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List of top Mathematics Questions

If $ 2x^2 + 3x - 2 = 0 $ and $ 3x^2 + \alpha x - 2 = 0 $ have one common root, then the sum of all possible values of $ \alpha $ is:

The sum of the order and degree of the differential equation: \[ \frac{d^y}{dx^t} = c + \left( \frac{d^y}{dx^t} \right)^{\frac{3}{2}} \] is:

The general solution of the differential equation \[ (x + y)y \,dx + (y - x)x \,dy = 0 \] is:

The general solution of the differential equation $$ (y^2 + x + 1) \, dy = (y + 1) \, dx $$ is:

Match the items of List-I with those of List-II (Here $ \Delta $ denotes the area of $ \triangle ABC $).

Then the correct match is

A line $ L $ intersects the lines $ 3x - 2y - 1 = 0 $ and $ x + 2y + 1 = 0 $ at the points $ A $ and $ B $. If the point $ (1,2) $ bisects the line segment $ AB $ and $ \frac{a}{b} x + \frac{b}{a} y = 1 $ is the equation of the line $ L $, then $ a + 2b + 1 = ? $

If the origin is shifted to a point $ P $ by the translation of axes to remove the $ y $-term from the equation $ x^2 - y^2 + 2y - 1 = 0 $, then the transformed equation of it is:

If the equation of the pair of straight lines passing through the point $ (1, 1) $ and perpendicular to the pair of lines $ 3x^2 + 11xy - 4y^2 = 0 $ is $ ax^2 + 2hxy + by^2 + 2gx + 2fy + 12 = 0 $, then find $ 2(a + h - b - g + f - 12) = ? $

Let $ f(x) = 3 + 2x $ and $ g_n(x) = (f \circ f \circ \dots \text{n times}) (x) $. If for all $ n \in \mathbb{N} $, the lines $ y = g_n(x) $ pass through a fixed point $ (a, \beta) $, then $ \alpha + \beta = ? $

Let $ a>1 $ and $ 0<b<1 $. -∞$ f : \mathbb{R} \to [0, 1] $ is defined by $ f(x) = \begin{cases} a^x & \text{if } x<0 b^x & \text{if } 0 \leq x \leq 1 \end{cases} $, then $ f(x) $ is:

Let $ \overline{X} $ and $ \overline{Y} $ be the arithmetic means of the runs of two batsmen A and B in 10 innings respectively, and $ \sigma_A, \sigma_B $ are the standard deviations of their runs in them. If batsman A is more consistent than B, then he is also a higher run scorer only when

If $ P(x) = x^5 + ax^4 + bx^3 + cx^2 + dx + e $ is a polynomial such that: \[ P(0) = 1, \quad P(1) = 2, \quad P(2) = 5, \] \[ P(3) = 10, \quad P(4) = 17, \] then find the value of $ P(5) $=

If $ y = \tan(\log x) $, then $ \frac{d^2y}{dx^2} $ is given by:

If $ A(1,0,2) $, $ B(2,1,0) $, $ C(2,-5,3) $, and $ D(0,3,2) $ are four points and the point of intersection of the lines $ AB $ and $ CD $ is $ P(a,b,c) $, then $ a + b + c = ? $

If a polygon of $ n $ sides has 275 diagonals, then $ n $ is:

If the slope of one line of the pair of lines $ 2x^2 + hxy + 6y^2 = 0 $ is thrice the slope of the other line, then $ h $ = ?

If a circle of radius 4 cm passes through the foci of the hyperbola $ \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 $ and is concentric with the hyperbola, then the eccentricity of the conjugate hyperbola of that hyperbola is:

If a tangent to the hyperbola $ x^2 - \frac{y^2}{3} = 1 $ is also a tangent to the parabola $ y^2 = 8x $, then the equation of such tangent with the positive slope is:

The number of positive divisors of 1080 is:

A line $ L $ passing through the point $ (2,0) $ makes an angle $ 60^\circ $ with the line $ 2x - y + 3 = 0 $. If $ L $ makes an acute angle with the positive X-axis in the anticlockwise direction, then the Y-intercept of the line $ L $ is?

If the point $ P $ represents the complex number $ z = x + iy $ in the Argand plane and if \[ \frac{z\bar{z} + 1}{z - 1} \] is a purely imaginary number, then the locus of $ P $ is:

A common tangent to the circle $ x^2 + y^2 = 9 $ and the parabola $ y^2 = 8x $ is

If \[ A = \begin{bmatrix} 1 & 0 & 2\\ 2 & 1 & 3 \\3 & 2 & 4 \end{bmatrix}, \] then evaluate $ A^2 - 5A + 6I $=

S is the sample space and A, B are two events of a random experiment. Match the items of List A with the items of List B.

Then the correct match is:

The distance from a point $ (1,1,1) $ to a variable plane $\pi$ is 12 units and the points of intersections of the plane with X, Y, Z-axes are $ A, B, C $ respectively. If the point of intersection of the planes through the points $ A, B, C $ and parallel to the coordinate planes is $ P $, then the equation of the locus of $ P $ is: