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List of top Mathematics Questions

In a triangle ABC, if $ r_1 = 2r_2 = 3r_3 $, then $\sin A$: $\sin B$: $\sin C$ = Options:

The domain of the real valued function $ f(x) = \frac{1}{\sqrt{log_{0.5}(2x-3)}} + \sqrt{4 - 9x^2} $ is:

Simplify the expression: $ 4 + \frac{1}{4 + \frac{1}{4 + \frac{1}{4 + \cdots}}} $

The difference of the order and degree of the differential equation \[ \left(\frac{d^2y}{dx^2} \right)^{-7/2} - \left(\frac{d^3y}{dx^3} \right)^2 - \left(\frac{d^2y}{dx^2} \right)^{-5/2} - \left(\frac{d^4y}{dx^4} \right) = 0 \]

If the differential equation $$ x \, dy + (y + y^2 x) \, dx = 0 $$ with condition $ y = 1 $ at $ x = 1 $, then the solution is:

The solution of the differential equation \[ x dy - y dx = \sqrt{x^2 + y^2} dx \] when $ y(\sqrt{3}) = 1 $ is:

The angle subtended by the chord $ x + y - 1 = 0 $ of the circle $ x^2 + y^2 - 2x + 4y + 4 = 0 $ at the origin is:

The system of equations $ x + 2y + 3z = 6 $, $ x + 3y + 5z = 9 $, $ 2x + 5y + az = 12 $ has no solution when $ a = $:

Point (-1, 2) is changed to (a, b) when the origin is shifted to the point (2, -1) by translation of axes. Point (a, b) is changed to (c, d) when the axes are rotated through an angle of 45$^{\circ}$ about the new origin. (c, d) is changed to (e, f) when (c, d) is reflected through y = x. Then (e, f) = ?

In a triangle ABC, if $ (a-b)(s-c) = (b-c)(s-a) $, then $ r_1 + r_3 = $:

If $\lim_{n\rightarrow\infty}[(1+\frac{1}{n^{2}})(1+\frac{4}{n^{2}})(1+\frac{9}{n^{2}})\cdots(1+\frac{n^{2}}{n^{2}})]^{\frac{1}{n}}=ae^{b}$, then a+b=

If the area of the circum-circle of the triangle formed by the line 2x + 5y + a = 0 and the positive coordinate axes is $\frac{29\pi}{4}$ sq. units, then |a| =

If m and M denote the mean deviations about mean and about median respectively of the data 20, 5, 15, 2, 7, 3, 11, then the mean deviation about the mean of m and M is:

If $ y = f(x) $ is a thrice differentiable function and a bijection, then \[ \frac{d^2x}{dy^2} \left(\frac{dy}{dx}\right)^3 + \frac{d^2y}{dx^2} = ? \]

If all the letters of the word MASTER are permuted in all possible ways and words (with or without meaning) thus formed are arranged in dictionary order, then the rank of the word MASTER is:

If set $ A $ contains 8 elements, then the number of subsets of $ A $ which contain at least 6 elements is:

If $ \alpha, \beta, \gamma $ are roots of the equation $ x^3 + ax^2 + bx + c = 0 $, then $ \alpha^{-1} + \beta^{-1} + \gamma^{-1} $ is:

Find the shortest distance between the skew lines $\vec{r} = (-\hat{i} - 2\hat{j} - 3\hat{k}) + t(3\hat{i} - 2\hat{j} - 2\hat{k})$ and $\vec{r} = (7\hat{i} + 4\hat{k}) + s(\hat{i} - 2\hat{j} + 2\hat{k})$.

The perpendicular distance from the point $ (-1,1,0) $ to the line joining the points $ (0,2,4) $ and $ (3,0,1) $ is:

A line $ L $ passes through $ (1,2,-3) $ and $ (3,3,-1) $, and a plane $ \pi $ passes through $ (2,1,-2), (-2,-3,6), (0,2,-1) $. If $ \theta $ is the angle between $ L $ and $ \pi $, then $ 27 \cos^2 \theta = $ ?

Let a and b be two non-collinear vectors of unit modulus. If u = a − (a · b)b and v = a × b, then ∥v∥ = ?

In a consignment of 15 articles, it is found that 3 are defective. If a sample of 5 articles is chosen at random from it, then the probability of having 2 defective articles is:

The normal drawn at a point $ (2, -4) $ on the parabola $ y^2 = 8x $ cuts again the same parabola at $ (\alpha, \beta) $. Then $ \alpha + \beta $ is:

The locus of the midpoints of the chords of the hyperbola $ x^2 - y^2 = a^2 $ which touch the parabola $ y^2 = 4ax $ is:

If the product of the eccentricities of the ellipse $ \frac{x^2}{16} + \frac{y^2}{b^2} = 1 $ and the hyperbola $ \frac{x^2}{9} - \frac{y^2}{16} = 1 $ is 1, then the value of $ b^2 $ is: