WBJEE Maths Test - 2

Question 1

The 10th term of the expansion of (x-1)¹¹ (in decreasing powers of x) is

Accepted Answer

-11C&#8322;x2

Answer

-x

Answer

-11 x

Answer

-x2

Question 2

The term independent of x in the expansion of ((x²) - (1/3x))⁹ is equal to

Accepted Answer

28/243

Answer

28/81

Answer

-(28/243)

Answer

-(28/81)

Question 3

x=7 touches the circle x² + y² - 4x - 6y - 12 = 0, then the co-ordinates of the point of contact are

Accepted Answer

(7,3)

Answer

(7,4)

Answer

(7,8)

Answer

(7,2)

Question 4

If in the expansion of ((x⁴) - (1/x³))¹⁵, x^-17 occurs in the rth term, then

Accepted Answer

r = 12

Answer

r = 10

Answer

r = 11

Answer

r = 13

Question 5

[(-1 + √(-3))/2]³ⁿ +[(-1 - √(-3))/2]³ⁿ is equal to

Accepted Answer

Answer

Answer

Answer

Question 6

Accepted Answer

0

Answer

272

Answer

-54

Answer

54

Question 7

x² + y² + 2(2K+3)x - 2Ky +(2K+3)² + K² - r² = 0 represents the family of circles with centres on the line

Accepted Answer

x + 2y + 3 = 0

Answer

x - 2y - 3 = 0

Answer

x + 2y - 3 = 0

Answer

x - 2y + 3 = 0

Question 8

Accepted Answer

0

Answer

2

Answer

3

Answer

4

Question 9

Accepted Answer

2 log 2

Answer

log 2

Answer

3 log 3

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

- 2abc

Answer

abc

Answer

a² + b² + c²

Question 12

The solution of the equation (1+x²)(1+y)dy+(1+x)(1+y²)dx=0 is

Accepted Answer

tan⁻¹x+(1/2)log(1+x²)+tan⁻¹y+(1/2)log(1+y²)=c

Answer

tan⁻¹x+log(1+x²)+tan⁻¹y+log(1+y²)=c

Answer

tan⁻¹x-(1/2)log(1+x²)+tan⁻¹y-(1/2)log(1+y²)=c

Answer

none of these

Question 13

The differential equation of family of curves y=a cos(x+b) is

Accepted Answer

(d²y/dx²)+y=0

Answer

(d²y/dx²)-y=0

Answer

(d²y/dx²)+2y=0

Answer

none of these

Question 14

If z 1 and z 2 are two non-zero complex numbers such that |z₁ + z₂| = |z₁| + |z₂| , then Arg z₁ − Arg z₂ is

Accepted Answer

0

Answer

&minus;&pi;

Answer

Answer

&pi;/2

Question 15

The differential of sin^-1[(1 - x)/(1 + x)] with respect to √x is equal to

Accepted Answer

-2/(1 + x)

Answer

1/(2√x)

Answer

√x/(1 - x)

Answer

1

Question 16

The function f(x)=|x| is defined on [-1,1]. It does not satisfy the Rolle's theorem because

Accepted Answer

f is not differentiable in (-1,1)

Answer

f is not continuous at [-1,1]

Answer

f(-1)≠f(1)

Answer

f(-1)=f(1)≠0

Question 17

In an ellipse the distance between the foci is 6 and it's minor axis is 8. Then its eccentricity is

Accepted Answer

3/5

Answer

4/5

Answer

Answer

1/2

Question 18

Accepted Answer

0

Answer

abc

Answer

a + b + c

Answer

a² + b² + c²

Question 19

If S′ and S are the foci of the ellipse (x²/a²)+(y²/b²)=1 and P(x,y) be a point on it, then the value of SP + S′P is

Accepted Answer

2a

Answer

2b

Answer

a-b

Answer

a+b

Question 20

The vertices of a hyperbola are (2, 0), (-2, 0) and the foci are (3, 0), (-3, 0). The equation of the hyperbola is

Accepted Answer

x²/4 - y²/5 = 1

Answer

x²/5 - y²/4 = 1

Answer

x²/5 - y²/2 = 1

Answer

x²/2 - y²/5 = 1

Question 21

If e and e ′ are the eccentricities of the hyperbola x² ∕ a² − y² ∕ b² = 1 and its conjugate hyperbola, the value of 1 ∕ e² + 1 ∕ e′² is

