WBJEE Maths Test - 8

Question 1

In the expansion of the number of terms free from radicals is

Accepted Answer

730

Answer

715

Answer

725

Answer

750

Question 2

The coefficient of x^-9 in the expansion of ((x²/2) - (2/x))⁹ is

Accepted Answer

-512

Answer

512

Answer

521

Answer

251

Question 3

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

Accepted Answer

540

Answer

0

Answer

120

Answer

420

Question 4

Equation x²+2ax-b²=0 has real roots

α

,

β

and equation x²+2px-q²=0 has real roots

γ

,

δ

. If the circle C is drawn with the points (

α

,

γ

), (

β

,

δ

) as extremities of a diameter, then the equation of C is

Accepted Answer

x²+y²+2ax+2py-b²-q²=0

Answer

x²+y²+2ax+2py+b²+q²=0

Answer

x²+y²-2ax-2py+b²+q²=0

Answer

x²+y²+2ax-2py+b²-q²=0

Question 5

The equation of circle which passes through (4,5) and whose centre is (2,2) is

Accepted Answer

x²+y²-4x-4y-5=0

Answer

x²+y²+4x+4y-5=0

Answer

x²+y²-4x=13

Answer

x²+y²-4x-4y+5=0

Question 6

If the cube roots of unity are 1,ω,ω² then the roots of the equation (x - 2)³+27 = 0 are

Accepted Answer

-1,2,-3ω,2-3ω²

Answer

-1,-1,-1

Answer

-1,-ω,ω²

Answer

-1,2 + 3ω,2 + 3ω²

Question 7

Let z₁ and z₂ be two complex numbers whose principle argument are α and β then, arg (z₁.z₂) =

Accepted Answer

Answer

α + β + π

Answer

α + β - π

Answer

α + β - 2π

Question 8

If m and n are integers, then what is the value of sin mx sin nxdx . If m ≠ n

Accepted Answer

0

Answer

Answer

Answer

mn

Question 9

Accepted Answer

0

Answer

-1

Answer

1

Answer

Question 10

Accepted Answer

&pi; &#8725; 8

Answer

&pi; &#8725; 2

Answer

&pi; &#8725; 4

Answer

&pi; &#8725; 6

Question 11

Accepted Answer

0

Answer

(p - q)(q - r)(r - p)

Answer

pqr

Answer

p + q + r

Question 12

Accepted Answer

0

Answer

4abc

Answer

abc

Answer

2

Question 13

The area bounded by the parabola y²=4ax and the straight line y=2ax is

Accepted Answer

Answer

Answer

Answer

Question 14

The solution of the differential equation 2xy(dy/dx)=x²+3y² is (where c is a constant)

Accepted Answer

x²+y²=px³

Answer

x³+y²=px²

Answer

(x²/2)+(y³/2)=y²+p

Answer

x²+y³=px²

Question 15

What is the solution of x²y²dy = (1−xy³) dx?

Accepted Answer

2x³y³= 3x²+ c

Answer

x³y³= x²+ c

Answer

x³y³= x²+ x + c

Answer

x³y³= 3x²+ c

Question 16

If
then f ′(1) =

Accepted Answer

&minus;2/9

Answer

&minus;1/9

Answer

&minus; 1/3

Answer

1/3

Question 17

The curve represented by x = 2(cos t + sin t), y = 5 (cos t - sin t) is

Accepted Answer

an ellipse

Answer

a circle

Answer

a parabola

Answer

a hyperbola

Question 18

The eccentric angles of the extremities of the latus-rectum intersecting positive x-axis of the ellipse ((x²/a²) + (y²/b²) = 1) are given by

Accepted Answer

tan⁻¹((b/ae))

Answer

tan⁻¹( (ae/b))

Answer

tan⁻¹((be/a))

Answer

tan⁻¹((a/be))

Question 19

If <img alt="" src="https://cn.edurev.in/ApplicationImages/Temp/2156407_6a9e82db-b1c6-45e9-8659-85307c90bfdb_lg.PNG">

Accepted Answer

4

Answer

0

Answer

1

Answer

3

Question 20

The slopes of the common tangents to the hyperbola x²/y - y²/16 = 1 and y²/9 - x²/16 = 1 are

Accepted Answer

-1, 1

Answer

-2, 2

Answer

1, 2

Answer

2, 1

Question 21

The foci of the hyperbola 9x² - 16y² + 18x + 32y - 151 = 0 are

Accepted Answer

(4, 1), (-6, 1)

