WBJEE Maths Test - 3

Question 1

The term independent of x in the expansion of [(√(x/3))+(√3/x²)]¹⁰ is

Accepted Answer

5/3

Answer

3/5

Answer

21/20

Answer

20/21

Question 2

The term independent of x in the expansion of ((2x) - (3/x))⁶ is

Accepted Answer

Answer

Answer

Answer

Question 3

The coefficient of x³ in ((√x⁵) + (3/√x³))⁶ is

Accepted Answer

540

Answer

0

Answer

120

Answer

420

Question 4

The radical axis of the circles, belongs to the coaxial system of circles whose limiting points are (1,3) and (2,6) is

Accepted Answer

x + 3y - 15 = 0

Answer

x - 3y + 15 = 0

Answer

x - 3y - 15 = 0

Answer

2x + 3y - 15 = 0

Question 5

If a < 0 < b then

Accepted Answer

a+b

Answer

b-a

Answer

a-b

Answer

0

Question 6

The centre and radius of the circle with the segment of the line x+y=1 cut of by the coordinate axes as diameter are

Accepted Answer

(1 ∕ 2,1 ∕ 2), 1 ∕ √2

Answer

(1,1) ,√2

Answer

(1 ∕ 2, 1 ∕ 2),√2

Answer

(0,0), 1

Question 7

If (a+ib)(c+id)(e+if)(g+ih) = A+iB, then (a²+b²)(c²+d²)(c²+f²)(g²+h²) =

Accepted Answer

A2 + B2

Answer

A - B

Answer

A + B

Answer

A2 - B2

Question 8

If we express [(cos 2θ - i sin2θ)⁴(cos4θ + i sin4θ)^-5]/[(cos3θ + i sin 3θ)^-2(cos3θ - i sin3θ)]^-9 in the form of x + iy,we get

Accepted Answer

(cos49θ) - (i sin 49θ)

Answer

(cos49θ) + (i sin 49θ)

Answer

(cos 23θ) + (i sin 23θ)

Answer

(cos 21θ) + (i sin 21θ)

Question 9

The area bounded by two curves y²=4ax and x²=4ay is

Accepted Answer

16/3)a² sq.unit

Answer

(16/3)sq.unit

Answer

(32/3)sq.unit

Answer

(32/3)a² sq.unit(

Question 10

Accepted Answer

Answer

log a - log b

Answer

log a + log b

Answer

Question 11

If a, b, c are different and then x =

Accepted Answer

0

Answer

a

Answer

b

Answer

c

Question 12

The orthogonal trajectories of the family y²=4ax+4a² is the family :

Accepted Answer

y²=4ax+4a²

Answer

x²=4ay+4a²

Answer

y²=4ay+4a²x

Answer

x²=4ax+4a²y

Question 13

The solution of the differential equation x{y d²y/dx² + (dy/dx)²}=y dy/dx is :

Accepted Answer

ax²+by²=1

Answer

ax+by+c

Answer

ax2+by=0

Answer

ax+by2=0

Question 14

Accepted Answer

1/2

Answer

1/3

Answer

1/4

Answer

None of these

Question 15

Accepted Answer

1 + a²+ b²+ c²

Answer

1 − a²+ b²+ c²

Answer

1 + a²+ b²− c²

Answer

1 + a²− b² + c²

Question 16

If siny=x sin (a+y), (dy/dx)=

Accepted Answer

[(sin²(a+y))/(sina)]

Answer

sin(a+y)

Answer

sin&sup2;(a+y)

Answer

sin[(a+y)/(sina)]

Question 17

The differential of sin⁻¹[(1-x)/(1+x)] w.r.t. √x is equal to

Accepted Answer

(-2/(1+x))

Answer

(1/2&radic;x)

Answer

(√x/(1-x))

Answer

1

Question 18

The major axis of an ellipse is three times the minor axis, then the eccentricity is

Accepted Answer

Answer

2/3

Answer

Answer

1/3

Question 19

The eccentricity of ellipse 4x² + 9y² = 36 is

Accepted Answer

&radic;5/3

Answer

1/2&radic;3

Answer

1/&radic;3

Answer

&radic;5/6

Question 20

The parametric equations of the hyperbola x²/a² - y²/b² = 1 are

Accepted Answer

x = a sec θ, y = b tan θ

Answer

x = a tan θ, y = b secθ

Answer

x = √2a, y = b

Answer

none of these

Question 21

The eccentricity of the conic 9x² - 16y² = 144 is

Accepted Answer

5/4

Answer

4/5

Answer

4/3

Answer

&radic;7

Question 22

tan⁻¹(1/4) + tan⁻¹(2/9) is equal to

Accepted Answer

tan⁻¹(1/2)

Answer

1/2 cos⁻¹(3/5)

Answer

1/2 sin⁻¹(3/5)

Answer

1/2 tan⁻¹(3/5)

Question 23

Let f(x) = tan^-1 {φ(x)}, where φ(x)is monotonically increasing for 0 < x < π/2. Then f(x) is

Accepted Answer

increasing in (0, π/2)

Answer

decreasing in (0, π/2)

Answer

increasing in (0, π/4) and decreasing in (π/4, π/2)

Answer

none of these

Question 24

If A and B are two matrices such that AB = B and BA = A, then A² + B² =

Accepted Answer

A + B

Answer

2 AB

Answer

2 BA

Answer

AB

Question 25

A function f(x) is defined as f (x) = [1 − x²] , − 1 ≤ x ≤ 1 , where [x] denotes the greatest integer not exceeding x. The function f(x) is discontinuous at x = 0 because

Accepted Answer

The right-hand limit is = the left-hand limit ≠ value of the function f(x)

Answer

The right-hand limit does not exit

Answer

The left-hand limit does not exist

Answer

The right-hand and left-hand limit are not equal

Question 26

A square tank of capacity 250 cubic m has to be dug out. The cost of land is Rs 50 per sq.m. The cost of digging increases with the depth and for the whole tank is 400 (depth)² rupees. The dimensions of the tank for the least total cost are

Accepted Answer

depth=2.5m, side=10m

Answer

side=10m, depth=3.5m

Answer

side=10m, depth=10m

Answer

side=2.5m, depth=2.5m

Question 27

If z₁,z₂,z₃ are complex numbers such that |1/z₁+1/z₂+1/z₃|=1, then |z₁+z₂+z₃| is equal to

Accepted Answer

Answer

less than 1

Answer

greater than 1

Answer

<h5>equal to 3</h5>

Question 28

The normals to the parabola y²=4ax from the point (5a,2a) are

Accepted Answer

y=x-3a and y=-2x+12a

Answer

y=2x+12a and y=x+3a

Answer

y=-3x+33a and y=x+2a

Answer

y=x+3a and y=3x+12a

Question 29

The slope of the normal at the point (at²,2at) of the parabola y²=4ax is

Accepted Answer

-t

Answer

1/t

Answer

t

Answer

-1/t

Question 30

In how many different ways can the letters of the word 'AUCTION'  be arranged so that the vowels always come together?

Accepted Answer

Answer

Answer

Answer

WBJEE Sample Papers, Section Wise & Full Maths Test - 3 Free Online Test

MCQ Practice Test & Solutions: WBJEE Maths Test - 3 (75 Questions)

The term independent of x in the expansion of [(√(x/3))+(√3/x²)]¹⁰ is

The term independent of x in the expansion of ((2x) - (3/x))⁶ is

The coefficient of x³ in ((√x⁵) + (3/√x³))⁶ is

The radical axis of the circles, belongs to the coaxial system of circles whose limiting points are (1,3) and (2,6) is

If a < 0 < b then

The centre and radius of the circle with the segment of the line x+y=1 cut of by the coordinate axes as diameter are

If (a+ib)(c+id)(e+if)(g+ih) = A+iB, then (a²+b²)(c²+d²)(c²+f²)(g²+h²) =

If we express [(cos 2θ - i sin2θ)⁴(cos4θ + i sin4θ)^-5]/[(cos3θ + i sin 3θ)^-2(cos3θ - i sin3θ)]^-9 in the form of x + iy,we get

The area bounded by two curves y²=4ax and x²=4ay is

If a, b, c are different and then x =

The orthogonal trajectories of the family y²=4ax+4a² is the family :

The solution of the differential equation x{y d²y/dx² + (dy/dx)²}=y dy/dx is :

If siny=x sin (a+y), (dy/dx)=

The differential of sin⁻¹[(1-x)/(1+x)] w.r.t. √x is equal to

The major axis of an ellipse is three times the minor axis, then the eccentricity is

The eccentricity of ellipse 4x² + 9y² = 36 is

The parametric equations of the hyperbola x²/a² - y²/b² = 1 are

The eccentricity of the conic 9x² - 16y² = 144 is

tan⁻¹(1/4) + tan⁻¹(2/9) is equal to

Let f(x) = tan^-1 {φ(x)}, where φ(x)is monotonically increasing for 0 < x < π/2. Then f(x) is

If A and B are two matrices such that AB = B and BA = A, then A² + B² =

A function f(x) is defined as f (x) = [1 − x²] , − 1 ≤ x ≤ 1 , where [x] denotes the greatest integer not exceeding x. The function f(x) is discontinuous at x = 0 because

A square tank of capacity 250 cubic m has to be dug out. The cost of land is Rs 50 per sq.m. The cost of digging increases with the depth and for the whole tank is 400 (depth)² rupees. The dimensions of the tank for the least total cost are

If z₁,z₂,z₃ are complex numbers such that |1/z₁+1/z₂+1/z₃|=1, then |z₁+z₂+z₃| is equal to

The normals to the parabola y²=4ax from the point (5a,2a) are

The slope of the normal at the point (at²,2at) of the parabola y²=4ax is

In how many different ways can the letters of the word 'AUCTION' be arranged so that the vowels always come together?

