JEE (Advanced) 2018 MATHEMATICS QUESTION BANK

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1 JEE (Advanced) 08 MATHEMATICS QUESTION BANK Ans. A [ : a multiple of ] and B [ : a multiple of 5], then A B ( A means complement of A) A B A B A B A B A { : 5 0}, B {, }, C {,5}, then A ( B C) {(, ), (, )} {(, ), (, )} {(, ), (, ), (, )} {(,), (,), (,), (5,5)} Ans. log0. ( ) log0. 09( ), then lies in the interval (, ) (, ) (, ) Ans. log : logy : logz ( y z):( z ) : ( y) then y z y z. y. z y z Ans. y z y z For positive integers n,n the value of the epression n n 5 n 7 ( ) ( ) ( ) ( ) n i i i i where i a real number if and only if n n n n n n n 0, n 0 Ans. 5, then the value of the epression Ans. the sum of first n terms of an A.P. be equal to the sum of its first m terms, ( m n), then the sum of its first ( m n) terms will be 0 n m m n Ans. r 7 p Ans. p, q, r are in A.P. and are positive, the roots of the quadratic equation p q r 0 are all real for p 7 r All p and r a root of the given equation b c) b( c a) c( a b) 0, then the other will be b c) b( c a) b( c a) b c) c( a b) b c) No p and r There are four balls of different colours and four boes of colours same as those of the balls. The number of ways in which the balls, one in each bo, could be placed such that a ball does not go to bo of its own colour ( ) / ( ) 5 / approimately equal to a b for small values of, then ( a, b) = 5, 5 5 5,,,

2 Ans. log ( ) 5 The value of in the epression 0 [ ], if the third term in the epansion 0,00,000 0 Ans equal to!!! e 5 e 9 e 5 e Ans. (log) S, then S = (n)! n0 n ( ) Related: VITEEE, BITSAT and all other Engineering Entrance Eams Questions The circular wire of diameter 0cm cut and placed along the circumference of a circle of diameter metre. The angle subtended by the wire at the centre of the circle equal to, then cosec cot equal to Page of cot cot cot cot The general solution of sin sin sin cos cos cos Ans. n 8 n 8 5 cos 7 sin 0, then the general value of n n Ans. cos cos7 cos cos5 0, then n The equation cos sin n has ( n n ) 8 n cos n n ( ) n 8 No solution Only one solution Two solutions Three solutions Ans. tan tan y tan z, then y z equal to yz 0 yz Ans. tan a b tan a b

3 Ans. cos cos a b a b cos u logtan, then cos h u equal to Ans. a b cos cos cos cos a a cos b a b cos sec cosec tan sin cosh sec, then tan cos sin Page of 5 cot b cos cos a cos b tanh Ans. The medians AD and BE of a triangle with vertices A ( 0, b), B (0, 0) and C (a, 0) are perpendicular to each other, if a b a b Both and The angle between the pair of straight lines y sin y sin (cos ), Ans. The pair of lines represented by a 5y ( a ) y 0 are perpendicular to each other for Two values of a a For one value of a For no value of a Ans. Let PQ and RS be tangents at the etremeties of the diameter PR of a circle of radius r. If PS and RQ intersect at a point X on the circumference of the circle, then r equals Ans. PQ. RS PQ RS PQ. RS PQ RS The angle of intersection of the curves y / and y sin, cot ( / ) cot cot ( ) Ans. The vectors PQ RS cot ( / ) AB i 5j k and AC 5i 5j k are the sides of a triangle ABC. The length of the median through A unit 5 unit 5 unit 0 unit The points D, E, F divide BC, CA and AB of the triangle ABC in the ratio :, : and : 7 respectively and the point K divides AB in the ratio :, then ( AD BE CF) : CK equal to : : 5 5 : Ans. y z the lines and 9 Ans. 9 y k z intersect, then k = 0

4 A square ABCD of diagonal a folded along the diagonal AC so that the planes DAC and BAC are at right angle. The shortest dtance between DC and AB a a / a / 5 ( / ) a Ans. Related: BITSAT Mathematics Sample Paper f : R R and g : R R are defined by f( ) and g ( ) 7, then the values of such that g ( f( )) 8 are,,,, lim( )tan True statement for lim 0 Does not et Lies between 0 and 0 Lies between and Greater then Ans. d d tan Ans. dy ( ) ( y ) a ( y ), then d y y y sec Let / / sin y y dy,then equal to d y y Page of 5 Does not et f : R R and g : R R be continuous functions, then the value of the integral [ f ( ) f( )] [ g( ) g( )] d 0 Ans. The numbers P, Q and R for which the function f( ) Pe Qe R satfies the conditions f(0), log 9 and [ f() R]d are given by f (log) 0 P, Q, R P 5, Q, R

5 P 5, Q, R P 5, Q, R Ans. The order of the differential equation whose general solution given by 5 Ans. dy d y The order and degree of the differential equation are d d,,,, The degree of the differential equation d y dy d y log d d d C y C e e C sin( C ) C 5 Related: VITEEE Maths Practice Paper Ans. ABC an equilateral triangle. E and F are the middle- points of the sides CA and AB respectively. Forces of magnitudes N, PN, N, P N and Q N act at a point and are along the lines BC, BE, CA, CF and AB respectively. If the system in equilibrium, then Ans. P N, Q N P N, Q N P N, Q N P N, Q N Page 5 of 5

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