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WBJEE Previous Year - 2011 - JEE MCQ


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240 Questions MCQ Test WBJEE Sample Papers, Section Wise & Full Mock Tests 2024 - WBJEE Previous Year - 2011

WBJEE Previous Year - 2011 for JEE 2024 is part of WBJEE Sample Papers, Section Wise & Full Mock Tests 2024 preparation. The WBJEE Previous Year - 2011 questions and answers have been prepared according to the JEE exam syllabus.The WBJEE Previous Year - 2011 MCQs are made for JEE 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for WBJEE Previous Year - 2011 below.
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WBJEE Previous Year - 2011 - Question 1

The eccentricity of the hyperbola  4x2 – 9y2 = 36 is

Detailed Solution for WBJEE Previous Year - 2011 - Question 1

WBJEE Previous Year - 2011 - Question 2

The length of the latus rectum of the ellipse 16x2 + 25y2 = 400 is

Detailed Solution for WBJEE Previous Year - 2011 - Question 2

WBJEE Previous Year - 2011 - Question 3

The vertex of  the parabola  y2 + 6x – 2y + 13 = 0 is

( y −1)2= −6x − 12

( y −1)2= −6(x +12) = 4(-6/4)(x+2)

Vertex →(−2, 1)

WBJEE Previous Year - 2011 - Question 4

The coordinates of a moving point p are (2t2 + 4, 4t + 6). Then  its locus will be a

Detailed Solution for WBJEE Previous Year - 2011 - Question 4

WBJEE Previous Year - 2011 - Question 5

The equation  8x2 + 12y2 – 4x + 4y – 1 = 0  represents

Detailed Solution for WBJEE Previous Year - 2011 - Question 5

ax2 + by2+ 2hxy + 2gx + 2fy + c = 0

represents ellipse if h2 −ab< 0

3x2 + 12y2− 4x + 4y − 1 = 0

h =0, a= 3, b = 12

h2 −ab< 0

WBJEE Previous Year - 2011 - Question 6

If the straight line  y = mx lies outside of the circle x2 + y2 – 20y + 90 = 0, then the value of  m will satisfy

Detailed Solution for WBJEE Previous Year - 2011 - Question 6

x2 +m2 x2− 20mx + 90

x2 (1 + m2)− 20mx + 90 = 0

D <0

400m2 − 4× 90 (1 + m2) < 0

40m2 < 360

m2 < 9  ; |m |< 3

WBJEE Previous Year - 2011 - Question 7

The locus of the centre of a circle which passes through two variable points (a, 0), (–a, 0) is

Detailed Solution for WBJEE Previous Year - 2011 - Question 7

Centre lies on y-axis  locus  x = 0

WBJEE Previous Year - 2011 - Question 8

The  coordinates of the two points lying on  x + y = 4 and at a unit distance from the straight line 4x + 3y = 10 are

Detailed Solution for WBJEE Previous Year - 2011 - Question 8

Let  p (h, 4 − h)

|h + 2|= 5

h =3,−7 ;  p =1, 1

(3,1),(−7,11)

WBJEE Previous Year - 2011 - Question 9

The intercept on the line y = x by the circle x2 + y2 – 2x = 0 is  AB.  Equation of the circle with AB as diameter is

Detailed Solution for WBJEE Previous Year - 2011 - Question 9

x2 + y2 = 0

( 0, 0 ) , (1,1) as diametric ends (x − 0)(x−1) + (y + 0)(y −1) = 0

x2 +y2− x − y = 0

WBJEE Previous Year - 2011 - Question 10

If the coordinates of one end of a diameter of the circle  x2+y2+4x–8y+5=0, is (2,1), the coordinates of the other end is

Detailed Solution for WBJEE Previous Year - 2011 - Question 10

x2 + y2+ 9x − 8y + 5 = 0

Centre circle (–2, 4)

WBJEE Previous Year - 2011 - Question 11

If the three points A(1,6), B(3, –4) and C(x, y) are collinear then the equation satisfying by  x and y is

