WBJEE Maths Test - 4

Question 1

If the coefficients of 5th, 6th and 7th terms in the expansion of (1 + x)ⁿ, n ∈ N, are in A.P., then n is equal to

Accepted Answer

Answer

Answer

Answer

Question 2

The angle between tangents drawn from origin to the circle (x-7)² + (y+1)²=25 is

Accepted Answer

Answer

Answer

Answer

Question 3

If in the expansion of (1 + x)²⁰, the coefficients of rth and (r + 4)th terms are equal, then r is

Accepted Answer

Answer

Answer

Answer

Question 4

If the co-efficients of rth and (r+1)th terms in the expansion of (3+7x)²⁹ are equal, the r is equal to

Accepted Answer

Answer

Answer

Answer

Question 5

Circles x²+y²-6x-2y+1=0 and x²+y²+2x-8y+13=0

Accepted Answer

touch each other

Answer

do not touch each other

Answer

do not intersect

Answer

intersect at two points

Question 6

If = a + ib , then a and b are

Accepted Answer

Answer

Answer

Answer

Question 7

Find real values of x and y for which the complex numbers -3 + ix²y and x² + y + 4i are conjugates of each other.

Accepted Answer

x = 1,y = -4

Answer

x = -2,y = -1

Answer

x = 2,y = 2

Answer

x = 2,y = -2

Question 8

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 9

If a < 0 < b then

Accepted Answer

Answer

Answer

Answer

Question 10

If a ≠ 6, b, c satisfy = 0 then abc =

Accepted Answer

Answer

Answer

Answer

Question 11

Accepted Answer

Answer

Answer

Answer

Question 12

Accepted Answer

Answer

Answer

Answer

Question 13

Accepted Answer

Answer

Answer

Answer

Question 14

The solution of the equation ydx-2xdy=0 gives parabolas whose common axis and the tangent at the vertex respectively, are :

Accepted Answer

Answer

Answer

Answer

Question 15

The solution of the equation xdy-ydx=0 is

Accepted Answer

Straight line passing (0,0)

Answer

Rectangular hyperbola

Answer

Parabola with vertex at (0,0)

Answer

Circle with centre at (0,0)

Question 16

If f(x)=log_x²log(x), then at x=e, f'(x)=

Accepted Answer

Answer

Answer

Answer

Question 17

For real values of x the minimum value of [(1-x+x²)/(1+x+x²)] is

Accepted Answer

Answer

Answer

Answer

Question 18

The eccentricity of the ellipse 9x² + 5y² − 30y = 0 is

Accepted Answer

Answer

Answer

Answer

Question 19

The eccentricity of the ellipse 4x² + 9y² + 8x + 36y + 4 = 0 is

Accepted Answer

<p>&radic;5/3</p>

Answer

Answer

Answer

<p>&radic;2/3</p>

Question 20

If the two intersecting lines intersect the hyperbola and neither of them is a tangent to it, then number of intersecting points are

Accepted Answer

Answer

Answer

Answer

Question 21

If sin⁻¹x + sin⁻¹y = 2π/3, then cos⁻¹ x + cos⁻¹ y is equal to

Accepted Answer

Answer

Answer

Answer

Question 22

If φ (x) = f (x) + f (1 − x) and f ″ (x) < 0 in − 1,1 , then φ (x) strictly increases in the interval

Accepted Answer

Answer

Answer

Answer

Question 23

if f : R→R be such that f(1) = 4 and f^'(1) = 12 then

Accepted Answer

Answer

Answer

Answer

Question 24

If each element of a 3 x 3 matrix is multiplie by 3, then the determinant of the newly formed matrix is

Accepted Answer

Answer

Answer

Answer

Question 25

The minimum value of f(x) = x⁴-x²-2x+6 is

Accepted Answer

Answer

Answer

Answer

nonexistent

Question 26

The HCF of 155 and 1385 is

Accepted Answer

Answer

Answer

Answer

none of these

Question 27

The focus of the parabola x²-8x+2y+7=0 is

Accepted Answer

Answer

Answer

Answer

Question 28

The tangents at the points ( ,2at₁) , ( , 2at₂) on the parabola y² = 4ax are at right angles if

Accepted Answer

t₁t₂=-1

Answer

Answer

Answer

t₁t₂=-2

Question 29

In how many different ways can the letters of the word BOOKLET be arranged such that B and T always come together?

Accepted Answer

Answer

Answer

Answer

Question 30

The equation 16x² + y² + 8xy − 74 x − 78y + 212 = 0 represents

Accepted Answer

<p>A parabola</p>

Answer

<p>A circle</p>

Answer

<p>An ellipse</p>

Answer

A hyperbola

WBJEE Sample Papers, Section Wise & Full Maths Test - 4 Free Online Test

MCQ Practice Test & Solutions: WBJEE Maths Test - 4 (75 Questions)

If the coefficients of 5th, 6th and 7th terms in the expansion of (1 + x)ⁿ, n ∈ N, are in A.P., then n is equal to

The angle between tangents drawn from origin to the circle (x-7)² + (y+1)²=25 is

If in the expansion of (1 + x)²⁰, the coefficients of rth and (r + 4)th terms are equal, then r is

If the co-efficients of rth and (r+1)th terms in the expansion of (3+7x)²⁹ are equal, the r is equal to

Circles x²+y²-6x-2y+1=0 and x²+y²+2x-8y+13=0

If = a + ib , then a and b are

Find real values of x and y for which the complex numbers -3 + ix²y and x² + y + 4i are conjugates of each other.

