List of top Mathematics Questions

The lines \(L_1: y - x = 0\) and \(L_2: 2x + y = 0\) intersect the line \(L_3: y + 2 = 0\) at points \(P\) and \(Q\) respectively. The bisector of the angle between \(L_1\) and \(L_2\) divides the segment \(PQ\) internally at \(R\). Consider: Statement-I: \(PR : RQ = 2\sqrt{2} : \sqrt{5}\).
Statement-II: In any triangle, bisector of an angle divides that triangle into two similar triangles.
Which statement(s) is/are correct?
If \[ 2x^2 + 3xy - 2y^2 - 5x + 2fy - 3 = 0 \] represents a pair of straight lines, then one of the possible values of \(f\) is?
If \(A(\cos \alpha, \sin \alpha)\), \(B(\sin \alpha, -\cos \alpha)\), and \(C(1, 2)\) are the vertices of \(\triangle ABC\), then find the locus of its centroid.
Two dice are thrown and the sum of the numbers appeared on the dice is noted. If A is the event of getting a prime number as their sum and B is the event of getting a number greater than 8 as their sum, then find \(P(A \cap \overline{B})\).
Let \(X \sim B(n, p)\) with mean \(\mu\) and variance \(\sigma^2\). If \(\mu = 2\sigma^2\) and \(\mu + \sigma^2 = 3\), then find \(P(X \leq 3)\).
Line \(L_1\) passes through the points \(\mathbf{i} + \mathbf{j}\) and \(\mathbf{k} - \mathbf{i}\). Line \(L_2\) passes through the point \(\mathbf{j} + 2\mathbf{k}\) and is parallel to the vector \(\mathbf{i} + \mathbf{j} + \mathbf{k}\). If \(\mathbf{x}i + \mathbf{y}j + \mathbf{z}k\) is the point of intersection of the lines \(L_1\) and \(L_2\), then find \((y - x) =\)
A and B are two independent events of a random experiment and \(P(A)>P(B)\). If the probability that both A and B occur is \(\frac{1}{6}\) and neither of them occurs is \(\frac{1}{3}\), then the probability of the occurrence of B is:
In a triangle \(ABC\), if \(r_1 : r_2 = 3 : 4\) and \(r_1 : r_3 = 2 : 3\), then find the ratio \(a : b : c\).
In \(\triangle ABC\), if the line joining the circumcentre and incentre is parallel to \(BC\), then find \( \cos B + \cos C \).
If \[ \frac{2x^4 - 3x^2 + 4}{(x^2 + 1)(x^2 + 2)} = a + \frac{px + q}{x^2 + 1} + \frac{mx + n}{x^2 + 2}, \] then $\frac{n}{q} =$
Evaluate \[ (4 \cos^2 \frac{\pi}{20} - 1)(4 \cos^2 \frac{3\pi}{20} - 1)(4 \cos^2 \frac{5\pi}{20} - 1)(4 \cos^2 \frac{7\pi}{20} - 1)(4 \cos^2 \frac{9\pi}{20} - 1). \]
If $\cos 80^\circ + \cos 40^\circ - \cos 20^\circ = k$, then $\frac{4k}{3} =$
The number of integers greater than 6000 that can be formed by using the digits 0, 5, 6, 7, 8 and 9 without repetition is
The product of the four values of the complex number $(1+i)^{3/4}$ is
Evaluate \[ \frac{1}{3 . 5} + \frac{1}{5 . 7} + \frac{1}{7 . 9} + .s \text{ up to } 24 \text{ terms}. \]
If B is the inverse of a third order matrix A and det B = k, then $(\text{adj}(\text{adj} A))^{-1}=$
If $A = \begin{bmatrix} 2 & 2 & 1 \\ 1 & 3 & 1 \\ 1 & 2 & 2 \end{bmatrix}$ and $\alpha, \beta, \gamma$ are the roots of the equation represented by $|A - xI| = 0$, then $\alpha^2 + \beta^2 + \gamma^2 =$
The roots of the quadratic equation \( x^2 - 16 = 0 \) are:
In a binomial distribution, if \(n=4\) and \( P(X=0) = \frac{16}{81} \), then \( P(X=4) = \)
A packet contains 15 blue beads, 16 yellow beads and 19 orange beads. A bead is drawn at random from the packet. Find the probability that the bead drawn is:
1. an orange bead
2. a blue or a yellow bead
What quantity of water (in ml) should be added to reduce glycerin content from 60% to 50% in a 320ml body lotion?
When viewed from a point P which is 56 metres above a lake, the angle of elevation is 30 and from the same point, the angle of depression of its reflection in the lake 60. What is the height of the cloud?
A boy, Chintu while playing with modelling clay, changes a cone shaped toy into a spherical toy. The height of the cone was 20cm and radius of base was 5 cm. Find the radius and the surface area of the sphere
If HCF of the numbers 299, 253 and a third number 'A' is 23 and their LCM is 16445, then what is the number 'A'?
Bittu, a fruit seller purchased some fruit items and raised its price by 35%. But due to some urgency, he had to sell it immediately by giving 35% discount on the face value. Then, how much was the percentage gain or loss after giving discount?