Detailed Solution for WBJEE Previous Year - 2011 - Question 11

⇒ 1(3y+ 4x) − (y − 6x) +1(−4 −18) = 0

⇒ 3y+ 4x − y + 6x −12 = 0

⇒ 2y+ 10x − 22 = 0

y +5x= 11

WBJEE Previous Year - 2011 - Question 12

and θ lies in the second quadrant, then cosθ is equal to

Detailed Solution for WBJEE Previous Year - 2011 - Question 12

θ in 2nd quad Cosθ < 0

WBJEE Previous Year - 2011 - Question 13

The solutions set of  inequation  cos–1x < sin–1x is

Detailed Solution for WBJEE Previous Year - 2011 - Question 13

cos–1x < sin–1

WBJEE Previous Year - 2011 - Question 14

The number of solutions of  2sinx + cos x = 3 is

Detailed Solution for WBJEE Previous Year - 2011 - Question 14

√5 <3      No solution

WBJEE Previous Year - 2011 - Question 15

Detailed Solution for WBJEE Previous Year - 2011 - Question 15

 

WBJEE Previous Year - 2011 - Question 16

If  θ+ φ = π/4 then (1 + tanθ)(1 + tanφ)  is equal to

Detailed Solution for WBJEE Previous Year - 2011 - Question 16

WBJEE Previous Year - 2011 - Question 17

If sinθ and cosθ are the roots of the equation  ax2 – bx + c = 0, then a, b and c satisfy the relation

Detailed Solution for WBJEE Previous Year - 2011 - Question 17

 sinθ + cosθ = b/a

 sinθ . cosθ = c/a

WBJEE Previous Year - 2011 - Question 18

If  A and B are two matrices such that A+B and AB are both defined, then

Detailed Solution for WBJEE Previous Year - 2011 - Question 18

 Addition is defined if order of A is  equal to order of B

AB is defined if  m  = n

nxm nxm 

⇒ A, B are square matrices of same order

WBJEE Previous Year - 2011 - Question 19

  is a symmetric matrix, then the value of  x is

Detailed Solution for WBJEE Previous Year - 2011 - Question 19

A = AT

WBJEE Previous Year - 2011 - Question 20

Detailed Solution for WBJEE Previous Year - 2011 - Question 20

= -(-21-64)-((1-2i)(7(1+2i)+5i(5-3i)))+5i(1+2i)(5+3i)-15i)

= Real

WBJEE Previous Year - 2011 - Question 21

The equation of the locus of the point of intersection of the straight lines x sin θ + (1 – cos θ) y = a sin θ  and x sin θ – (1 + cos θ) y + a sin θ = 0 is

Detailed Solution for WBJEE Previous Year - 2011 - Question 21

y =  a sin θ

x = a cos θ.

x2 + y2= a2

WBJEE Previous Year - 2011 - Question 22

If sinθ + cosθ = 0 and 0 < θ < π, then θ

WBJEE Previous Year - 2011 - Question 23

The value of cos 15o – sin 15o is

Detailed Solution for WBJEE Previous Year - 2011 - Question 23

WBJEE Previous Year - 2011 - Question 24

he period of the function f(x) = cos 4x + tan 3x is

Detailed Solution for WBJEE Previous Year - 2011 - Question 24

WBJEE Previous Year - 2011 - Question 25

If y = 2x3 – 2x2 + 3x – 5, then for x = 2 and Δ x = 0.1 value of  Δ y is

Detailed Solution for WBJEE Previous Year - 2011 - Question 25

WBJEE Previous Year - 2011 - Question 26

The approximate value of 5√33 correct to 4 decimal places is

Detailed Solution for WBJEE Previous Year - 2011 - Question 26

WBJEE Previous Year - 2011 - Question 27

The value of  2-2  xcos + xsinx + 1

Detailed Solution for WBJEE Previous Year - 2011 - Question 27

WBJEE Previous Year - 2011 - Question 28

For the function f(x) = ecos x , Rolle’s theorem is

Detailed Solution for WBJEE Previous Year - 2011 - Question 28

WBJEE Previous Year - 2011 - Question 29

The general solution of the differential equation 

Detailed Solution for WBJEE Previous Year - 2011 - Question 29

WBJEE Previous Year - 2011 - Question 30

Detailed Solution for WBJEE Previous Year - 2011 - Question 30

WBJEE Previous Year - 2011 - Question 31

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WBJEE Previous Year - 2011 - Question 32

