WBJEE Maths Test - 13

Question 1

The positive integer just greater than (1 + .0001)¹⁰⁰⁰⁰ is

Accepted Answer

Answer

Answer

Answer

Question 2

The inverse point of (1, 2) with respect to the circle x² + y² - 4x - 6y + 9 = 0 is

Accepted Answer

Answer

Answer

Answer

Question 3

If the line lx+my=1 is a tangent line to the circle x²+y²=a2, the locus of (l,m) is

Accepted Answer

<p>a circle</p>

Answer

a straight line

Answer

an ellipse circle

Answer

<p>a parabola</p>

Question 4

[(-1+√-3)/2]³ⁿ + [(-1-√-3)/2]³ⁿ =

Accepted Answer

Answer

Answer

Answer

Question 5

The coefficients of three successive terms in the expansion of (1 + x)ⁿ are 165, 330 and 462 respectively, then the value of n will be

Accepted Answer

Answer

Answer

Answer

Question 6

If x is positive, then the first negative terms in the expansion of 1 + x 27 5 is

Accepted Answer

Answer

Answer

Answer

Question 7

If w is a cube root of unity, then the value of (1 + ω - ω)² (1 - ω + ω²) is

Accepted Answer

Answer

Answer

Answer

Question 8

Accepted Answer

Answer

Answer

Answer

Question 9

Accepted Answer

Answer

Answer

Answer

Question 10

Accepted Answer

Answer

Answer

Answer

Question 11

If m and n are integers, then what is the value of

Accepted Answer

Answer

Answer

<p>1 m &minus; n</p>

Answer

Question 12

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

Accepted Answer

Answer

Answer

Answer

Question 13

Accepted Answer

Answer

Answer

Answer

Question 14

The order and degree of the equation are

Accepted Answer

Answer

Answer

Answer

Question 15

The particular integral of (D² + 1)y = xe^2x is equal to

Accepted Answer

Answer

Answer

Answer

Question 16

If y=log logx, e^y(dy/dx)=

Accepted Answer

Answer

<p>(1/xlogx)</p>

Answer

Answer

Question 17

(d/dx)(log tan x)=

Accepted Answer

<h5>2 cosec 2x</h5>

Answer

<h5>cosec 2x</h5>

Answer

cosec (1/x)

Answer

cosec (-2x)

Question 18

If the normal at the point P(θ) to the ellipse ((x²/14)+(y²/5) = 1) intersects it again at the point Q(2θ), then cosθ is equal to

Accepted Answer

Answer

Answer

Answer

None of these

Question 19

If the latus rectum of an ellipse is one half of its minor axis, then its eccentricity is

Accepted Answer

Answer

Answer

Answer

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

Answer

Answer

Answer

<p>&radic;7</p>

Question 22

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)

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decreasing in (0, π/2)

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

Answer

none of these

Question 23

Sin (sin⁻¹1/2 + cos⁻¹1/2) equals

Accepted Answer

Answer

Answer

Answer

<p>1/&radic;2</p>

Question 24

If is finite, then the values of a,b are respectively

Accepted Answer

Answer

Answer

Answer

Question 25

If the value of a third order determinant is11, then the value of the square of the determinant formed by the co-factors will be

Accepted Answer

Answer

Answer

Answer

Question 26

Largest value of min (2 + x², 6 - 3x) when x > 0 is :

Accepted Answer

Answer

Answer

Answer

Question 27

If a complex number lies in the IIIrd quadrant then its conjugate lies in quadrant number

Accepted Answer

Answer

Answer

Answer

Question 28

The vertex of the parabola x ² + 8 x + 12 y + 4 = 0 is

Accepted Answer

<p>&minus; 4 , 1</p>

Answer

<p>4, &minus; 1</p>

Answer

− 4, − 1

Answer

Question 29

Axis of the parabola x² − 3 y − 6 x + 6 = 0 is

Accepted Answer

Answer

<p>x = &minus; 3</p>

Answer

<p>y = &minus; 1</p>

Answer

Question 30

Out of 15 points in a plane, no three are in a straight line except 8 points which are collinear. How many triangles can be formed by joining them?

Accepted Answer

Answer

Answer

Answer

WBJEE Sample Papers, Section Wise & Full Maths Test - 13 Free Online Test

MCQ Practice Test & Solutions: WBJEE Maths Test - 13 (75 Questions)

The positive integer just greater than (1 + .0001)¹⁰⁰⁰⁰ is

The inverse point of (1, 2) with respect to the circle x² + y² - 4x - 6y + 9 = 0 is

If the line lx+my=1 is a tangent line to the circle x²+y²=a2, the locus of (l,m) is

[(-1+√-3)/2]³ⁿ + [(-1-√-3)/2]³ⁿ =

The coefficients of three successive terms in the expansion of (1 + x)ⁿ are 165, 330 and 462 respectively, then the value of n will be

If x is positive, then the first negative terms in the expansion of 1 + x 27 5 is

If w is a cube root of unity, then the value of (1 + ω - ω)² (1 - ω + ω²) is

If m and n are integers, then what is the value of

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

The order and degree of the equation are

The particular integral of (D² + 1)y = xe^2x is equal to

If y=log logx, e^y(dy/dx)=

(d/dx)(log tan x)=

If the normal at the point P(θ) to the ellipse ((x²/14)+(y²/5) = 1) intersects it again at the point Q(2θ), then cosθ is equal to

If the latus rectum of an ellipse is one half of its minor axis, then its eccentricity is

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

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

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

Sin (sin⁻¹1/2 + cos⁻¹1/2) equals

If is finite, then the values of a,b are respectively

If the value of a third order determinant is11, then the value of the square of the determinant formed by the co-factors will be

Largest value of min (2 + x², 6 - 3x) when x > 0 is :

If a complex number lies in the IIIrd quadrant then its conjugate lies in quadrant number

The vertex of the parabola x ² + 8 x + 12 y + 4 = 0 is

Axis of the parabola x² − 3 y − 6 x + 6 = 0 is

Out of 15 points in a plane, no three are in a straight line except 8 points which are collinear. How many triangles can be formed by joining them?

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 - 13 Free Online Test

MCQ Practice Test & Solutions: WBJEE Maths Test - 13 (75 Questions)

The positive integer just greater than (1 + .0001)10000 is

The inverse point of (1, 2) with respect to the circle x2 + y2 - 4x - 6y + 9 = 0 is

If the line lx+my=1 is a tangent line to the circle x2+y2=a2, the locus of (l,m) is

[(-1+√-3)/2]3n + [(-1-√-3)/2]3n =

The coefficients of three successive terms in the expansion of (1 + x)n are 165, 330 and 462 respectively, then the value of n will be

If x is positive, then the first negative terms in the expansion of 1 + x 27 5 is

If w is a cube root of unity, then the value of (1 + ω - ω)2 (1 - ω + ω2) is

If m and n are integers, then what is the value of

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

The order and degree of the equation are

The particular integral of (D2 + 1)y = xe2x is equal to

If y=log logx, ey(dy/dx)=

(d/dx)(log tan x)=

If the normal at the point P(θ) to the ellipse ((x2/14)+(y2/5) = 1) intersects it again at the point Q(2θ), then cosθ is equal to

If the latus rectum of an ellipse is one half of its minor axis, then its eccentricity is

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

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

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

Sin (sin⁻11/2 + cos⁻11/2) equals

If is finite, then the values of a,b are respectively

If the value of a third order determinant is11, then the value of the square of the determinant formed by the co-factors will be

Largest value of min (2 + x2, 6 - 3x) when x > 0 is :

If a complex number lies in the IIIrd quadrant then its conjugate lies in quadrant number

The vertex of the parabola x 2 + 8 x + 12 y + 4 = 0 is

Axis of the parabola x 2 − 3 y − 6 x + 6 = 0 is

Out of 15 points in a plane, no three are in a straight line except 8 points which are collinear. How many triangles can be formed by joining them?

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 positive integer just greater than (1 + .0001)¹⁰⁰⁰⁰ is

The inverse point of (1, 2) with respect to the circle x² + y² - 4x - 6y + 9 = 0 is

If the line lx+my=1 is a tangent line to the circle x²+y²=a2, the locus of (l,m) is

[(-1+√-3)/2]³ⁿ + [(-1-√-3)/2]³ⁿ =

The coefficients of three successive terms in the expansion of (1 + x)ⁿ are 165, 330 and 462 respectively, then the value of n will be

If w is a cube root of unity, then the value of (1 + ω - ω)² (1 - ω + ω²) is

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

The particular integral of (D² + 1)y = xe^2x is equal to

If y=log logx, e^y(dy/dx)=

If the normal at the point P(θ) to the ellipse ((x²/14)+(y²/5) = 1) intersects it again at the point Q(2θ), then cosθ is equal to

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

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

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

Sin (sin⁻¹1/2 + cos⁻¹1/2) equals

Largest value of min (2 + x², 6 - 3x) when x > 0 is :

The vertex of the parabola x ² + 8 x + 12 y + 4 = 0 is

Axis of the parabola x² − 3 y − 6 x + 6 = 0 is