12th Maths Important 5 Mark Question Paper

St. Britto Hr. Sec. School - Madurai

12th Maths Important 5 Mark Question Paper-Aug 2020

Time : 2.00 Hours

Part - A

Generic 5 - Answer All Question

Two cards are drawn simultaneously from a well shuffled pack of 52 cards. Find the mean and
variance of the number of red cards.

Solve the differential equation: (x³ +y³ ) dy-x² ydx=0

By vector method, prove that cos(α + β) = cos α cos β - sin α sin β

Solve \(\left(y+\sqrt{x^2+y^2}\right)\)dx − xdy = 0, y(1) = 0

Find the point of intersection of the lines \(\frac { x-1 }{ 2 } =\frac { y-2 }{ 3 } =\frac { z-3 }{ 4 } \) and \(\frac { x-4 }{ 5 } =\frac { y-1 }{ 2 } =z\)

If F is the constant force generated by the motor of an automobile of mass M, its velocity is given by
M \(\frac{dV}{dt}\)=F-kV, where k is a constant. Express V in terms of t given that V = 0 when t = 0.

Solve the differential equation: (x² +y²)dy = xy dx. It is given that y(1) = 1 and y(x₀ ) = e. Find the value of x .

Find the equation of the circle passing through the points(1,1), (2,-1) , and(3,2) .

Solve :\(x=\frac{dy}{dx}sin\left(\frac{y}{x}\right)+x-ysin\left(y\frac{y}{x}\right)=,y(1)=\frac{\pi}{2}\)

Solve (x² -3y²) dx xydy= 0.

Let z₁ ,z₂ , and z₃ be complex numbers such that \(\left| { z }_{ 1 } \right| =\left| { z }_{ 2 } \right| =\left| { z }_{ 3 } \right| \) = r > 0 and z₁ +z₂ +z₃ ≠ 0 prove

that \(\left| \frac { { z }_{ 1 }{ z }_{ 2 }+{ z }_{ 2 }{ z }_{ 3 }+{ z }_{ 3 }{ z }_{ 1 } }{ { z }_{ 1 }+{ z }_{ 2 }+{ z }_{ 3 } } \right| \) =r

If the Cartesian equation of a plane is 3x - 4y + 3z = -8, find the vector equation of the plane in the standard form.

Solve the Linear differential equation: \(\frac{dy}{dx}\)+\(\frac{3y}{x}\)=\(\frac{1}{x^2}\), given that y=2 when x=1

Solve the equation (2x-3)(6x-1)(3x-2)(x-12)-7=0

Suppose that f (x) given below represents a probability mass function

X

1

2

3

4

5

6

f(X)

c²

2c²

3c²

4c²

c

2c

Find
(i) the value of c
(ii) Mean and variance.

Solve the differential equation: tan y \(\frac{dy}{dx}\)=cos(x+y)+cos(x-y)

Solve :x² dy+y(x+y)dx=0 given that y=1 when x=1.

Let X be a random variable denoting the life time of an electrical equipment having probability
density function

f(x) = \(\begin{cases} k e^{ − 2x} \quad forx > 0 \\ 0 \quad forx ≤ 0 \end{cases}\)

Find
(i) the value of k
(ii) Distribution function
(iii) P(X < 2)
(iv) calculate the probability that X is at least for four unit of time
(v) P(X = 3)

Form the equation whose roots are the squares of the roots of the cubic equation x³+ax²+bx+c = 0.

Solve ye^y dx=(y³ +2xe^y)dy

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12th Maths Important 5 Mark Question Paper

St. Britto Hr. Sec. School - Madurai

12th Maths Important 5 Mark Question Paper-Aug 2020

Part - A

Generic 5 - Answer All Question

Two cards are drawn simultaneously from a well shuffled pack of 52 cards. Find the mean and variance of the number of red cards.

Solve the differential equation: (x3 +y3 ) dy-x2 ydx=0

By vector method, prove that cos(α + β) = cos α cos β - sin α sin β

Solve \(\left(y+\sqrt{x^2+y^2}\right)\)dx − xdy = 0, y(1) = 0

Find the point of intersection of the lines \(\frac { x-1 }{ 2 } =\frac { y-2 }{ 3 } =\frac { z-3 }{ 4 } \) and \(\frac { x-4 }{ 5 } =\frac { y-1 }{ 2 } =z\)

If F is the constant force generated by the motor of an automobile of mass M, its velocity is given by M \(\frac{dV}{dt}\)=F-kV, where k is a constant. Express V in terms of t given that V = 0 when t = 0.

Solve the differential equation: (x2 +y2)dy = xy dx. It is given that y(1) = 1 and y(x0 ) = e. Find the value of x .

Find the equation of the circle passing through the points(1,1), (2,-1) , and(3,2) .

Solve :\(x=\frac{dy}{dx}sin\left(\frac{y}{x}\right)+x-ysin\left(y\frac{y}{x}\right)=,y(1)=\frac{\pi}{2}\)

Solve (x2 -3y2) dx xydy= 0.

If the Cartesian equation of a plane is 3x - 4y + 3z = -8, find the vector equation of the plane in the standard form.

Solve the Linear differential equation: \(\frac{dy}{dx}\)+\(\frac{3y}{x}\)=\(\frac{1}{x^2}\), given that y=2 when x=1

Solve the equation (2x-3)(6x-1)(3x-2)(x-12)-7=0

Suppose that f (x) given below represents a probability mass function X 1 2 3 4 5 6 f(X) c2 2c2 3c2 4c2 c 2c Find (i) the value of c (ii) Mean and variance.

Solve the differential equation: tan y \(\frac{dy}{dx}\)=cos(x+y)+cos(x-y)

Solve :x2 dy+y(x+y)dx=0 given that y=1 when x=1.

Form the equation whose roots are the squares of the roots of the cubic equation x3+ax2+bx+c = 0.

Solve yey dx=(y3 +2xey)dy

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Tamilnadu Stateboardszs - Class

Two cards are drawn simultaneously from a well shuffled pack of 52 cards. Find the mean and
variance of the number of red cards.

Solve the differential equation: (x³ +y³ ) dy-x² ydx=0

If F is the constant force generated by the motor of an automobile of mass M, its velocity is given by
M \(\frac{dV}{dt}\)=F-kV, where k is a constant. Express V in terms of t given that V = 0 when t = 0.

Solve the differential equation: (x² +y²)dy = xy dx. It is given that y(1) = 1 and y(x₀ ) = e. Find the value of x .

Solve (x² -3y²) dx xydy= 0.

Suppose that f (x) given below represents a probability mass function

X

1

2

3

4

5

6

f(X)

c²

2c²

3c²

4c²

c

2c

Find
(i) the value of c
(ii) Mean and variance.

Solve :x² dy+y(x+y)dx=0 given that y=1 when x=1.

Form the equation whose roots are the squares of the roots of the cubic equation x³+ax²+bx+c = 0.

Solve ye^y dx=(y³ +2xe^y)dy