Answer

(2, 1), (-6, 1)

Answer

(-2, 5), (-2, -3)

Answer

(-2, 4), (-2, -2)

Question 22

The function is increasing in

Accepted Answer

(0, &infin;)

Answer

(1, &infin;)

Answer

(2,2e)

Answer

Question 23

The value of cos⁻¹(cos 5π/3) + sin⁻¹ (sin 5π/3) is

Accepted Answer

0

Answer

&pi;/2

Answer

5&pi;/3

Answer

10&pi;/3

Question 24

is equal to

Accepted Answer

&pi;/180

Answer

1

Answer

0

Answer

&infin;

Question 25

The system of linear equation x + y + z = 2, 2x + y - z = 3, 3x + 2y + kz = 4 has a unique solution, then

Accepted Answer

k &ne; 0

Answer

-1 < k < 1

Answer

-2 < k < 2

Answer

k = 0

Question 26

For all real x, the minimum value of (1 - x + x²)/(1 + x + x²) is

Accepted Answer

1/3

Answer

0

Answer

1

Answer

3

Question 27

If the vertices O,A,B of any equilateral triangle are situated at z=0, z=z₁ and z=z₂ respectively, then which of the following are true ?

Accepted Answer

∣ arg z₁ - arg z₂ ∣ = π/3

Answer

∣ z₁ ∣ - ∣ z₂ ∣ = ∣ z₁ +z₂ ∣

Answer

∣ z₁ + z₂ ∣ = ∣ z₁ ∣

Answer

∣z₁ + z₂ ∣ = ∣ z₁ ∣ + ∣ z₂ ∣

Question 28

Which of the following points lie on the parabola x²=4ay ?

Accepted Answer

x=2at , y=at²

Answer

x=at² , y=2at

Answer

x=2at² , y=at

Answer

None of the above

Question 29

The length of the normal chord to the parabola y² = 4x which subtends a right angle at the vertex is

Accepted Answer

Answer

Answer

2

Answer

1

Question 30

P,Q,R and S have to deliver lecture, then in how many ways can the lectures be arranged?

Accepted Answer

Answer

Answer

Answer

WBJEE Sample Papers, Section Wise & Full Maths Test - 8 Free Online Test

MCQ Practice Test & Solutions: WBJEE Maths Test - 8 (75 Questions)

In the expansion of the number of terms free from radicals is

The coefficient of x^-9 in the expansion of ((x²/2) - (2/x))⁹ is

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

Equation x²+2ax-b²=0 has real roots $α$ , $β$ and equation x²+2px-q²=0 has real roots $γ$ , $δ$ . If the circle C is drawn with the points ( $α$ , $γ$ ), ( $β$ , $δ$ ) as extremities of a diameter, then the equation of C is

The equation of circle which passes through (4,5) and whose centre is (2,2) is

If the cube roots of unity are 1,ω,ω² then the roots of the equation (x - 2)³+27 = 0 are

Let z₁ and z₂ be two complex numbers whose principle argument are α and β then, arg (z₁.z₂) =

If m and n are integers, then what is the value of sin mx sin nxdx . If m ≠ n

The area bounded by the parabola y²=4ax and the straight line y=2ax is

The solution of the differential equation 2xy(dy/dx)=x²+3y² is (where c is a constant)

What is the solution of x²y²dy = (1−xy³) dx?

If
then f ′(1) =

The curve represented by x = 2(cos t + sin t), y = 5 (cos t - sin t) is

The eccentric angles of the extremities of the latus-rectum intersecting positive x-axis of the ellipse ((x²/a²) + (y²/b²) = 1) are given by

If

The slopes of the common tangents to the hyperbola x²/y - y²/16 = 1 and y²/9 - x²/16 = 1 are

The foci of the hyperbola 9x² - 16y² + 18x + 32y - 151 = 0 are

The function is increasing in

The value of cos⁻¹(cos 5π/3) + sin⁻¹ (sin 5π/3) is

is equal to

The system of linear equation x + y + z = 2, 2x + y - z = 3, 3x + 2y + kz = 4 has a unique solution, then

For all real x, the minimum value of (1 - x + x²)/(1 + x + x²) is

If the vertices O,A,B of any equilateral triangle are situated at z=0, z=z₁ and z=z₂ respectively, then which of the following are true ?