Detailed Solution for WBJEE Previous Year - 2011 - Question 32

WBJEE Previous Year - 2011 - Question 33

 The degree and order of the differential equation     are repectively

Detailed Solution for WBJEE Previous Year - 2011 - Question 33

WBJEE Previous Year - 2011 - Question 34

Detailed Solution for WBJEE Previous Year - 2011 - Question 34

WBJEE Previous Year - 2011 - Question 35

The function f(x) = ax + b is strictly increasing for all real x if

Detailed Solution for WBJEE Previous Year - 2011 - Question 35

 f′ (x) = a f′(x) > 0   ⇒ a > 0

WBJEE Previous Year - 2011 - Question 36

Detailed Solution for WBJEE Previous Year - 2011 - Question 36

WBJEE Previous Year - 2011 - Question 37

Detailed Solution for WBJEE Previous Year - 2011 - Question 37

WBJEE Previous Year - 2011 - Question 38

The general solution of the differential equation 

Detailed Solution for WBJEE Previous Year - 2011 - Question 38

WBJEE Previous Year - 2011 - Question 39

Detailed Solution for WBJEE Previous Year - 2011 - Question 39

WBJEE Previous Year - 2011 - Question 40

Detailed Solution for WBJEE Previous Year - 2011 - Question 40

C2 → C2 – C3

C3 → C3 + C2

C3 → C3 + ωC1

C2 → C2 – C1

WBJEE Previous Year - 2011 - Question 41

4 boys and 2 girls occupy seats in a row at random. Then the probability that the two girls occupy seats side by side is

Detailed Solution for WBJEE Previous Year - 2011 - Question 41

WBJEE Previous Year - 2011 - Question 42

A coin is tossed again and again. If tail appears on first three tosses, then the chance that head appears on fourth toss is

Detailed Solution for WBJEE Previous Year - 2011 - Question 42

p = 1.1.1.1/2 = 1/2

WBJEE Previous Year - 2011 - Question 43

The coefficient of xn in the expansion of 

Detailed Solution for WBJEE Previous Year - 2011 - Question 43

WBJEE Previous Year - 2011 - Question 44

The sum of the series 

Detailed Solution for WBJEE Previous Year - 2011 - Question 44

WBJEE Previous Year - 2011 - Question 45

The number (101)100– 1 is divisible by

Detailed Solution for WBJEE Previous Year - 2011 - Question 45

WBJEE Previous Year - 2011 - Question 46

If A and B are coefficients of xn in the expansions of (1+ x)2n and (1+x)2n – 1 respectively, then A/B is equal to

Detailed Solution for WBJEE Previous Year - 2011 - Question 46

A = 2nCn  

B = 2n – 1Cn

WBJEE Previous Year - 2011 - Question 47

If n > 1 is an integer and x ≠0, then (1 + x)n – nx – 1is divisible by

Detailed Solution for WBJEE Previous Year - 2011 - Question 47

(1 + x)n = nC0 + nC1x + nC2x² + nC3x3 + .......              

= 1 + nx + x² (nC2 + nC3 x + .........)  (1 + x)n – nx – 1

= x² (nC2+ nC3x + ........)

