MODEL TEST PAPER II Time : hours Maximum Marks : 00 Geeral Istructios : (i) (iii) (iv) All questios are compulsory. The questio paper cosists of 9 questios divided ito three Sectios A, B ad C. Sectio A comprises of 0 questios of oe mark each. Sectio B comprises of questios of four marks each ad Sectio C comprises of 7 questios of six marks each. There is o overall choice. However, a iteral choice has bee provided i questios of four marks each ad questios of six marks each. You have to attempt oly oe of the alteratives i all such questios. SECTION A. Let A = {, } ad B = {, }. Fid the umber of relatios from A to B.. Fid the value of si 85.. Write the egatio of the followig statemet : Sum of ad is.. Write the coverse of the statemet : If the sum of digits of a umber is divisible by 9 the the umber is divisible by 9. 5. Write the solutio of. Fid the sum of the series 0 x x 0. ( + ) + ( + ) + ( + ) +... to terms. 7. A die is throw. Fid the probability of gettig a umber less tha or equal to. 8. Five marbles are draw from a bag which cotais 7 blue marbles ad black marbles. What is the probability that all will be blue? 9. Fid the geeral solutio of cos.

0. What is y-itercept of the lie passig through the poit (, ) ad perpedicular to the lie x + y =? SECTION B ta x si x. Evaluate : lim x 0 x lim x 0 cos ax cos bx x. Differetiate cot x with respect to x by the first priciple.. Fid the square root of 5 + i. How may diagoals are there i a polygo with sides? 5. Prove the followig by the priciple of mathematical iductio...,... N Usig priciple of mathematical iductio prove that + 5 is divisible by 9 for all N.. Fid the domai ad rage of f x x 5 7. Fid the value of so that betwee a ad b. a a b b may be the geometric mea Fid the sum of the followig series upto terms :. +. +. +...

8. If p is the legth of perpedicular from the origi to the lie whose itercepts o the axes are a ad b, the show that. p a b 9. Fid the legth of the axes, eccetricity ad legth of the latus-rectum of the hyperbola 5x y = 5. Fid the equatio of the circle passig through the poit of itersectio of the lies x + y = 0 ad x 7y = 0 ad whose cetre is the poit of itersectio of the lies x + y + = 0 ad x y + = 0. 0. Usig sectio formula, prove that the three poits (,, 0), (,, ) ad (, 0, ) are colliear.. O her vacatios Veea visits four cities (A, B, C, D) i a radom order. What is the probability that she visits.. Prove that (i) A before B? A before B ad B before C? cot x cot x cot x cot x cot x cot x =. SECTION C. I a survey of 00 persos it was foud that 8 read magazie A, 0 read magazie B, read magazie C, 8 read magazies A ad B, 0 read magazies A ad C, 5 read magazies B ad C ad read all the three magazies. Fid : (i) How may read oe of the three magazies? How may read magazie C oly?. The rd, th ad 5 th terms i the expasio of (x + a) are respectively 8, 80 ad 50, fid the values of x, a ad. The coefficiets of (r ) th, r th ad (r + ) th terms i the expasio of (x + ) are i the ratio : : 5. Fid ad r.

5. Fid the sum of the followig series upto terms :... 5. Prove that cos 0 cos 0 cos 0 cos 80 = 7. Solve the followig system of iequalities graphically : x + y 0, x + y, x y 0, x 0, y 0. 8. Fid the geeral solutio of cos cos cos If ta x, x, fid x x x si,cos ad ta 9. Fid the mea deviatio about the media for the followig data : Marks 0 0 0 0 0 0 0 0 0 50 50 0 Number of girls 8 0 0 ANSWERS... It is false that sum of ad is.. If a umber is divisible by 9 the the sum of the digits of the umber is divisible by 9. 5. i 7. 8..

9.., z. 0. 9 b a or. ± ( + i).. cosec x. (5, ); (0, ) 7. or 7 0 9. Legth of trasverse axis =, legths of cojugate axis = 5,. (i) Legth of latus rectum 5 x + y + x y = 0.. (i) 0 0. = 7, a =, x = = 7 ad r =. 5. 7. 9 0 9 8 7 5 Y x y = 0 O 5 7 8 9 0 x + y = 0 X e, x + y = 8.,, z or,,. 8 0 0 9..