WBJEE Sample Papers, Section Wise & Full Mock Tests 2026

WBJEE Sample Papers, Section Wise & Full Mock Tests 2026

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WBJEE Sample Papers, Section Wise & Full Maths Test - 3 Free Online Test

MCQ Practice Test & Solutions: WBJEE Maths Test - 3 (75 Questions)

The term independent of x in the expansion of [(√(x/3))+(√3/x2)]10 is

The term independent of x in the expansion of ((2x) - (3/x))6 is

The coefficient of x3 in ((√x5) + (3/√x3))6 is

The radical axis of the circles, belongs to the coaxial system of circles whose limiting points are (1,3) and (2,6) is

If a < 0 < b then

The centre and radius of the circle with the segment of the line x+y=1 cut of by the coordinate axes as diameter are

If (a+ib)(c+id)(e+if)(g+ih) = A+iB, then (a2+b2)(c2+d2)(c2+f2)(g2+h2) =

If we express [(cos 2θ - i sin2θ)4(cos4θ + i sin4θ)-5]/[(cos3θ + i sin 3θ)-2(cos3θ - i sin3θ)]-9 in the form of x + iy,we get

The area bounded by two curves y2=4ax and x2=4ay is

If a, b, c are different and then x =

The orthogonal trajectories of the family y2=4ax+4a2 is the family :

The solution of the differential equation x{y d2y/dx2 + (dy/dx)2}=y dy/dx is :

If siny=x sin (a+y), (dy/dx)=

The differential of sin⁻1[(1-x)/(1+x)] w.r.t. √x is equal to

The major axis of an ellipse is three times the minor axis, then the eccentricity is

The eccentricity of ellipse 4x2 + 9y2 = 36 is

The parametric equations of the hyperbola x2/a2 - y2/b2 = 1 are

The eccentricity of the conic 9x2 - 16y2 = 144 is

tan⁻1(1/4) + tan⁻1(2/9) is equal to

Let f(x) = tan-1 {φ(x)}, where φ(x)is monotonically increasing for 0 < x < π/2. Then f(x) is

If A and B are two matrices such that AB = B and BA = A, then A2 + B2 =

A function f(x) is defined as f (x) = [1 − x2] , − 1 ≤ x ≤ 1 , where [x] denotes the greatest integer not exceeding x. The function f(x) is discontinuous at x = 0 because

A square tank of capacity 250 cubic m has to be dug out. The cost of land is Rs 50 per sq.m. The cost of digging increases with the depth and for the whole tank is 400 (depth)2 rupees. The dimensions of the tank for the least total cost are

If z₁,z₂,z₃ are complex numbers such that |1/z₁+1/z₂+1/z₃|=1, then |z₁+z₂+z₃| is equal to

The normals to the parabola y2=4ax from the point (5a,2a) are

The slope of the normal at the point (at2,2at) of the parabola y2=4ax is

In how many different ways can the letters of the word 'AUCTION' be arranged so that the vowels always come together?

WBJEE Sample Papers, Section Wise & Full Mock Tests 2026

WBJEE Sample Papers, Section Wise & Full Mock Tests 2026

Top Courses for JEE

About this JEE Practice Test

Explore more JEE Study Resources

The term independent of x in the expansion of [(√(x/3))+(√3/x²)]¹⁰ is

The term independent of x in the expansion of ((2x) - (3/x))⁶ is

The coefficient of x³ in ((√x⁵) + (3/√x³))⁶ is

If (a+ib)(c+id)(e+if)(g+ih) = A+iB, then (a²+b²)(c²+d²)(c²+f²)(g²+h²) =

If we express [(cos 2θ - i sin2θ)⁴(cos4θ + i sin4θ)^-5]/[(cos3θ + i sin 3θ)^-2(cos3θ - i sin3θ)]^-9 in the form of x + iy,we get

The area bounded by two curves y²=4ax and x²=4ay is

The orthogonal trajectories of the family y²=4ax+4a² is the family :

The solution of the differential equation x{y d²y/dx² + (dy/dx)²}=y dy/dx is :

The differential of sin⁻¹[(1-x)/(1+x)] w.r.t. √x is equal to

The eccentricity of ellipse 4x² + 9y² = 36 is

The parametric equations of the hyperbola x²/a² - y²/b² = 1 are

The eccentricity of the conic 9x² - 16y² = 144 is

tan⁻¹(1/4) + tan⁻¹(2/9) is equal to

Let f(x) = tan^-1 {φ(x)}, where φ(x)is monotonically increasing for 0 < x < π/2. Then f(x) is

If A and B are two matrices such that AB = B and BA = A, then A² + B² =

A function f(x) is defined as f (x) = [1 − x²] , − 1 ≤ x ≤ 1 , where [x] denotes the greatest integer not exceeding x. The function f(x) is discontinuous at x = 0 because

A square tank of capacity 250 cubic m has to be dug out. The cost of land is Rs 50 per sq.m. The cost of digging increases with the depth and for the whole tank is 400 (depth)² rupees. The dimensions of the tank for the least total cost are

The normals to the parabola y²=4ax from the point (5a,2a) are

The slope of the normal at the point (at²,2at) of the parabola y²=4ax is