List of top Mathematics Questions

The general solution of the differential equation \[ \frac{dy}{dx} = \frac{2xy-4x+y-2}{2xy+x-4y-2} \] is:
Variance of the following discrete frequency distribution is \begin{tabular}{|l|c|c|c|c|c|} \hline Class Interval & 0-2 & 2-4 & 4-6 & 6-8 & 8-10
\hline Frequency (\(f_i\)) & 2 & 3 & 5 & 3 & 2
\hline \end{tabular}
A straight line passing through the origin \( O \) meets the parallel lines \( 4x + 2y = 9 \) and \( 2x + y + 6 = 0 \) at the points \( P \) and \( Q \) respectively. Then the point \( O \) divides the line segment \( PQ \) in the ratio
If \( 3\sqrt{2}x - 4y = 12 \) is a tangent to the hyperbola \(\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1\) and \(\frac{5}{4}\) is its eccentricity, then \( a^2 - b^2 = \)
If $ P(\bar{A}) = 0.3,\ P(B) = 0.4,\ P(A \cap \bar{B}) = 0.5 $, then find $ P(B / (A \cup \bar{B})) $
If the distance between the foci of a hyperbola H is 26 and distance between its directrices is \( \frac{50}{13} \), then the eccentricity of the conjugate hyperbola of the hyperbola H is
Evaluate the integral: \[ I = \int_0^x \frac{t^2}{\sqrt{a^2 + t^2}} dt \]
The lengths of the two focal chords of the parabola \( y^2 = 16x \) is 25 units each. If these two chords cut the parabola at \( A, B, C, D \), then the area (in sq. units) of the quadrilateral formed by \( A, B, C, D \) is:
If the tangent drawn at the point \( (x_1,y_1) \), \(x_1,y_1 \in N \) on the curve \( y = x^4 - 2x^3 + x^2 + 5x \) passes through origin, then \( x_1+y_1 = \)
The general solution of the differential equation \( \sec(x - y + 1) dy = dx \) is:
A line \(L_1\) passing through the point of intersection of the lines \(x-2y+3=0\) and \(2x-y=0\) is parallel to the Line \(L_2\). If \(L_2\) passes through origin and also through the point of intersection of the lines \(3x-y+2=0\) and \(x-3y-2=0\), then the distance between the lines \(L_1\) and \(L_2\) is
Find the slope of the line perpendicular to the line $ 3x + 4y - 12 = 0 $.
In a binomial distribution, if \(n=4\) and \( P(X=0) = \frac{16{81} \), then \( P(X=4) = \)}
The area of the region (in sq.units) bounded by the curves \(x^2 + y^2 = 16\) and \(x^2 + y^2 = 6x\) is?
If \(P(\alpha, \beta)\) is a point on the curve \(9x^2 + 4 y^2 = 144\) in the first quadrant and the minimum area of the triangle formed by the tangent of the curve at \(P\) with the coordinate axes is \(S\), then find \(S\).
If \( \left(\frac{2}{3},0\right) \) is the centroid of the triangle formed by the lines \( 4x^2 - y^2 = 0 \) and \( lx + my + n = 0 \), then \( l+m+n= \):
The general solution of the differential equation \[ \frac{dy}{dx} = \frac{2x^2 - xy - y^2}{x^2 - y^2} \]
If the difference of the roots of the equation $x^2 - 7x + 10 = 0$ is same as the difference of the roots of the equation $x^2 - 17x + k = 0$, then a divisor of $k$ is
If \((\alpha, \beta)\) is the external centre of similitude of the circles \[ x^2 + y^2 = 3 \] and \[ x^2 + y^2 - 2x + 4y + 4 = 0, \] then find \(\frac{\beta}{\alpha}\).
If the sum of the roots of the quadratic equation $ x^2 - 5x + k = 0 $ is 5, find the value of $ k $.
If \( A = (0, 4, -3),\ B = (5, 0, 12),\ C = (7, 24, 0) \), then \( \angle BAC = \)
If \( A + B = \frac{\pi}{4} \), then \( \dfrac{\cos B - \sin B}{\cos B + \sin B} \) is equal to:
If \( x \ne (2n+1)\frac{\pi{4} \), then the general solution of \( \cos x + \cos 3x = \sin x + \sin 3x \) is}
In \( \triangle ABC \), if \( \sin^2 B = \sin A \) and \( 2\cos^2 A = 3\cos^2 B \), then the triangle is:
The number of ways of arranging 3 red, 2 white, and 4 blue flowers of different sizes into a garland such that no two blue flowers come together is: