k 100 QUESTIONS 1.

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Maths IIT-JEE ‘Best Approach’ (MC SIR)

100 QUESTIONS

1. The equation ln

)1k(1

k1

)1k(k

= F(k) ·

kn

k1

1k11n ll is true for all k wherever defined.

F(100) has the value equal to

(A) 100 (B) 1011

(C) 5050 (D) 1001

2. If P is the number of natural numbers whose logarithms to the base 10 have the characteristic p and q isthe number of natural numbers logarithms of whose reciprocals to the base 10 havethe characterist ic –q then log10P – log10Q has the value equal to(A) p – q (B) p + q – 1 (C) p – q + 1 (D) p – q – 1

3. If the equation 12 8 4

5 4 y 2

log (log (log x))log (log (log (log x)))

= 0 has a solution for ‘x’ when x < y < b, y a, where ‘b’ is as

large as possible and ‘c’ is as small as possible, then the value of (a + b + c) is equal to(A) 18 (B) 19 (C) 20 (D) 21

4. Number of positive integers x for which f (x) = x3 – 8x2 + 20x – 13, is a prime number, is(A) 1 (B) 2 (C) 3 (D) 4

5. If are roots of the equation x2 – 2mx + m2 – 1 = 0 then the number of integral values of m for which (–2, 4) is(A) 0 (B) 1 (C) 2 (D) 3

6. The range of k for which the inequality k cos2x – k cos x + 1 0 x (– , ) is

(A) k > – 12 (B) k > 4 (C) – 1

2 k 4 (D) 12 k 5

7. The number of pairs of integer (x, y) that satisfy the following two equations :

y)xytan(x)xycos( is

(A) 1 (B) 2 (C) 4 (D) 6

8. The value of the expression sin x sin3x sin9xcos3x cos9x cos27x

equals

(A) 12

(tan 9x – tan x) (B) 12

(tan 9x – tan 3x)

(C) 12

(tan 27x – tan x) (D) 12

(tan 27x – tan 3x)

9. Let – 4 x

4 and –

4 y

4 . Let a be a real number such that

x3 + sinx – 2a = 0 and 4y3 + siny cos y + a = 0. If the value of cos (x + 2y) is k, then find the value of3 + 4k(A) 6 (B) 7 (C) 8 (D) 4


Maths IIT-JEE ‘Best Approach’ (MC SIR)10. cos( – ) = 1 and cos( + ) = 1/e, where , [–, ], numbers of pairs of , which satisfy

both the equations is(A) 0 (B) 1 (C) 2 (D) 4

11. Statement-I : In any ABC, maximum value of r1 + r2 + r3 = 9R2

Statement-II : In any ABC, R 2r(A) Statement-I is true, Statement-II is true and Statement-II is correct explanation for Statement-I(B) Statement-I is true, Statement-II is true and Statement-II is NOT correct explanation for State-ment-I(C) Statement-I is true, Statement-II is false(D) Statement-I is false, Statement-II is true

12. A circle is inscribed in an equilateral triangle whose side length is 2. Then another circle is inscribedexternally tangent to the first circle but inside the triangle as shown, and then another and another. If thisprocess continues indefinitely, the total area of all the circles is

(A) 38 (B) 4

8 (C) 5

8 (D) 6

8

13. If the distances of the sides BC, CA, AB of ABC from its circumcentre are d1, d2, d3 respectively then

the value of 1 2 3

a b cd d d is

(A) 1 2 3

abcd d d (B)

1 2 3

1 abc2 d d d (C)

1 2 3

1 abc3 d d d (D)

1 2 3

1 abc4 d d d

14. Number of 7 digit numbers the sum of whose digits is 61 is :(A) 12 (B) 24 (C) 28 (D) none

15. A question paper on mathematics consists of twelve questions divided into three parts A, B and C, eachcontaining four questions . In how many ways can an examinee answer five questions, selecting atleastone from each part .(A) 624 (B) 208 (C) 2304 (D) none

