KET 0 TEST PAPER WITH ANSWER KEY (HELD ON TUESDAY th MAY, 0). If a and b ae the oots of a + b = 0, then a +b is equal to a b () a b a b () a + b Ans:. If the nd and th tems of G.P. ae and esectively, then the sum of st si tems is 89 9 Ans: () 89 () 89. The middle tem of eansion of () 8 9 () 0 Ans: (). If æ0 ö ç + è 0 ø MATHEMATIS 0 a y abc b y = ¹ 0, then the aea of the c y taingle whose vetices ae æ y ö æ y ö æ y ö ç,, ç,, ç, è a a ø è b b ø è c c ø is abc Ans: () () abc 8 () 8 ODEB. The shaded egion shown in fig. is given by the inequation Y (0, ) O (, 0) (9, ) + y ³ 0 y and y () + y ³ 0 y and y ³ + y 0 y and y ³ () + y ³ 0 y ³ and y ³ Ans: ~ [ Ù q] is logically equivalent to. ( ) Ans: Ú ( ~q) () Ù ( ~q) ~[ Ù ( ~q] ) () ~ ( Ú q) (Bonus) Note: In the question in lace of ( ) it should be ( ~). The value of sin Ans: () X æ ö æö ç + sin ç è ø èø () () is equal to /
ODEB 8. If the eccenticity of the hydebola a y = is b and + y = 0 is a focal chod of the hyebola, then the length of tansvese ais is equal to () () Ans: () 9. If a = i + j+ k, b = and the angle between a and b is, then the aea of the tiangle fomed by these two vectos as two sides is () () Ans: 0. Let a = i j+ k if b is a vecto such that a.b= b and a b =, then b = () () Ans:. If diection cosines of a vecto of magnitude ae Ans: 9,, and a > 0, then vecto is i + j+ k () i j+ k i j+ k () i + j+ k (Bonus) Note: In the question in lace of a 9 it should be. Equation of line assing though the oint (,,) and aallel to the line of intesection of the lane y z + = 0 and + y + z = is () () Ans: () y z y z y z y z. Foot of eendicula dawn fom the oigin to the lane y + z = 9 is (,, ) () (,, ) (,, ) () (,, ) Ans: (). If two dice ae thown simultaneously, then the obability that the sum of the numbes which come u on the dice to be moe than is 8 Ans: (). If y f ( ) () () 8 ' = + and f =, then dy at = is d () () 0 Ans: (). If = acos q,y= asin q, then tan q () tan q sec q () Ans: ædy ö + ç èd ø is /
ODEB. Sloe of Nomal to the cuve = ( ) is y at,0 () () Ans: 8. ò Ans: ( + ) / ( ) / ( ) / 9. If f :R R f(f()) 9 9 0 Ans: () 0. Evaluate Ans: d is equal to + () + () ( ) / ( ) / is defined by ( ) cos sin sin cos + + f =, find + () 0 9 () 9 ()0 () (Bonus) Note: In the question Sign of Degee is Missing. A man takes a ste fowad with obability 0. and one ste backwad with obability 0., then the obability that at the end of eleven stes he is one ste away fom the stating oint is (0.8) () (0.) (0.) Ans: () () (0.). ò 0 æsin+ cosö logç d è cos ø log log 8 Ans:. Aea bound by y =, y 8 () log () log = and = 0 is sq. units () sq. units sq. units () sq. units Ans:. Let a= i+ j+ k,b= i j+ kandc= i+ jk, a vecto in the lane a and b whose ojection on c is is i + j k () i + jk i + j k () i j+ k Ans: (). The mean deviation fom the data,0,0,,,0, : (). (). Ans: (). The obability distibution of is 0 find the value of k 0. k k k 0. () 0. 0. () 0. Ans:. If the function g() is defined by 00 99 98 g() = + + ++ + +, then g'(0) = 00 99 98 () 00 00 () Ans: /
ODEB 8. A bo contains ed mables numbes fom though and white mables though.find the obability that a mable dawn at andom is white and odd numbeed. () () Ans: () 9. lim 0 cos is () Ans: 0. () ì 8if f() = í is continuous, find k. îk if > Ans: (). If f() =, Find () () f (.8) f ().8. (). () 0. Ans: c. If = ct and y =, find dy at t =. t d Ans: () ()0. A balloon which always emains sheical is being inflated by uming in 0 cubic centimetes of gas e second. Find the ate at which the adius of the balloon is inceasing when the adius is cms. Ans:. ò cm / sec 90 cm / sec 0 sin d + cos () () cm / sec 9 cm / sec + sin + () sin + sin + () cos + Ans: (). ò æ+ sin ö e ç d è+ cos ø is æ ö e tan ç + è ø æ ö () tan ç + è ø e + () e sin + Ans:. If, w, w ae thee cube oots of unity, then ( w w )( w w ) + is () () Ans: (). Solve fo æö ç = > è+ ø tan tan, 0 () () Ans: () 8. The system of linea equations + y+ z =, + y+ z = 0 and + y+ az = b has no solutions when a= b¹ () a= b¹ 0 b= a = () b= a¹ 0 Ans: () /
0 0 9. The value of tan ( ) tan ( 89 ) / + is 0 sin () 0 ( ) sin( ) 0 sin () 0 ( ) sin( ) Ans: () ( + 0. If ) A B+ = + + +, then cosec æ ö ç + cot sec = è Aø B Ans: ()0 (). The emainde obtained when! +! +! +... +! is divided by is 9 ()8 () Ans:. If a sin + cos b, then a = b = () a = b = a = 0 b = () a = 0 b = Ans:. If Ans: 0 A = é ù 0, then A equal to é0 ù 0 é 0ù 0 () () é 0ù 0 é0 ù 0. The function f ( ) [ ] ODEB =, whee [] denotes geatest intege function in continuous at () (). Ans: (). If y æl ö log, èl+ ø = ç Ans: then dy d () () is equal to. The two cuves y + = 0 and y y = touch each othe () cut at ight angle cut at angle Ans: () () cut at angle. If is eal, then the minimum value of 8 + is () () Ans: 8. d ò cos is equal to + () () 0 Ans: () 9. The ode of diffeential equation of all cicles of given adius a is () () Ans: () 0. The solution of diffeential equation Ans: () + y = () + y = () y = + + y = dy y d + = is
ODEB. If sin + sin y = and cos + cos y =, then tan ( + y) = 8 8 Ans: (). If () () éa ù A = a and A =, then a = ± () ± ± () ± Ans:. If P = and Q =, then dq d = P + () P P () P Ans: (). A line asses though (, ) and eendicula in the line + y = its yintecets is Ans:. Let f : R R f is () () be defined by ( ) oneone () onto f = " Î R, then bijective () f is not defined Ans: (). The solution set of the inequation (, ) () (, ) + < 0 is + (,) È (,) () (,) È(,) Ans:. f ( ) æö = tan ç < < and è ø ( ) g() = +. Find domain of (f + g) Ans: é ö, ë ø é ù, ë û () æ ù ç, è û () (, ) 8. Wite the set builde fom A = {, } A = { : is a eal numbe} () A = { : is a intege} A = { : is a oot of the equation = } () A = { : is a oot of the equation + = 0} Ans: 9. If the oeation Å is defined by a Å b = a + b fo all eal numbes a and b, then ( Å ) Å = 8 () 8 8 () 8 Ans: () 0. If Z = ( + i) ( i+ ) ( 8+ i) 0 () () Ans:, then Z is equal to /