WBJEE Previous Year - 2011 - Question 48

If  nC4, nC5 and nC6  are in A.P., then n is

Detailed Solution for WBJEE Previous Year - 2011 - Question 48

nC4, nC5 and nC6

WBJEE Previous Year - 2011 - Question 49

The number of diagonals in a polygon is 20. The number of sides of the polygon is

Detailed Solution for WBJEE Previous Year - 2011 - Question 49

nC2 –n = 20  

n = 8

WBJEE Previous Year - 2011 - Question 50

Detailed Solution for WBJEE Previous Year - 2011 - Question 50

WBJEE Previous Year - 2011 - Question 51

Let a , b, c be three real numbers such that a + 2b + 4c = 0. Then the equation ax2 + bx + c = 0

Detailed Solution for WBJEE Previous Year - 2011 - Question 51

WBJEE Previous Year - 2011 - Question 52

If the ratio of the roots of the equation px2 + qx + r = 0 is a : b, then ab/(a + b)is

Detailed Solution for WBJEE Previous Year - 2011 - Question 52

WBJEE Previous Year - 2011 - Question 53

If α and β are the roots of the equation x2 + x + 1 = 0, then the equation whose roots are α19 and β7 is

Detailed Solution for WBJEE Previous Year - 2011 - Question 53

 α  and β are the roots of x2 + x + 1 = 0

α = ω

β=ω2 

α19 = ω

β7 = ω2

x2 – (α19 + β7)x + α19 β7 = 0

Thou, x2 – (ω + ω 2) x + ω . ω 2 = 0

x2 + x + 1 = 0

WBJEE Previous Year - 2011 - Question 54

For the real parameter t, the locus of the complex number z = (1 – t²) + i√(1 + t2) in the complex plane is

Detailed Solution for WBJEE Previous Year - 2011 - Question 54

 Let z = x + iy  

x = 1 – t2 

y2 = 1 + t2

Thus, x + y2 = 2          

y2 = 2 – x        

y2 = – (x – 2)    

Thus  parabola

WBJEE Previous Year - 2011 - Question 55

if x + 1/x = 2cosθ, then for any integer n , xn + 1/xn

Detailed Solution for WBJEE Previous Year - 2011 - Question 55

x + 1/x = 2cosθ

Let x = cos θ + 1 sin θ

1/x = cosθ − 1sinθ

thus, xn + 1/xn = 2 cos nθ

WBJEE Previous Year - 2011 - Question 56

If ω ≠ 1 is a cube root of unity, then the sum of the series S = 1 + 2ω + 3ω ² + .......... + 3nω 3n – 1 is

Detailed Solution for WBJEE Previous Year - 2011 - Question 56

S = 1 + 2ω + 3ω ² + .......... + 3nω 3n – 1

Sω = ω + ω ² + .......... + (3n-1)ω 3n – 1 + 3nωn

s(1 – ω) = 1 + ω + ω² + ...........+ ω3n–1 – 3nω3h

 = 0 – 3n

WBJEE Previous Year - 2011 - Question 57

If log3x + log3y = 2 + log32 and log3(x + y) = 2, then

Detailed Solution for WBJEE Previous Year - 2011 - Question 57

log3x + log3y = 2 + log32

⇒ x.y = 18  log (x + y) = 2  

⇒  x + y = 9

we will get x = 3 and y = 6

WBJEE Previous Year - 2011 - Question 58

If log 7 2 = λ, then the value of log49 (28) is

Detailed Solution for WBJEE Previous Year - 2011 - Question 58

  log4928 = log724 × 7

WBJEE Previous Year - 2011 - Question 59

The sequence log a, log a2/b, loga3/b2,  ....... is

Detailed Solution for WBJEE Previous Year - 2011 - Question 59

log a . (2log a – log b)(3log a – 2 log b)

 = T2 – T1 = log a – log b

= T3– T2 = log a – log b

WBJEE Previous Year - 2011 - Question 60

If in a triangle ABC, sin A, sin B, sin C are in A.P., then

Detailed Solution for WBJEE Previous Year - 2011 - Question 60

WBJEE Previous Year - 2011 - Question 61