Which of the following points lie on the parabola x²=4ay ?

The length of the normal chord to the parabola y² = 4x which subtends a right angle at the vertex is

P,Q,R and S have to deliver lecture, then in how many ways can the lectures be arranged?

WBJEE Sample Papers, Section Wise & Full Mock Tests 2026

WBJEE Sample Papers, Section Wise & Full Mock Tests 2026

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About this JEE Practice Test

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WBJEE Sample Papers, Section Wise & Full Maths Test - 8 Free Online Test

MCQ Practice Test & Solutions: WBJEE Maths Test - 8 (75 Questions)

In the expansion of the number of terms free from radicals is

The coefficient of x-9 in the expansion of ((x2/2) - (2/x))9 is

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

Equation x2+2ax-b2=0 has real roots α,β and equation x2+2px-q2=0 has real roots γ,δ. If the circle C is drawn with the points (α,γ), (β,δ) as extremities of a diameter, then the equation of C is

The equation of circle which passes through (4,5) and whose centre is (2,2) is

If the cube roots of unity are 1,ω,ω2 then the roots of the equation (x - 2)3+27 = 0 are

Let z1 and z2 be two complex numbers whose principle argument are α and β then, arg (z1.z2) =

If m and n are integers, then what is the value of sin mx sin nxdx . If m ≠ n

The area bounded by the parabola y2=4ax and the straight line y=2ax is

The solution of the differential equation 2xy(dy/dx)=x2+3y2 is (where c is a constant)

What is the solution of x2y2dy = (1−xy3) dx?

If then f ′(1) =

The curve represented by x = 2(cos t + sin t), y = 5 (cos t - sin t) is

The eccentric angles of the extremities of the latus-rectum intersecting positive x-axis of the ellipse ((x2/a2) + (y2/b2) = 1) are given by

If

The slopes of the common tangents to the hyperbola x2/y - y2/16 = 1 and y2/9 - x2/16 = 1 are

The foci of the hyperbola 9x2 - 16y2 + 18x + 32y - 151 = 0 are

The function is increasing in

The value of cos⁻1(cos 5π/3) + sin⁻1 (sin 5π/3) is

is equal to

The system of linear equation x + y + z = 2, 2x + y - z = 3, 3x + 2y + kz = 4 has a unique solution, then

For all real x, the minimum value of (1 - x + x2)/(1 + x + x2) is

If the vertices O,A,B of any equilateral triangle are situated at z=0, z=z₁ and z=z₂ respectively, then which of the following are true ?

Which of the following points lie on the parabola x2=4ay ?

The length of the normal chord to the parabola y2 = 4x which subtends a right angle at the vertex is

P,Q,R and S have to deliver lecture, then in how many ways can the lectures be arranged?

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 coefficient of x^-9 in the expansion of ((x²/2) - (2/x))⁹ is

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

Equation x²+2ax-b²=0 has real roots $α$ , $β$ and equation x²+2px-q²=0 has real roots $γ$ , $δ$ . If the circle C is drawn with the points ( $α$ , $γ$ ), ( $β$ , $δ$ ) as extremities of a diameter, then the equation of C is

If the cube roots of unity are 1,ω,ω² then the roots of the equation (x - 2)³+27 = 0 are

Let z₁ and z₂ be two complex numbers whose principle argument are α and β then, arg (z₁.z₂) =

The area bounded by the parabola y²=4ax and the straight line y=2ax is

The solution of the differential equation 2xy(dy/dx)=x²+3y² is (where c is a constant)

What is the solution of x²y²dy = (1−xy³) dx?

If
then f ′(1) =

The eccentric angles of the extremities of the latus-rectum intersecting positive x-axis of the ellipse ((x²/a²) + (y²/b²) = 1) are given by

The slopes of the common tangents to the hyperbola x²/y - y²/16 = 1 and y²/9 - x²/16 = 1 are

The foci of the hyperbola 9x² - 16y² + 18x + 32y - 151 = 0 are

The value of cos⁻¹(cos 5π/3) + sin⁻¹ (sin 5π/3) is

For all real x, the minimum value of (1 - x + x²)/(1 + x + x²) is

Which of the following points lie on the parabola x²=4ay ?

The length of the normal chord to the parabola y² = 4x which subtends a right angle at the vertex is