List of top Mathematics Questions on types of differential equations

Let the system of equations \(x+2y+3z = 5\), \(2x+3y+z = 9\), \(4x+3y+λz = μ\) have an infinite number of solutions. Then \(λ + 2μ\) is equal to

If \( m_1 \) and \( m_2 \) are the slopes of the direct common tangents drawn to the circles \[ x^2 + y^2 - 2x - 8y + 8 = 0 \quad \text{and} \quad x^2 + y^2 - 8x + 15 = 0 \] then \( m_1 + m_2 \) is:

If the focus of an ellipse is \((-1,-1)\), equation of its directrix corresponding to this focus is \(x + y + 1 = 0\) and its eccentricity is \(\frac{1}{\sqrt{2}}\), then the length of its major axis is:

The axis of a parabola is parallel to Y-axis. If this parabola passes through the points \( (1,0), (0,2), (-1,-1) \) and its equation is \( ax^2 + bx + cy + d = 0 \), then \( \frac{ad}{bc} \) is:

If \( (1,1) \) is the vertex and \( x + y + 1 = 0 \) is the directrix of a parabola. If \( (a, b) \) is its focus and \( (c, d) \) is the point of intersection of the directrix and the axis of the parabola, then \( a + b + c + d \) is:

A circle \( S \) passes through the points of intersection of the circles \( x^2 + y^2 - 2x - 3 = 0 \) and \( x^2 + y^2 - 2y = 0 \). If \( x + y + 1 = 0 \) is a tangent to the circle \( S \), then the equation of \( S \) is:

If the common chord of the circles \( x^2 + y^2 - 2x + 2y + 1 = 0 \) and \( x^2 + y^2 - 2x - 2y - 2 = 0 \) is the diameter of a circle \( S \), then the centre of the circle \( S \) is:

If the normal drawn at the point \((2, -1)\) to the ellipse \(x^2 + 4y^2 = 8\) meets the ellipse again at \((a, b)\), then \(17a\) is:

P(\( \theta \)) is a point on the hyperbola \( \frac{x^2}{a^2} - \frac{y^2}{9} = 1 \), S is its focus lying on the positive X-axis and Q = (0,1). If SQ = \( \sqrt{26} \) and SP = 6, then \( \theta \) is:

A circle \( S \equiv x^2 + y^2 + 2gx + 2fy + 6 = 0 \) cuts another circle \[ x^2 + y^2 - 6x - 6y - 6 = 0 \] orthogonally. If the angle between the circles \( S = 0 \) and \[ x^2 + y^2 + 6x + 6y + 2 = 0 \] is 60°, then the radius of the circle \( S = 0 \) is:

The point of intersection of two tangents drawn to the hyperbola \[ \frac{x^2}{a^2} - \frac{y^2}{4} = 1 \] lie on the circle \[ x^2 + y^2 = 5. \] If these tangents are perpendicular to each other, then \( a \) is:

If the coefficient of x⁷ in (\(ax^2 +\frac{ 1}{2bx}^{11}\)) and x^-7 in (\(ax - \frac{1}{3bx^2}^{11}\)), are euual then

\(lim _{n→∞}{(2^½-2^½)(2^½-2^½)….(2^½-^2{\frac{1}{2n+1}})}\) is equal to

Let s₁, s₂, s₃,…..,s₁₀ respectively be the sum to 12 terms of 10 A.P.s whose first terms are 1,2,3, …. ,10 and the common differences are 1, 3, 5, …. , 19 respectively. Then  \(10∑^{10}_{i=1} s_i\) is

\(max\\{0≤x≤π}\) \(\{x−2\,\, sin. x \,\,cos+\frac{1}{3} sin\,\, 3x \}=\)

The negation of the statement \(((A\land(B\lor C)) ⇒ (A\lor B)) ⇒ A\) is

If the system of equations  
x + y + az = b  
2x + 5y + 2z = 6  
x + 2y + 3z = 3  
Has infinitely many solutions, then 2a + 3b is equal to

if \(2x^y+3y^x=20\) then \(\frac{dy}{dx}\) at (2,2) is equal to:

If the point \((α ,\frac{7√3}{3}) \)lies on the curve traced by the mid-points of the line segments of the lines x cosθ + y sinθ = 7, θ ∈ (0 , \(\frac{π}{2}\) )  between the coordinates axes, then α is equal to 

Two dice A and B are rolled, Let the numbers obtained on A and B be α and β respectively. If the variance of α - β is \(\frac{p}{q}\), where p and q are coprime, then the sum of the positive divisors of p is equal to