JEE Mains Maths TopicWise Questions

8/10/2019 JEE Mains Maths TopicWise Questions

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Complex numbers

01. If zl =1 and z ;t 1. then all the values o f ~lie on1 - z

a) a line not passing through the origin b) lzl = .J2

c) the x-axis d) the y-axis Ans. d

02. A particle P struts from the point z 0 = 1+2i. where i = I t moves first horizontally a way fromorigin by 5 units and then vertically a way from origin by 3 units to reach a point z 1. From z 1 the

pruticle moves fi units in the direction of he vector i + j and then it moves though an angle t in2

anti clockwise direction on a circle with centre at origin. to reach a point z 2. The point z 2 is given by

a) 6 7i

c) 7 6i

Paragraph question

b) -7 6i

d) -6 7i

Let A. B. C be three sets of complex numbers as defined as follows:

A = { z Im z) 1}

B={z : l z -2 - i l=3

C = {z: Re 1-i)z) = J }03. Then number of elements in the set A n B n C is

a) 0 b) 1 c) 2

Ans. d

Ans. b

d)

04. Let z be any point in A n B n C. Then lz + 1 il2 + l z - 5 -il 2 1ie between

a) 25 and 29

c) 35 and 39

b) 30 and 34

d 40 and 44

Ans. c

05. Let z be any point in A n B n C and let w be any point satisfYing lw - 2- il


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2c) - q - 2p) 2q - p )

9

2d) - 2p-q) 2q - p )

9

07. Let a, b, c, p, q be real mun bers. Suppose a . ~are the roots of he equation x 2+ 2px+q=O and a.,. .. are~

the roots of he equation ax 2+2bx+c=O, where fi {-1, 0, 1}. Ans. b

Statement- I : p 2 - q) b 2 - ac) 0

Statement -2 b t pa or c t qa

Progression

08. I fx is the fist te1m of an infinite G.P., whose sum is 10, then Ans. a

a ) O < x < l O b ) - 5 < x < 5 c) - lO


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/


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~ G ~_ : ~ + 32) ~ _ + ~ G is Ans. aa) 310o) 30) 31)) 15 c) 11

Matrices

16. Let a, band c be tlrree distinct real munbers and f x) be a quadratic polynomial satisfYing the equation

[:::: ~ [ ~ ~ ~ 1 ] = [ ~ : :~ ]

4c2

4c 1 f(2) 3c 2 + 3c

Let V be the point oflocal maxima ofy = ftx) and A be the point where y=ftx) meets the x-axis and Bbe a point on y=ftx) such that AB subtends a right angle at V. Find the area of he region lyingbetween the curve and chord AB.

Passage type question

An 125 . 2s. - umt

3

Let 2 1 0 and x ~ X 2 X 3 be tluee column matJ.ices such that[1 0 0]3 2 1

AX, = [HX, =mnd AX, =mnd let X be a 3 X3 matrix whose columns are x,, X,, x,.17. Value of det x) is Ans. c

a) -2 b) -1 c) 3 d) 0

18. Sum ofthe elements o 1 is Ans. b

a) 1 b) 0 c) 4 d)

19. l f [a] = [3 2 OJ X [ l hen a equals Ans. awww.examrace.com


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Determinants

20. The value of A for which the system ofequationsx + y + Az = 4 . x - 2y+ z +4 = 0 . 2x-y-z=2 has nosolution is Ans. b

a) -3 b - 2 c) 0 d) 3

21. Reasoning type Ans. b

Consier the system of equations ax+by =0, ex+ dy = 0, where a. b. c. d E {0. 1} Statement- 1 : Theprobability that the system of equations has a unique solu tion is 3/8

Statemet- 2 : The probability that the system of equations has a solutions is 1.

INEQUALITIES

22. A straight line tluough the vertex P of a ttiangle PQR inteisects the side QR at the pointS and thecircumcircle of he triangle PQR at the point T. I fS is not the centre of he circumcircle, then

Ans. b, d

1 1 2

a) PS + ST < ,JQS xSR

1 1 4c - - --,===

PS ST JQS xSR

1 1 4d - - >

PS ST QR

n n n 1 n23. Let sn = and Tn = >for n=I. 2. 3, .. Then.

k=l n + kn + k k=O n + kn + k

t

a) Sn 3v3

t

c) Tn 3v3

Ans. a, c

24. Let E denotes the complement of an event E. Let E. F. G be pairwise independent events such thatP(G)>O and P(E n F n )=0. Then P(E n F G) equals Ans. c

a) P(E ) + P(F ) b) P(E) -P(F ) c) P(E )-P(F) d) P(E)-P(F )

25. Reasoning type Ans. b

Consider the system of equations

b 0 d 0 h b dE

{0 1}

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Statement- 2 : The probability that the system of equations has a solution is 1.

ELEMENTARY TRIGONOMETRY

26. If 8 and are acute angles such that sin 8 = Yz cos = 1/3, then 8 lies in

a) ]1t/ 3, 1t 2[ b) ]n:/2, 21t/3[

3. ]21t/3, 41t/3[ d) None of these Ans. b

Ans. b

SOLUTION OF TRIANGLES AND APPLICATIONS OF TRIGONOMETRY

28. If a. b. c denote the lengths ofthe sides of a triangle opposite angles A. B. C of a triangle ABC. thenthe correct relation among a. b. c. A. Band Cis given by Ans. b

a) b +c) sin B + C)/2) = a cos A/2)

b) b - c) cos A/2) = a sin B - C)/2)

c) b - cO cos A/2) = 2a sin B - C)/20

d) b - c) sin B- C)/2) = a cos A/2)

29. Let a. b. c be the sides of a triangle. No two of them are euqlal and AE R. If the roots of the equations.x 2+2 a+b+c)x+3.A ab+bc+ca)=O are real. then Ans. a

a) .1.5/3

c) AE 113, 5/3) d) AE 4/3, 5/3)

TRIGONOMETRIC EQUATIONS

30. 0 ~ 8 ~ 2 1 t2sin2

8-5s in8+2>0. then therangeof8 is Ans. a

a) O,n:/6)u 5n:/5,21t) b) 0,51t/6)U 1t,21t) www.examrace.com

31 The munber of solutions of he pair of equations 2 sin cos 29 = 0 and 2 cos 2 3 s ine= 0 in the


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31. The mun ber of solutions. of he pair of equations 2 sin cos 29 0 and 2 cos 3 s ine 0 in theinterval [0 21t] is Ans. c

a 0 b 1 c 2 d 4

INVERSE TRIGONOMETRIC FUNCTIONS

a x b X

c x ~ d .J1 x 2 Ans. c

CARTESIAN SYSTEM OF RECTANGULAR COORDINATES AND

STRAIGHT LINES

33. Reasoning type Ans. c

Lines Lt: y x = 0 and L2: 2x y = 0 intersect the line L3: y 2 = 0 at P and Q respectively. Thebisector of he acute angle between Lt and L2 intersect L3 = a t R.

Statement- 1: The mtio PR: RQ equals 2 J2: J because

Statement- 2: In any tJ.iangle bisector of an angle divides the triangle into two similar triangles.

34. Matrix match type

Column- I Column-

p K = - 9

b One ofL1. L2. L3 is parallel to at least q K =-6/5

one of the other two

rK=5/6

d Lt. L 2 L 3 do not form a ttiangle s K = -9

Ans:

p q r s

a p q r swww.examrace.com

c p q r s


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c p q r s

d p q r s

CIRCLES AND SYSTEM OF CIRCLES

35. Let ABCD be a quadrilateral with area K. with side AB paTallel to the side CD and AB = 2CD. Let ADbe perpendicular to AB and CD. I f a circle is drawn inside the quachilateral ABCD touching all thesides. then its radius is Ans. b

a) 3 b) 2 c) 3/2 d) 1

36. PointE and Fare given by Ans. a

a) c.J3 /2, 3/2 , c.J3,o) b) .J3/2, 112 , c.J3,o)

c) .J312, 3/2), .J312, 112) d) .J312, .J312), .J312, 112)

PAIR OF STRAIGHT LINES

37. Area ofthe ttiangle fonned by the angle bisectors ofthe pair oflines x 2 l + 2 y 1 =0 and the linex+y=3 in square units) is Ans. b

a) 1 b) 2 c) 3 d) 4

38. Let a and b be non-zero real numbers. Then the equation ax 2 + by 2 +c) x 2 - 5 x y + 6 y 2 ) =0represents Ans. b

a) four straight lines. wh en c=O and a. bare of the same sign.

b) two straight lines and a circle. when a = b. and cis of sign opposite to that o f a.

c) Two stJ:aight lines and a hyperbola. when a and bare o f he same sign and cis sign opposite to thato f a

d) a circle and an ellipse. when a and bare of the same sign and cis of sign opposi te to that o f a .

CONIC SECTION PARABOLA, ELLIPSE, HYPERBOLA)

39. Let P x ~ .yJ) and Q x2. y2). Y1


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yp y y pbe one ofthe end points of ts latus rectmn. IfC is the focus ofthe hyperbola nearest to the point A.then area of he triangle ABC is

a) 1-.J213

c) l+ . f i i 3

b) ,J3/2 1

d) 1 J3 2 1

THREE DIMENSIONAL GEOMETRY

41. Reasoning type

Consider the planes 3x-6y-2z=l5 and 2x+y-2z=5

Ans. b

Statement -1: The parametiic equations of he line of ntersection of the given planes are x=3+ 14t.y=1+2t. z=15t.

Statement- 2: The vector 14i + 2j + 15k is parallel to the line of ntersection of the given planes.Ans.d

Linked comprehension type

. . x+1 y+2 z+1Consider the lines L : = = andI 3 1 2

x - 2 y + 2 z - 3L. 1 - 2 - 3

42. The unit vector perpendicular to both L 1 and L 2 is

a) - i+ 7 j +7k b)- i - 7 j + 5 k

J sJ3

c) - i + 7 j + 5 k d)7i - 7 j - k

sJ3 J

43. The shortest- distance between L 1 and L 2 is

a) 0 b ) 1 7 / c) 4115J3

Ans. b

Ans. d

d) 17 ;s.J3

44. The distance ofthe point (1. 1. 1) from the plane passing through the point (-1. -2. -1) and whosenormal perpendicular to both the lines L 1 and L 2 is Ans. c

b) 7 ; J75 c) 13/.J75 d) 2 3 / F s www.examrace.com

. e nmn er or s t nc t rea va ues o r tor w c t e vectors -. : + + , . : + , an


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i + A2 k, are coplanar, is Ans. c

a) zero b) one c) two d) tlrree

46. The edges o f a parallelepiped aTe o f unit lengths and aTe parallel to non-coplanar unit vectors a. b, csuch that a. b =b. c=c. a=1/2. Then the vohune ofthe parallelepiped is

a)1 b) 1 Ans. a

J2 2.J2

c)J3 d) _2 J

FUNCTIONS

47. Let X andY are two nonempty sets. Let f X 7 Y be a function. For A c X and B c Y, define

f A)= {f x): XE A}f- 1 B) = {xE X/f x)E B}. then

a) f C 1 B)) = B

c) C 1 f A)) = A

b) f C 1 B)) c B

d) C 1 f A)) c A

LIMITS AND CONTINUITY

Ans. b

f 1i a- n )nx - t a n x) sin nx h . al b th al48. I m 2 = 0, w ere n IS a nonzero re nmn ers, en a IS equ tox ~ O X

a) 0 b ~n+1

c) n d) n +l in

49. Forx>O, lim sinx) x+ l lxynx) isx ~ O

a) 0

DIFFERENTIATION

d 2x50. - 2 equalsdy

a) ~ ;r

b) 1

Ans. d

Ans. c

c) 1 d) 2

Ans. b

b) - ~ ;r ~ r www.examrace.com

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x - l t51. Let g x) = ; 0 < x < 2. m and n ar e integers, m = = 0, n > 0, and let p be the left hand

log cosm x -1)

detivative oflx -1 Ia tx =1. If limg(x) = p, thenx ~

Ans. c

a) n = 1, m = 1 b)n=1 ,m=-1

c) n = 2 . m = 2 d ) n > 2 , m = n

APPLICATIONS OF DERIVATIVES

52. The tangent to the curve y=ex drawn at the point (c. ec intersects the line joining the points c -1, ee-l)and c+1. ec+l Ans. a

a) on the left ofx = c b) on the ti.ght ofx = c

c) at no point d) at all point

53. Let the ftmction g: -oo,oo) (-1t/ 2, tl 2) be given by g u) = tan- 1 eu)- 1t/ 2, then g is

a) even and is strictly increasing in 0. oo Ans. c

b) odd and is strictly decreasing in -oo, oo

c) odd and is snictly increasing in oo, oo

d) neither even nor odd. but in strictly increasing in -oo, oo

INDEFINITE INTEGRAION

54. Reasoning type Ans. d

Let F x) be an indefinite integral ofsin 2 x.

Statement 1 : The ftmction F x) satisfies F x+1t) = F x) for all real x.

Statement 2 : si n 2 1t+ x) = si n 2 x for all real x.

ex55. Let I= 4 x 2x dx,e + e +1

-X

J = _x e _2x dx . Then for an arbinary constant C, the value of J-Ie + e +1equals Ans. c

1 (e4x_e2x+1]a) - log 4x x + C2 e + e +1

1 e2x +ex + 1]b) - l o g 2 + C2 ex -ex +1

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DEFINITE INTEGRALS

sec2f (t) dt56. lim 2 equals

x ~ 1 t t 4x2-1t2/16

8a) - f (2 )t

b) ~ f 2 )t

57. Multiple correct answer type

Ans. a

4. 4f 2)

Let f x) be a non constant twice differentiable function defined on -oo, oo) such that f x) = f 1-x) and

f (=0 Then Ans. a, b, c, d

a) f(x)vanishes atlesttwice on [0, 1] b) r ~ )=o112 1) f x sin x dx = 0

-112 2

1/2 1

d) jf(t)esinm dt= jf l-t)esinm dt0 112

DIFFERENTIAL EQUATIONS

58. The differentiation equation dy = determines a family of circles withdx y

a) variable radii and a fixed centre 0, 1)

b) variable radii and a fixed centre 0, -1)

c) fixed radius 1 and a variable centres along the x-axis

d) fixed radius 1 and variable centres along they-axis . Ans. c

59. Reasoning type

Let a solution y=y x) ofthe differential equation x x

-1 dy- y.JYCi dx O satisfY y 2)= 2 / J3

Statement 1: y x) = sec sec- 1 x - 1t/ 6)

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JEE Mains Maths TopicWise Questions