16. Number of ways in which 7 green bottles and 8 blue bottles can be arranged in a row if exactly 1 pair ofgreen bottles is side by side, is (Assume all bottles to be alike except for the colour).(A) 84 (B) 360 (C) 504 (D) 84

17. The number of triplets x, y, z N, x < y < z such that x + y + z = 100 is(A) 784 (B) 1617 (C) 4851 (D) 4704



18. The largest real value for x such that 38

!kx

)!k4(5 k4

0k

k4

is

(A) 522 (B) 522 (C) 522 (D) 522

19. Let a = 14 4011 and for each n 2, let bn = nC1 + nC2 · a + nC3 · a2 + ........ + nCn · an – 1. The valueof (b2006 – b2005) is equal(A) 28 (B) 29 (C) 210 (D) 211

20. Let 'X' denotes the value of the product(1 + a + a2 + a3 + ....... )(1 + b + b2 + b3 + ..... )

where 'a' and 'b' are the roots of the quadratic equation 11x2 – 4x – 2 = 0and 'Y' denotes the numerical value of the infinite series

.......5log2log5log2log5log2log5log2log

3210 4b

3b

4b

2b

4b

1b

4b

0b

where b = 2000 then the value of (XY) equals

(A) 51

(B) 613

(C) 1511

(D) 3522

21. The sum of the infinite series .....631

451

301

181

91

is

(A) 31

(B) 41

(C) 51

(D) 32

22. Let a (0, 1] satisfies the equation a2008 – 2a + 1 = 0 and S = 1 + a + a2 + .... + a2007. Sum of allpossible value(s) of S, is(A) 2010 (B) 2009 (C) 2008 (D) 2

23. The value of n 1n

n 1

n( 1)5

equals

(A) 512

(B) 524

(C) 536

(D) 516

24. The sum of the series !3!2!13

+ !4!3!24

+ !5!4!35

+........ + )!2008()!2007()!2006(2008

is equal to

(A) )!2008(·22)!2008(

(B) )!2008(·21)!2008(

(C) )!2008(·22)!2008(

(D) )!2008(·23)!2008(

25. Value of S = 2017 + 1 1 1 12016 2015 ...... 2 14 4 4 4

is :

(A) 20161 12016 13 4

(B) 2017

1 12017 13 4

(C) 20171 12017 13 4

(D) 20174 4 12017 13 9 4


Maths IIT-JEE ‘Best Approach’ (MC SIR)26. Statement-1: Let u, v, w satisfy the equations uvw = – 6, uv + vw + wu = – 5, u + v + w = 2

where u > v > w, then the set of value(s) of 'a' for which the points P(u, – w) andQ(v, a2) lies on the same side of the line 4x – y + 5 = 0 are given by (– 3, 3).

Statement-2: If two points M(x1, y1) and N(x2, y2) lies on the same side of the line ax + by + c = 0,then (ax1 + by1 + c) (ax2 + by2 + c) > 0.

(A) Statement-1 is true, statement-2 is true and statement-2 is correct explanation for statement-1.(B) Statement-1 is true, statement-2 is true and statement-2 is NOT the correct explanation for statement-1.(C) Statement-1 is true, statement-2 is false.(D) Statement-1 is false, statement-2 is true.

27. If A (1, p2) ; B (0, 1) and C (p, 0) are the coordinates of three points then the value of p for which thearea of the triangle ABC is minimum, is

(A) 3

1 (B) – 3

1(C)

31

or – 3

1(D) none

28. Consider the lines, L1: 14y

3x

; L2 = 13y

4x

; L3 : 24y

3x

and L4 : 23y

4x

Statement-1 : The quadrilateral formed by these four lines is a rhombus.Statement-2 : If diagonals of a quadrilateral formed by any four lines are unequal and intersect at right

angle then it is a rhombus.(A) Statement-1 is true, statement-2 is true and statement-2 is correct explanation for statement-1.(B) Statement-1 is true, statement-2 is true and statement-2 is NOT the correct explanation for statement-1.(C) Statement-1 is true, statement-2 is false.(D) Statement-1 is false, statement-2 is true.

