WBJEE Maths Test - 14

Question 1

The coefficients x^p and x^q in the expansion of (1+x)^(p+q) (where p and q are positive integers) are

Accepted Answer

<h5>equal</h5>

Answer

equal but of opposite signs

Answer

reciprocal of each other

Answer

none of these

Question 2

The first three terms in the expansion of (1 + ax)ⁿ (n ≠ 0) are 1, 6x and 16x ². Then the values of a and n are respectively

Accepted Answer

Answer

Answer

Answer

Question 3

In the expansion of (1+x)⁽²ⁿ⁺²⁾ the maximum coefficient is :

Accepted Answer

[(2n+2)!/{(n+1)!}²]

Answer

[(2n!)/(n!)²]

Answer

[(2n+2)!/{n!(n+1)!}]

Answer

[(2n)!/{n!(n+1)!}]

Question 4

The polar of a point P w.r.t a circle of radius a touching both x and y axis and lying in the first quadrant is x + 2y = 4a. The coordinates of P are

Accepted Answer

Answer

Answer

Answer

Question 5

The limiting point of the system of co-axial circles x²+y²-6x-6y+4=0, x²+y²-2x-4y+3=0 is

Accepted Answer

Answer

Answer

Answer

Question 6

Accepted Answer

<p>e /2 &minus; 1</p>

Answer

Answer

<p>e &minus; 1/  2</p>

Answer

<p>e &minus; 3/  2</p>

Question 7

Find the value of

Accepted Answer

<p>&omega;</p>

Answer

Answer

<p>&omega; 2</p>

Answer

Question 8

Accepted Answer

Answer

Answer

Answer

Question 9

Accepted Answer

Answer

Answer

Answer

Question 10

Accepted Answer

Answer

Answer

Answer

Question 11

Let f(x) be a function satisfying f ′ x = f x with f(0) = 1 and g(x) be a function that satisfies f(x) + g(x) = x², then value of integral
is equal to

Accepted Answer

Answer

Answer

Answer

Question 12

Accepted Answer

Answer

Answer

Answer

Question 13

Accepted Answer

Answer

Answer

Answer

Question 14

If x dy = y(dx + y dy), y > 0 and y (1) = 1, then y (-3) is equal to

Accepted Answer

Answer

Answer

Answer

Question 15

Solution of cos x dy/dx+y sin x =1 is

Accepted Answer

y sec x = tan x + c

Answer

y sec x tan x = c

Answer

y tan x = secx + c

Answer

y tan x = sec x tan x + c

Question 16

If y = 2^ax and

\frac{d y}{d x}

= log 256 at x = 1, then a =

Accepted Answer

Answer

Answer

Answer

Question 17

The number of points at which the function f(x)=|x-0.5|+|x-1|+tanx is not differentiable in (0,2) is

Accepted Answer

Answer

Answer

Answer

Question 18

The eccentricity of the conic 9x² + 25y² = 225 is

Accepted Answer

Answer

Answer

Answer

Question 19

S and T are the foci of an ellipse and B is an end of the minor axis. If STB is an equilateral triangle then the eccentricity of the ellipse is

Accepted Answer

$\frac{1}{2}$

Answer

$\frac{1}{2}$

Answer

$\frac{1}{2}$

Answer

$\frac{1}{2}$

Question 20

The st. line lx + my + n = 0 touches the hyperbola x²/a² - y²2/b² = 1 if

Accepted Answer

a²l² - b²m² = n²

Answer

a²l² + m² = n²b²

Answer

a² + b² = n²(l²+ m²)

Answer

a²l² + b²m² = n²

Question 21

The line y = 4x + c touches the hyperbola x² - y² = 1 if

Accepted Answer

Answer

Answer

Answer

Question 22

The equation x + e^x = 0 has

Accepted Answer

only one real root

Answer

only two real roots

Answer

no real root

Answer

none of these

Question 23

tan⁻¹(1/7)+2tan⁻¹(1/3)=

Accepted Answer

Answer

Answer

Answer

Question 24

Accepted Answer

Answer

Answer

Answer

log a /log b

Question 25

If A is a singular matrix, then Adj A is

Accepted Answer

<h5>singular</h5>

Answer

non-singular

Answer

<h5>symmetric</h5>

Answer

not defined

Question 26

The maximum value of x³ - 3x in [0,2] is

Accepted Answer

Answer

Answer

Answer

Question 27

If |z₁|=|z₂| and amp. z₁+amp.z₂=0, then

Accepted Answer

z₁̅ =z₂

Answer

Answer

z₁+z₂=0

Answer

z₁̅=z₂̅

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 line y=mx+c touches the parabola x²=4ay if

Accepted Answer

Answer

Answer

Answer

Question 30

Five digit number divisible by 3 is formed using the digits 0, 1 , 2, 3, 4 and 5 without repetition. Total number of such numbers is

Accepted Answer

Answer

Answer

Answer

WBJEE Sample Papers, Section Wise & Full Maths Test - 14 Free Online Test

MCQ Practice Test & Solutions: WBJEE Maths Test - 14 (75 Questions)

The coefficients x^p and x^q in the expansion of (1+x)^(p+q) (where p and q are positive integers) are