Accepted Answer

1

Answer

3

Answer

2

Answer

0

Question 22

Sin (sin⁻¹1/2 + cos⁻¹1/2) equals

Accepted Answer

1

Answer

0

Answer

1/2

Answer

1/&radic;2

Question 23

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 24

If the function f (x) = increases for all x, then

Accepted Answer

b ∈ (−7, −1) ∪ (2,3)

Answer

b ∈ (−1,2)

Answer

b ∈ (−7,3) − {−1}

Answer

none of these

Question 25

If A is a square matrix such that A² = I, then A⁻¹ is equal to

Accepted Answer

A

Answer

2 A

Answer

0

Answer

A + I

Question 26

If 2 cos θ =x+1/x and 2 cos φ =y+1/y, then the value of cos (θ+φ) will be

Accepted Answer

1/2[xy+1/xy]

Answer

Answer

Answer

Question 27

If the function f(x) = 2x³ - 9ax² + 12a²x + 1, where a > 0, attains its max. and min. at p and q respectively such that p² = q then a equals

Accepted Answer

2

Answer

1/2

Answer

1

Answer

3

Question 28

If the parabola y²=4ax passes thro' the point (1,-2), then the tangent at this point is

Accepted Answer

x+y+1=0

Answer

x+y-1=0

Answer

x-y-1=0

Answer

x-y+1=0

Question 29

The line x-y+2=0 touches the parabola y²=8x at the point

Accepted Answer

(2,4)

Answer

(2,-4)

Answer

(1,2&radic;2)

Answer

(4,-4&radic;2)

Question 30

The number of 7 digit numbers which can be formed using the digits 1, 2, 3, 2, 3, 3, 4 is

Accepted Answer

420

Answer

840

Answer

2520

Answer

5040

WBJEE Sample Papers, Section Wise & Full Maths Test - 2 Free Online Test

MCQ Practice Test & Solutions: WBJEE Maths Test - 2 (75 Questions)

The 10th term of the expansion of (x-1)¹¹ (in decreasing powers of x) is

The term independent of x in the expansion of ((x²) - (1/3x))⁹ is equal to

x=7 touches the circle x² + y² - 4x - 6y - 12 = 0, then the co-ordinates of the point of contact are

If in the expansion of ((x⁴) - (1/x³))¹⁵, x^-17 occurs in the rth term, then

[(-1 + √(-3))/2]³ⁿ +[(-1 - √(-3))/2]³ⁿ is equal to

x² + y² + 2(2K+3)x - 2Ky +(2K+3)² + K² - r² = 0 represents the family of circles with centres on the line

The solution of the equation (1+x²)(1+y)dy+(1+x)(1+y²)dx=0 is

The differential equation of family of curves y=a cos(x+b) is

If z 1 and z 2 are two non-zero complex numbers such that |z₁ + z₂| = |z₁| + |z₂| , then Arg z₁ − Arg z₂ is

The differential of sin^-1[(1 - x)/(1 + x)] with respect to √x is equal to

The function f(x)=|x| is defined on [-1,1]. It does not satisfy the Rolle's theorem because

In an ellipse the distance between the foci is 6 and it's minor axis is 8. Then its eccentricity is

If S′ and S are the foci of the ellipse (x²/a²)+(y²/b²)=1 and P(x,y) be a point on it, then the value of SP + S′P is

The vertices of a hyperbola are (2, 0), (-2, 0) and the foci are (3, 0), (-3, 0). The equation of the hyperbola is

If e and e ′ are the eccentricities of the hyperbola x² ∕ a² − y² ∕ b² = 1 and its conjugate hyperbola, the value of 1 ∕ e² + 1 ∕ e′² is

Sin (sin⁻¹1/2 + cos⁻¹1/2) equals

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

If the function f (x) = increases for all x, then

If A is a square matrix such that A² = I, then A⁻¹ is equal to

If 2 cos θ =x+1/x and 2 cos φ =y+1/y, then the value of cos (θ+φ) will be

If the function f(x) = 2x³ - 9ax² + 12a²x + 1, where a > 0, attains its max. and min. at p and q respectively such that p² = q then a equals

If the parabola y²=4ax passes thro' the point (1,-2), then the tangent at this point is

The line x-y+2=0 touches the parabola y²=8x at the point

The number of 7 digit numbers which can be formed using the digits 1, 2, 3, 2, 3, 3, 4 is

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WBJEE Sample Papers, Section Wise & Full Mock Tests 2026