29. Given a ABC whose vertices are A(x1, y1) ; B(x2, y2) ; C(x3, y3).Let there exists a point P(a, b) such that 6a = 2x1 + x2 + 3x3 ; 6b = 2y1 + y2 + 3y3Statement-1 : Area of triangle PBC must be less than the area of ABCStatement-2 : P lies inside the triangle ABC(A) Statement-1 is true, statement-2 is true and statement-2 is correct explanation for statement-1.(B) Statement-1 is true, statement-2 is true and statement-2 is NOT the correct explanation for statement-1.(C) Statement-1 is true, statement-2 is false.(D) Statement-1 is false, statement-2 is true.

30. As shown in the figure, three circles which have the same radius r, havecentres at (0, 0) ; (1, 1) and (2, 1). If they have a common tangent line,as shown then, their radius 'r' is

(A) 2

15 (B) 10

5

(C) 21

(D) 2

13

rr

r

C1

C2

CO x

y

1 2

1

31. Real number x, y satisfies x2 + y2 = 1. If the maximum and minimum value of the expression z = 4 y7 x

are

M and m respectively, then the value (2M + 6m).(A) 1 (B) 2 (C) 3 (D) 4


Maths IIT-JEE ‘Best Approach’ (MC SIR)32. The value of 'c' for which the set, {(x, y)x2 + y2 + 2x 1} {(x, y)x y + c 0} contains only

one point in common is :(A) (, 1] [3, ) (B) {1, 3}(C) {3} (D) { 1}

33. If the coordinates of two consecutive vertices of a regular hexagon are (2, 0) and (4, 2 3 ), then theequation of the circumcircle of the hexagon which contains the origin is(A) x2 + y2 – 4 3 y – 4 = 0 (B) x2 + y2 + 4 3 y – 4 = 0

(C) x2 + y2 + 4 3 x – 4 = 0 (D) x2 + y2 – 4 3 x – 4 = 0

34. If g(x) = 71

74 xx4cos21x2cos2xcos4

, then find the value of )100(gg .

(A) 99 (B) 100 (C) 101 (D) 102

35. Given f (x) = x1

8x1

8

and g (x) = )x(cosf

4)x(sinf

4 then g(x) is

(A) periodic with period /2 (B) periodic with period (C) periodic with period 2 (D) aperiodic

36. The graph of the function y = g (x) is shown.

The number of solutions of the equation 211)x(g , is

(A) 4 (B) 5(C) 6 (D) 8

37. The total number of function f : {1, 2, 3} {1, 2, 3, 4, 5} such that f(i) f (j) i < j is equal to(A) 30 (B) 35 (C) 44 (D) 56

38. The roots of the equation x3 – 10x + 11 = 0 are u, v, and w. The value of (tan–1u + tan–1v + tan–1w)equals

(A) – 1 (B) 1tan 1 (C) 1 (D) 1tan 1

39. The value of 12

r 1

1tanr 5r 7

is equal to :

(A) tan–1 3 (B) 4

(C) 1 1sin10

(D) cot–1 2

40.xsin)ee(

1x)1n(nxLim x

n1n

1x

where n = 100 is equal to

(A) e

5050

(B) e

100

(C) – e

5050

(D) – e

4950



41. 20x x

1.........)xcos1()xcos1()xcos1(Lim

equals

(A) 0 (B) 21

(C) 1 (D) 2

42. If x is a real number in [0, 1] then the value of Limitm

Limitn [1 + cos2m (n ! x)] is given by

(A) 1 or 2 according as x is rational or irrational(B) 2 or 1 according as x is rational or irrational(C) 1 for all x(D) 2 for all x

43. If

1999

xxn

n 1lim ,2000n n 1

then the value of x is equal to :

(A) 1998 (B) 1999 (C) 2000 (D) 2001

44. If both f (x) & g(x) are differentiable functions at x = x0, then the function defined as,h(x) = Maximum {f(x), g(x)}(A) is always differentiable at x = x0(B) is never differentiable at x = x0(C) is differentiable at x = x0 when f(x0) g(x0)(D) cannot be differentiable at x = x0 if f(x0) = g(x0).

45. Let f (x) = x3 – x2 – 3x – 1 and h (x) = )x(g)x(f

where h is a rational function such that

(a) it is continuous every where except when x = – 1, (b)

)x(hLimx

and (c)21)x(hLim

1x

.

Find )x(g2)x(f)x(h3Lim0x

(A) – 394

(B) 394

(C) 439

(D) – 439

46. If x = t3 + t + 5 & y = sin t then d ydx

2

2 =

(A)

3 1 6

3 1

2

2 3

t t t t

t

sin cos(B)

3 1 6

3 1

2

2 2

t t t t

t

sin cos

(C)

3 1 6

3 1

2

2 2

t t t t

t

sin cos(D) cos t

t3 12



47. Let u(x) and v(x) are differentiable functions such that )x(v)x(u

= 7. If )x('v)x('u

= p and '

)x(v)x(u

= q, then

qpqp

has the value equal to

(A) 1 (B) 0 (C) 7 (D) – 7

48. Limitx 0

1x x

a arc xa

b arc xb

tan tan

has the value equal to

(A)a b

3(B) 0 (C)

( )a ba b

2 2

2 26

(D) a ba b

2 2

2 23

49. Let C be the curve y = x3 (where x takes all real values). The tangent at A meets the curve again at B. Ifthe gradient at B is K times the gradient at A then K is equal to

(A) 4 (B) 2 (C) – 2 (D) 41

50. The x-intercept of the tangent at any arbitrary point of the curve 22 yb

xa = 1 is proportional to:

(A) square of the abscissa of the point of tangency(B) square root of the abscissa of the point of tangency(C) cube of the abscissa of the point of tangency(D) cube root of the abscissa of the point of tangency .

51. A variable ABC in the xy plane has its orthocentre at vertex 'B' , a fixed vertex 'A' at the origin and the

third vertex 'C' restricted to lie on the parabola y = 1 +36x7 2

. The point B starts at the point (0, 1) at time

t = 0 and moves upward along the y axis at a constant velocity of 2 cm/sec. How fast is the area of the

triangle increasing when t =27

sec.

(A) 557

(B) 657

(C) 667

(D) 367

52. Let f (x) = 1x71x31x21x3x35x3

111

852

32

. Then the equation f (x) = 0 has

(A) no real root (B) atmost one real root(C) atleast 2 real roots(D) exactly one real root in (0,1) and no other real root.

53. The set of values of p for which the equation ln x px = 0 possess three distinct roots is

(A)

e1,0 (B) (0, 1) (C) (1,e) (D) (0,e)



54. Let F (x) = xcos

xsin

)tarcsin1( dte2

on

2,0 then

(A) F'' (c) = 0 for all c

2,0 (B) F''(c) = 0 for some c

2,0

(C) F' (c) = 0 for some c

2,0 (D) F (c) 0 for all c

2,0

55. Which one of the following can best represent the graph of the function f (x) = 3x4 – 4x3?

(A) (B) (C) (D)

56. The graph of y = f ''(x) for a function f is shown. Number ofpoints of inflection for y = f (x) is(A) 4 (B) 3(C) 2 (D) 1

57. A rectangle has one side on the positive y-axis and one side on the positive x - axis. The upper right hand

vertex of the rectangle lies on the curve y = nxx2 . The maximum area of the rectangle is

(A) e–1 (B) e – ½ (C) 1 (D) e½

58. If x,y,z R , x + y + z = 4 and x2 + y2 + z2 = 6, then the maximum possible value of z is :

(A) 1 (B) 2 (C) 5 (D) 23

59. Let A, B, C, D be (not necessarily square) real matrices such thatAT = BCD; BT = CDA; CT = DAB and DT = ABC

for the matrix S = ABCD, consider the two statements.I S3 = SII S2 = S4

(A) II is true but not I (B) I is true but not II(C) both I and II are true (D) both I and II are false.

60. Matrix A satisfies A2 = 2A – I where I is the identity matrix then for n 2, An is equal to (n N)(A) nA – I (B) 2n – 1A – (n – 1)I (C) nA – (n – 1)I (D) 2n – 1A – I

61. First row of a matrix A is [1 3 2]. If adj 2 4

A 1 2 13 5 2

then a possible value of det(A) is :

(A) 1 (B) 2 (C) –1 (D) –2



62. Let A =

222

222

222

yxz1)xyz(2)yzx(2)xyz(2xzy1)zxy(2)yzx(2)zxy(2zyx1

then det. A is equal to

(A) (1 + xy + yz + zx)3 (B) (1 + x2 + y2 + z2)3

(C) (xy + yz + zx)3 (D) (1 + x3 + y3 + z3)2

63. If sin q cos q and x, y, z satisfy the equationsx cos p – y sin p + z = cos q + 1x sin p + y cos p + z = 1 – sin qx cos(p + q) – y sin (p + q) + z = 2

then find the value of x2 + y2 + z2.(A) 1 (B) 2 (C) 3 (D) 4

64. dxxsin·)x101sin( 99 equals

(A) 100

)x)(sinx100sin( 100 + C (B)

100)x)(sinx100cos( 100

+ C

(C) 100

)x)(cosx100cos( 100 + C (D)

101)x)(sinx100sin( 101

+ C

65. dxx1x1cosx1sec

)x1(e

2

21

221

2

x1tan

(x > 0)

(A) Cxtan.e 1x1tan (B) C2

xtan.e21x1tan

(C) Cx1sec.e2

21x1tan

(D) Cx1eccos.e2

21x1tan

66. The value of the definite integral

02a )x1)(x1(

dx (a > 0) is

(A) 4

(B) 2

(C) (D) some function of a.

67. Let Cn =

n1

1n1

1

1dx

)nx(sin)nx(tan then n

2n

C·nLim

equals

(A) 1 (B) 0 (C) – 1 (D) 21



68. If

0

14

2

adx

x1tan·

x11axx

a1Lim is equal to

k

2 where k N equals

(A) 4 (B) 8 (C) 16 (D) 32

69. The area of the region defined by x2 + y2 2 and y sin x is

(A) 3

2 (B)

3

3 (C)

2

2 (D)

2

3

70. A function y = f(x) satisfies the condition f '(x) sin x + f(x) cos x = 1, f(x) being bounded when x 0. If

I = /2

0

f(x) dx then

(A) 2 < I <

2

4 (B) 4

< I < 2

2 (C) 1 < I < 2

(D) 0 < I < 1

71. The tangent at any point P on the curve y = f(x) meets the x and y axes at L and M respectively and thenormal at P meets these axes at Q and R respectively. If the centre of the circle through O, Q, P and M,where O is the origin lies on the line whose equation is y = 2x then the differentiable equation of the curveis

(A) dy x 2ydx y 2x

(B)

dy y 2xdx x 2y

(C)

dy 2x ydx 2x y

(D)

dy x ydx x y

72. If P has (n + 1) and Q has n fair coins, which they flip, then probability that P gets more heads than Q is

(A) 13 (B) 1

2 (C) 14 (D) 2

3

73. In a binomial distribution B 1n,P4

if the probability of at least one success is greater than or equal to

910 , then n is greater than

(A) 10 10

1log 4 log 3 (B)

10 10

1log 4 log 3 (C)

10 10

9log 4 log 3 (D)

10 10

4log 4 log 3

74. A natural number x is randomly selected from the set of first 100 natural numbers. The probability that it

satisfies the inequality. x + 100

x > 50 is

(A) 11/19 (B) 11/13 (C) 11/20 (D) 11/10

75. On a normal standard die one of the 21 dots from any one of the six faces is removed at random witheach dot equally likely to be chosen. The die is then rolled. The probability that the top face has an oddnumber of dots is

(A) 115

(B) 125

(C) 2111

(D) 116


Maths IIT-JEE ‘Best Approach’ (MC SIR)76. The number 'a' is randomly selected from the set {0, 1, 2, 3, ...... 98, 99}. The number 'b' is selected

from the same set. Probability that the number 3a + 7b has a digit equal to 8 at the units place, is

(A) 161

(B) 162

(C) 164

(D) 163

77. ABCD and EFGC are squares and the curve y = xk passes through the origin D and the points B and

F. The ratio BCFG

is

(A) 2

15 (B)

213

(C) 4

15 (D)

413

78. Let L1 : x + y = 0 and L2 : x – y = 0 are tangent to a parabola whose focus is S(1, 2).

If the length of latus-rectum of the parabola can be expressed as n

m (where m and n are coprime)

then the value of (m + n) is.(A) 10 (B) 11 (C) 12 (D) 13

79.71MB If P is any point on ellipse with foci S1 & S2 and eccentricity is 21

such that

PS1S2 = PS2S1 = , S1PS2 = , then 2cot , 2

cot , 2cot are in

(A) A.P. (B) G.P. (C) H.P. (D) NOT A.P., G.P. & H.P.

80. In ABC, B is (3, 0) and C is (9, 0). The vertex A moves in such a way that cot B2

. cot C2

= 4 is satisfied,

then the locus of A is the conic whose eccentricity is :

(A) 25

(B) 35

(C) 45

(D) 54

81. Latus rectum of the conic satisfying the differential equation, x dy + y dx = 0 and passing through thepoint (2, 8) is :

(A) 4 2 (B) 8 (C) 8 2 (D) 16

82. The foci of a hyperbola coincide with the foci of the ellipse 19y

25x 22

. Then the equation of the

hyperbola with eccentricity 2 is

(A) 14y

12x 22

(B) 112y

4x 22

(C) 3x2 – y2 + 12 = 0 (D) 9x2 – 25y2 – 225 = 0



83. For some non zero vector V , if the sum of V

and the vector obtained from V by rotating it by an angle

2 equals to the vector obtained from V by rotating it by then the value of , is

(A) 2n ± 3

(B) n ± 3

(C) 2n ± 3

2(D) n ±

32

where n is an integer.

84. Consider ABC with A )a( ; B ( )b & C ( )c . If b a c. ( ) = b b a c. . ; b a = 3;

c b = 4 then the angle between the medians AM

& BD

is

(A) cos1 15 13

(B) cos1 1

13 5

(C) cos1 15 13

(D) cos1 1

13 5

85. If the vectors a , b , c are non-coplanar and l, m, n are distinct scalars, then

a m b n c b m c n a c m a n b

= 0 implies :

(A) l m + m n + n l = 0 (B) l + m + n = 0(C) l 2 + m

2 + n 2 = 0 (D) l 3 + m

3 + n 3 = 0

86. If b

and c are two non-collinear vectors such that

a. b c 4 and 2a b c x 2x 6 b sin y c

then the point (x,y) always lies on

(A) y = –x (B) y = 1 (C) y2

(D) x = 1

87. If H represent the harmonic mean between the abscissae, and K that between the ordinates of thepoints, in which a circle x2 + y2 = c2 is cut by a chord lx + my = , where l and m are the directioncosines of the unit vector in the xy plane, then lH + mK has the value equal to

(A)

2c2 (B)

2c2

(C)

2c2 (D)

2c2

2

88. Let a, b and c be three non-coplanar unit vectors such that the angle between every pair of them is

3 .

If a b b c pa qb rc , where p, q and r are scalar, then the value of

2 2 2

2

p 2q rq

is

(A) 2 (B) 4 (C) 6 (D) 8

89. PQR is a triangular park with PQ = PR = 200 m. A T. V. tower stands at the mid-point of QR. If theangles of elevation of the top of the tower at P, Q and R are respectively 45º, 30º and 30º, then the heightof the tower (in m) is(A) 50 2 (B) 100 (C) 50 (D) 100 3



90. The upper 34

th portion of a vertical pole subtends an angle tan–1 3

5 at a point in the horizontal

plane through it's foot and at a distance 40 m from the foot. A possible height of the vertical poleis :(A) 60 m (B) 20 m (C) 40 m (D) 80 m

91. The mode of the following frequency distribution is

i

Class 1 10 11 20 21 30 31 40 41 50f 5 7 8 6 4

(A) 24 (B) 23.83 (C) 27.16 (D) None of these

92. Suppose a population A has 100 observations 101, 102, ..... 200 and other polulation B has100 observations 151, 152, ..... 250. If VA and VB represent the variance of two population respectively

then A

B

VV

is-

(A) 9/4 (B) 4/9 (C) 2/3 (D) 1

93. If the standard deviation of the numbers 2, 3, a and 11 is 3.5, then which of the following is true ?(A) 3a2 – 23 a + 44 = 0 (B) 3a2 – 26a + 55 = 0(C) 3a2 – 32a + 84 = 0 (D) 3a2 – 34a + 91 = 0

94. Statement 1 : ~ (p ~ q) is equivalent to p qStatement 2 : ~ (p ~ q) is a tautology(A) Statement–1 is true, Statement–2 is true, Statement–2 is a correct explanation forstatement–1(B) Statement–1 is true, Statement–2 is true; Statement–2 is not a correct explanation for statement–1.(C) Statement–1 is true, statement–2 is false.(D) Statement–1 is false, Statement–2 is true

95. Consider the following statementsP : Suman is brilliantQ : Suman is richR : Suman is honestThe negation of the statement “Suman is brilliant and dishonest if and only if Suman is rich” can beexpressed as

(A) ~ Q P ~ R^ (B) ~ Q ~ P R^

(C) ~ P ~ R Q^ (D) ~ P Q ~ R^

96. If , , are the roots of x3 – 3x2 + 3x + 7 = 0 and w is a complex cube root of unity, then

11

11

11

(A) w (B) 2w (C) 2w2 (D) 3w2


Maths IIT-JEE ‘Best Approach’ (MC SIR)97. Number of values of z (real or complex) simultaneously satisfying the system of equations

1 + z + z2 + z3 + .......... + z17 = 0 and 1 + z + z2 + z3 + .......... + z13 = 0 is(A) 1 (B) 2 (C) 3 (D) 4

98. If z1 & 1z represent adjacent vertices of a regular polygon of n sides with centre at the origin & if

12zRezIm

1

1 then the value of n is equal to :

(A) 8 (B) 12 (C) 16 (D) 24

99. Number of ordered pair(s) (z, ) of the complex numbers z and satisfying the system of equations,z3 + 7 = 0 and z5 . 11 = 1 is :(A) 7 (B) 5 (C) 3 (D) 2

100. If A and B be two complex numbers satisfying AB

BA

= 1. Then the two points represented by A and

B and the origin form the vertices of(A) an equilateral triangle(B) an isosceles triangle which is not equilateral(C) an isosceles triangle which is not right angled(D) a right angled triangle



ANSWER KEY100 QUESTIONS

1. B 2. C 3. B 4. C 5. D 6. C 7. A8. C 9. B 10. D 11. A 12. A 13. D 14. C15. A 16. C 17. A 18. A 19. C 20. C 21. A22. A 23. C 24. C 25. D 26. A 27. D 28. C29. A 30. B 31. D 32. D 33. A 34. B 35. A36. D 37. B 38. B 39. C 40. C 41. B 42. B43. C 44. C 45. A 46. A 47. A 48. D 49. A50. C 51. C 52. C 53. A 54. B 55. D 56. C57. A 58. B 59. C 60. C 61. A 62. B 63. B64. A 65. C 66. A 67. D 68. C 69. A 70. A71. B 72. B 73. A 74. C 75. C 76. D 77. A78. B 79. A 80. B 81. C 82. B 83. A 84. A85. B 86. D 87. A 88. B 89. B 90. C 91. B92. D 93. C 94. C 95. A 96. D 97. A 98. A99. D 100. A

k 100 QUESTIONS 1.

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