The first three terms in the expansion of (1 + ax)ⁿ (n ≠ 0) are 1, 6x and 16x ². Then the values of a and n are respectively

In the expansion of (1+x)⁽²ⁿ⁺²⁾ the maximum coefficient is :

The polar of a point P w.r.t a circle of radius a touching both x and y axis and lying in the first quadrant is x + 2y = 4a. The coordinates of P are

The limiting point of the system of co-axial circles x²+y²-6x-6y+4=0, x²+y²-2x-4y+3=0 is

Find the value of

Let f(x) be a function satisfying f ′ x = f x with f(0) = 1 and g(x) be a function that satisfies f(x) + g(x) = x², then value of integral
is equal to

If x dy = y(dx + y dy), y > 0 and y (1) = 1, then y (-3) is equal to

Solution of cos x dy/dx+y sin x =1 is

If y = 2^ax and $\frac{d y}{d x}$ = log 256 at x = 1, then a =

The number of points at which the function f(x)=|x-0.5|+|x-1|+tanx is not differentiable in (0,2) is

The eccentricity of the conic 9x² + 25y² = 225 is

S and T are the foci of an ellipse and B is an end of the minor axis. If STB is an equilateral triangle then the eccentricity of the ellipse is

The st. line lx + my + n = 0 touches the hyperbola x²/a² - y²2/b² = 1 if

The line y = 4x + c touches the hyperbola x² - y² = 1 if

The equation x + e^x = 0 has

tan⁻¹(1/7)+2tan⁻¹(1/3)=

If A is a singular matrix, then Adj A is

The maximum value of x³ - 3x in [0,2] is

If |z₁|=|z₂| and amp. z₁+amp.z₂=0, then

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

The line y=mx+c touches the parabola x²=4ay if

Five digit number divisible by 3 is formed using the digits 0, 1 , 2, 3, 4 and 5 without repetition. Total number of such numbers is

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 - 14 Free Online Test

MCQ Practice Test & Solutions: WBJEE Maths Test - 14 (75 Questions)

The coefficients xp and xq in the expansion of (1+x)(p+q) (where p and q are positive integers) are

The first three terms in the expansion of (1 + ax)n (n ≠ 0) are 1, 6x and 16x 2. Then the values of a and n are respectively

In the expansion of (1+x)(2n+2) the maximum coefficient is :

The polar of a point P w.r.t a circle of radius a touching both x and y axis and lying in the first quadrant is x + 2y = 4a. The coordinates of P are

The limiting point of the system of co-axial circles x2+y2-6x-6y+4=0, x2+y2-2x-4y+3=0 is

Find the value of

Let f(x) be a function satisfying f ′ x = f x with f(0) = 1 and g(x) be a function that satisfies f(x) + g(x) = x2, then value of integral is equal to

If x dy = y(dx + y dy), y > 0 and y (1) = 1, then y (-3) is equal to

Solution of cos x dy/dx+y sin x =1 is

If y = 2ax and dydx = log 256 at x = 1, then a =

The number of points at which the function f(x)=|x-0.5|+|x-1|+tanx is not differentiable in (0,2) is

The eccentricity of the conic 9x2 + 25y2 = 225 is

S and T are the foci of an ellipse and B is an end of the minor axis. If STB is an equilateral triangle then the eccentricity of the ellipse is

The st. line lx + my + n = 0 touches the hyperbola x2/a2 - y22/b2 = 1 if

The line y = 4x + c touches the hyperbola x2 - y2 = 1 if

The equation x + ex = 0 has

tan⁻1(1/7)+2tan⁻1(1/3)=

If A is a singular matrix, then Adj A is

The maximum value of x3 - 3x in [0,2] is

If |z₁|=|z₂| and amp. z₁+amp.z₂=0, then

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

The line y=mx+c touches the parabola x2=4ay if

Five digit number divisible by 3 is formed using the digits 0, 1 , 2, 3, 4 and 5 without repetition. Total number of such numbers 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 coefficients x^p and x^q in the expansion of (1+x)^(p+q) (where p and q are positive integers) are

The first three terms in the expansion of (1 + ax)ⁿ (n ≠ 0) are 1, 6x and 16x ². Then the values of a and n are respectively

In the expansion of (1+x)⁽²ⁿ⁺²⁾ the maximum coefficient is :

The limiting point of the system of co-axial circles x²+y²-6x-6y+4=0, x²+y²-2x-4y+3=0 is

Let f(x) be a function satisfying f ′ x = f x with f(0) = 1 and g(x) be a function that satisfies f(x) + g(x) = x², then value of integral
is equal to

If y = 2^ax and $\frac{d y}{d x}$ = log 256 at x = 1, then a =

The eccentricity of the conic 9x² + 25y² = 225 is

The st. line lx + my + n = 0 touches the hyperbola x²/a² - y²2/b² = 1 if

The line y = 4x + c touches the hyperbola x² - y² = 1 if

The equation x + e^x = 0 has

tan⁻¹(1/7)+2tan⁻¹(1/3)=

The maximum value of x³ - 3x in [0,2] is

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

The line y=mx+c touches the parabola x²=4ay if