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WBJEE Sample Papers, Section Wise & Full Maths Test - 2 Free Online Test

MCQ Practice Test & Solutions: WBJEE Maths Test - 2 (75 Questions)

The 10th term of the expansion of (x-1)11 (in decreasing powers of x) is

The term independent of x in the expansion of ((x2) - (1/3x))9 is equal to

x=7 touches the circle x2 + y2 - 4x - 6y - 12 = 0, then the co-ordinates of the point of contact are

If in the expansion of ((x4) - (1/x3))15, x-17 occurs in the rth term, then

[(-1 + √(-3))/2]3n +[(-1 - √(-3))/2]3n is equal to

x2 + y2 + 2(2K+3)x - 2Ky +(2K+3)2 + K2 - r2 = 0 represents the family of circles with centres on the line

The solution of the equation (1+x2)(1+y)dy+(1+x)(1+y2)dx=0 is

The differential equation of family of curves y=a cos(x+b) is

If z 1 and z 2 are two non-zero complex numbers such that |z1 + z2| = |z1| + |z2| , then Arg z1 − Arg z2 is

The differential of sin-1[(1 - x)/(1 + x)] with respect to √x is equal to

The function f(x)=|x| is defined on [-1,1]. It does not satisfy the Rolle's theorem because

In an ellipse the distance between the foci is 6 and it's minor axis is 8. Then its eccentricity is

If S′ and S are the foci of the ellipse (x2/a2)+(y2/b2)=1 and P(x,y) be a point on it, then the value of SP + S′P is

The vertices of a hyperbola are (2, 0), (-2, 0) and the foci are (3, 0), (-3, 0). The equation of the hyperbola is

If e and e ′ are the eccentricities of the hyperbola x2 ∕ a2 − y2 ∕ b2 = 1 and its conjugate hyperbola, the value of 1 ∕ e2 + 1 ∕ e′2 is

Sin (sin⁻11/2 + cos⁻11/2) equals

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

If the function f (x) = increases for all x, then

If A is a square matrix such that A2 = I, then A⁻1 is equal to

If 2 cos θ =x+1/x and 2 cos φ =y+1/y, then the value of cos (θ+φ) will be

If the function f(x) = 2x3 - 9ax2 + 12a2x + 1, where a > 0, attains its max. and min. at p and q respectively such that p2 = q then a equals

If the parabola y2=4ax passes thro' the point (1,-2), then the tangent at this point is

The line x-y+2=0 touches the parabola y2=8x at the point

The number of 7 digit numbers which can be formed using the digits 1, 2, 3, 2, 3, 3, 4 is

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 10th term of the expansion of (x-1)¹¹ (in decreasing powers of x) is

The term independent of x in the expansion of ((x²) - (1/3x))⁹ is equal to

x=7 touches the circle x² + y² - 4x - 6y - 12 = 0, then the co-ordinates of the point of contact are

If in the expansion of ((x⁴) - (1/x³))¹⁵, x^-17 occurs in the rth term, then

[(-1 + √(-3))/2]³ⁿ +[(-1 - √(-3))/2]³ⁿ is equal to

x² + y² + 2(2K+3)x - 2Ky +(2K+3)² + K² - r² = 0 represents the family of circles with centres on the line

The solution of the equation (1+x²)(1+y)dy+(1+x)(1+y²)dx=0 is

If z 1 and z 2 are two non-zero complex numbers such that |z₁ + z₂| = |z₁| + |z₂| , then Arg z₁ − Arg z₂ is

The differential of sin^-1[(1 - x)/(1 + x)] with respect to √x is equal to

If S′ and S are the foci of the ellipse (x²/a²)+(y²/b²)=1 and P(x,y) be a point on it, then the value of SP + S′P is

If e and e ′ are the eccentricities of the hyperbola x² ∕ a² − y² ∕ b² = 1 and its conjugate hyperbola, the value of 1 ∕ e² + 1 ∕ e′² is

Sin (sin⁻¹1/2 + cos⁻¹1/2) equals

If A is a square matrix such that A² = I, then A⁻¹ is equal to

If the function f(x) = 2x³ - 9ax² + 12a²x + 1, where a > 0, attains its max. and min. at p and q respectively such that p² = q then a equals

If the parabola y²=4ax passes thro' the point (1,-2), then the tangent at this point is

The line x-y+2=0 touches the parabola y²=8x at the point