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

If a < 0 < b then

If a ≠ 6, b, c satisfy = 0 then abc =

The solution of the equation ydx-2xdy=0 gives parabolas whose common axis and the tangent at the vertex respectively, are :

The solution of the equation xdy-ydx=0 is

If f(x)=log_x²log(x), then at x=e, f'(x)=

For real values of x the minimum value of [(1-x+x²)/(1+x+x²)] is

The eccentricity of the ellipse 9x² + 5y² − 30y = 0 is

The eccentricity of the ellipse 4x² + 9y² + 8x + 36y + 4 = 0 is

If the two intersecting lines intersect the hyperbola and neither of them is a tangent to it, then number of intersecting points are

If sin⁻¹x + sin⁻¹y = 2π/3, then cos⁻¹ x + cos⁻¹ y is equal to

If φ (x) = f (x) + f (1 − x) and f ″ (x) < 0 in − 1,1 , then φ (x) strictly increases in the interval

if f : R→R be such that f(1) = 4 and f^'(1) = 12 then

If each element of a 3 x 3 matrix is multiplie by 3, then the determinant of the newly formed matrix is

The minimum value of f(x) = x⁴-x²-2x+6 is

The HCF of 155 and 1385 is

The focus of the parabola x²-8x+2y+7=0 is

The tangents at the points ( ,2at₁) , ( , 2at₂) on the parabola y² = 4ax are at right angles if

In how many different ways can the letters of the word BOOKLET be arranged such that B and T always come together?

The equation 16x² + y² + 8xy − 74 x − 78y + 212 = 0 represents

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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 - 4 Free Online Test

MCQ Practice Test & Solutions: WBJEE Maths Test - 4 (75 Questions)

If the coefficients of 5th, 6th and 7th terms in the expansion of (1 + x)n, n ∈ N, are in A.P., then n is equal to

The angle between tangents drawn from origin to the circle (x-7)2 + (y+1)2=25 is

If in the expansion of (1 + x)20, the coefficients of rth and (r + 4)th terms are equal, then r is

If the co-efficients of rth and (r+1)th terms in the expansion of (3+7x)29 are equal, the r is equal to

Circles x2+y2-6x-2y+1=0 and x2+y2+2x-8y+13=0

If = a + ib , then a and b are

Find real values of x and y for which the complex numbers -3 + ix²y and x² + y + 4i are conjugates of each other.

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

If a < 0 < b then

If a ≠ 6, b, c satisfy = 0 then abc =

The solution of the equation ydx-2xdy=0 gives parabolas whose common axis and the tangent at the vertex respectively, are :

The solution of the equation xdy-ydx=0 is

If f(x)=logx2log(x), then at x=e, f'(x)=

For real values of x the minimum value of [(1-x+x2)/(1+x+x2)] is

The eccentricity of the ellipse 9x2 + 5y2 − 30y = 0 is

The eccentricity of the ellipse 4x2 + 9y2 + 8x + 36y + 4 = 0 is

If the two intersecting lines intersect the hyperbola and neither of them is a tangent to it, then number of intersecting points are

If sin⁻1x + sin⁻1y = 2π/3, then cos⁻1 x + cos⁻1 y is equal to

If φ (x) = f (x) + f (1 − x) and f ″ (x) < 0 in − 1,1 , then φ (x) strictly increases in the interval

if f : R→R be such that f(1) = 4 and f'(1) = 12 then

If each element of a 3 x 3 matrix is multiplie by 3, then the determinant of the newly formed matrix is

The minimum value of f(x) = x4-x2-2x+6 is

The HCF of 155 and 1385 is

The focus of the parabola x2-8x+2y+7=0 is

The tangents at the points ( ,2at1) , ( , 2at2) on the parabola y2 = 4ax are at right angles if

In how many different ways can the letters of the word BOOKLET be arranged such that B and T always come together?

The equation 16x2 + y2 + 8xy − 74 x − 78y + 212 = 0 represents

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

If the coefficients of 5th, 6th and 7th terms in the expansion of (1 + x)ⁿ, n ∈ N, are in A.P., then n is equal to

The angle between tangents drawn from origin to the circle (x-7)² + (y+1)²=25 is

If in the expansion of (1 + x)²⁰, the coefficients of rth and (r + 4)th terms are equal, then r is

If the co-efficients of rth and (r+1)th terms in the expansion of (3+7x)²⁹ are equal, the r is equal to

Circles x²+y²-6x-2y+1=0 and x²+y²+2x-8y+13=0

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

If f(x)=log_x²log(x), then at x=e, f'(x)=

For real values of x the minimum value of [(1-x+x²)/(1+x+x²)] is

The eccentricity of the ellipse 9x² + 5y² − 30y = 0 is

The eccentricity of the ellipse 4x² + 9y² + 8x + 36y + 4 = 0 is

If sin⁻¹x + sin⁻¹y = 2π/3, then cos⁻¹ x + cos⁻¹ y is equal to

if f : R→R be such that f(1) = 4 and f^'(1) = 12 then

The minimum value of f(x) = x⁴-x²-2x+6 is

The focus of the parabola x²-8x+2y+7=0 is

The tangents at the points ( ,2at₁) , ( , 2at₂) on the parabola y² = 4ax are at right angles if

The equation 16x² + y² + 8xy − 74 x − 78y + 212 = 0 represents