List of top Mathematics Questions

If Q \( (\alpha, \beta, \gamma) \) is the harmonic conjugate of the point P(0,-7,1) with respect to the line segment joining the points (2,-5,3) and (-1,-8,0), then \( \alpha - \beta + \gamma = \)
If the equation of the tangent of the hyperbola \( 5x^2 - 9y^2 - 20x - 18y - 34 = 0 \) which makes an angle \( 45^\circ \) with the positive X-axis in positive direction is \( x+by+c=0 \) then \( b^2+c^2 = \)
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
If two sides of a triangle are represented by \( 3x^2 - 5xy + 2y^2 = 0 \) and its orthocentre is (2,1), then the equation of the third side is
If \( \left(\frac{1}{10}, \frac{-1}{5}\right) \) is the inverse point of a point (-1, 2) with respect to the circle \( x^2+y^2-2x+4y+c=0 \) then c =
If \( ax^2 + 2hxy - 2ay^2 + 3x + 15y - 9 = 0 \) represents a pair of lines intersecting at (1,1), then ah =
If the point of contact of the circles \( x^2+y^2-6x-4y+9=0 \) and \( x^2+y^2+2x+2y-7=0 \) is \( (\alpha, \beta) \), then \( 7\beta = \)
A circle passing through the point (1,0) makes an intercept of length 4 units on X-axis and an intercept of length \(2\sqrt{11}\) units on Y-axis. If the centre of the circle lies in the fourth quadrant, then the radius of the circle is
If the equation of the circle lying in the first quadrant, touching both the coordinate axes and the line \( \frac{x}{3} + \frac{y}{4} = 1 \) is \( (x-c)^2+(y-c)^2=c^2 \), then c =
If the lines \(x+y-2=0\), \(3x-4y+1=0\) and \(5x+ky-7=0\) are concurrent at \((\alpha, \beta)\), then equation of the line concurrent with the given lines and perpendicular to \(kx+y-k=0\) is
An urn A contains 4 white and 1 black ball; urn B contains 3 white and 2 black balls; urn C contains 2 white and 3 black balls. One ball is transferred randomly from A to B; then one ball is transferred randomly from B to C. Finally, a ball is drawn randomly from C. Find the probability that it is black.
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
The transformed equation of \( 3x^2 - 4xy = r^2 \) when the coordinate axes are rotated about the origin through an angle of \( \tan^{-1}(2) \) in positive direction is
If the probability distribution of a discrete random variable X is given by \( P(X=k) = \frac{2^{-k(3k+1)}{2^c} \), k = 0, 1, 2, ..., \( \infty \) then P(X \( \le \) c) = } (The expression seems to be \( \frac{2^{-k}(3k+1)}{K} \) where K is a constant, or \(2^c\) is part of the constant. Assuming \(2^c\) is the normalization constant \(K\).)
If A(1,0), B(0,-2), C(2,-1) are three fixed points, then the equation of the locus of a point P such that area of \( \triangle \text{PAB} \) is equal to area of \( \triangle \text{PAC} \) is
In a binomial distribution, if \(n=4\) and \( P(X=0) = \frac{16{81} \), then \( P(X=4) = \)}
For a positive real number p, if the perpendicular distance from a point \( -\vec{i} + p\vec{j} - 3\vec{k} \) to the plane \( \vec{r} \cdot (2\vec{i} - 3\vec{j} + 6\vec{k}) = 7 \) is 6 units, then p =
An unbiased coin is tossed 8 times. The probability that head appears consecutively at least 5 times is
\( (\vec{a}+2\vec{b}-\vec{c}) \cdot ((\vec{a}-\vec{b}) \times (\vec{a}-\vec{b}-\vec{c})) = \)
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 box contains twelve balls of which 4 are red, 5 are green, and 3 are white. If three balls are drawn at random, the probability that exactly 2 balls have the same color is
There are three families \( F_1, F_2, F_3 \). \( F_1 \) has 2 boys and 1 girl; \( F_2 \) has 1 boy and 2 girls; \( F_3 \) has 1 boy and 1 girl. A family is randomly chosen and a child is chosen from that family randomly. If it is known that the child is a girl, the probability that she is from \( F_3 \) is
In \( \triangle ABC \), if \( r = 3 \) and \( R = 5 \) then \( \frac{1}{ab} + \frac{1}{bc} + \frac{1}{ca} = \)
An aeroplane is flying at a constant speed, parallel to the horizontal ground at a height of 5 kms. A person on the ground observed that the angle of elevation of the plane is changed from \(15^\circ\) to \(30^\circ\) in the duration of 50 seconds, then the speed of the plane (in kmph) is
Let \( \vec{a} = 2\vec{i} + \vec{j} - 2\vec{k} \) and \( \vec{b} = \vec{i} + \vec{j} \) be two vectors. If \( \vec{c} \) is a vector such that \( \vec{a} \cdot \vec{c} = |\vec{c}| \), \( |\vec{c} - \vec{a}| = 2\sqrt{2} \) and the angle between \( \vec{a} \times \vec{b} \) and \( \vec{c} \) is \( 30^\circ \), then \( |(\vec{a} \times \vec{b}) \times \vec{c| = \)}