. θ) cos θ + = sec θ 1+si θ 1 cos( 90 θ) 43) Base area ad volume of a solid right circular cylider are sq.cm, ad 69.3 cu.cm respectively. Fid its height ad curved surface area.( Take π = ) 7 44) I a class, 40% of the studets participated i Mathematics-quiz, 30% i Sciecequiz ad 10% i both the quiz programmes. If a studet is selected at radom from the class,fid the probability that the studet participated i Mathematics or Sciece or both quiz programmes. 45) a) A hollow cylidrical pipe is of legth 40 cm. Its iteral ad exteral radii are 4 cm ad 1 cm respectively. It is melted ad cast ito a solid cylider of legth 0 cm. Fid the radius of the ew solid. b) The followig table gives the umber of goals scored by 71 leadig players i Iteratioal Football matches. Fid the stadard deviatio of the data. Class Iterval Frequecy IV. ANSWER THE FOLLOWING:- x 10 = 0 46) a) o Costruct a ΔABC, i which BC = 4.5 cm, A=40 ad the media AM from A to BC is 4.7 cm. Fid the legth of the altitude from A to BC. b) Costruct a cyclic quadrilateral ABCD i which AB = 6 cm, AC = 7 cm, BC = 6 cm, ad = 4. cm. 47) a) Solve the followig equatios graphically (i) x 4 = 0 (ii) x 3x 10 = 0 (iii) (x 5) (x 1) = 0 (iv) (x + 1) (x 3) = 0 BELIEVE IN YOURSELF... YOU CAN DO ANYTHING b) A cyclist travels from a place A to a place B alog the same route at a uiform speed o di eret days. The followig table gives the speed of his travel ad the correspodig time he took to cover the distace. Speed i km / hr x Time i hrs y Draw the speed-time graph ad use it to fid (i) the umber of hours he will take if he travels at a speed of 5 km / hr (ii) the speed with which he should travel if he has to cover the distace i 40 hrs.

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GRADE 12 JUNE 2017 MATHEMATICS P2

GRADE 12 JUNE 2017 MATHEMATICS P2 NATIONAL SENIOR CERTIFICATE GRADE 1 JUNE 017 MATHEMATICS P MARKS: 150 TIME: 3 hours *JMATHE* This questio paper cosists of 14 pages, icludig 1 page iformatio sheet, ad a SPECIAL ANSWER BOOK. MATHEMATICS