List of top Mathematics Questions

The probability of choosing randomly a number \( c \) from the set \( \{1, 2, 3, \dots, 9\} \) such that the quadratic equation \( x^2 + 4x + c = 0 \) has real roots, is
Five persons A, B, C, D and E are in queue at a shop. The probability that A and B are always together is.
If the probability for A to fail in an examination is 0.2 and that for B is 0.3, then the probability that either A or B fail is.
Three vertices are chosen randomly from the seven vertices of a regular 7-sided polygon. The probability that they form the vertices of an isosceles triangle is.
If A, B, and C are three mutually exclusive and exhaustive events such that \( P(A) = 2P(B) = 3P(C) \). What is \( P(B) \)?
A multiple choice examination has 5 questions. Each question has three alternative answers of which exactly one is correct. The probability that a student will get 4 or more correct answers just by guessing is
If \( \theta \) be the angle between the vectors \( a = 2\hat{i} + 2\hat{j} - \hat{k} \) and \( b = 6\hat{i} - 3\hat{j} + 2\hat{k} \), then
If \( x, y \) and \( z \) are non-zero real numbers and \( a = x\hat{i} + 2\hat{j}, b = y\hat{j} + 3\hat{k} \) and \( c = x\hat{i} + y\hat{j} + z\hat{k} \) are such that \( a \times b = z\hat{i} - 3\hat{j} + \hat{k} \), then \( [abc] \) is equal to
If \( p = \hat{i} + \hat{j}, q = 4\hat{k} - \hat{j} \) and \( r = \hat{i} + \hat{k} \), then the unit vector in the direction of \( 3p + q - 2r \) is
The line \( \frac{x-3}{4} = \frac{y-4}{5} = \frac{z-5}{6} \) is parallel to the plane.
The angle between the lines \( \frac{x+4}{3} = \frac{y-1}{5} = \frac{z+3}{4} \) and \( \frac{x+1}{1} = \frac{y-4}{1} = \frac{z-5}{2} \)
The point of intersection of the lines \( \frac{x - 1}{1} = \frac{y - 1}{2} = \frac{z - 2}{3} \) and \( \frac{x - 5}{2} = \frac{y - 2}{1} = \frac{z - 5}{2} \)
If \( ^nC_3 = 220 \), then \( n = \ ? \)
There are 12 points in a plane out of which 3 points are collinear. How many straight lines can be drawn by joining any two of them?
A regular polygon of \( n \) sides has 170 diagonals. Then \( n \) is equal to:
The point \( (-3, -2) \) lies
The maximum of \( Z \) is where, \( Z = 4x + 2y \) subject to constraints \[ 4x + 2y \geq 46, \quad x + 3y \leq 24, \quad x, y \geq 0 \]
Maximum value of \( z = 12x + 3y \), subject to constraints \( x \geq 0, y \geq 0, x + y \leq 5 \) and \( 3x + y \leq 9 \) is
The equation of the pair of angle bisectors of the line \( x^2 - 4xy - 5y^2 = 0 \) is:
The distance of point \( (1, 2) \) from line \( x + y + 2 = 0 \) measured along the line parallel to \( 2x - y = 5 \) is equal to:
The slope of lines which makes an angle \( 45^\circ \) with the line \( 2x - y = -7 \)
If 2 and 3 are intercepts of a line \( L = 0 \), then the distance of \( L \equiv 0 \) from the origin is
\(y = tan^{-1} (\frac{4 sin 2x}{cos 2x - 6sin^2x})\) then \(\frac{dy}{dx}\) at \(x=0\).

lim(x→0)\((\frac {1+tanx}{1+sinx})^{cosec x}\) = ?

20 meters of wire is available to fence of a flowerbed in the form of a circular sector. If the flowerbed is to have maximum surface area, then the radius of the circle is