List of top Mathematics Questions

If \( \alpha, \beta \) are the roots of \( x^2 - 5x - 68 = 0 \) and \( \gamma, \delta \) are the roots of \( x^2 - 5\alpha x - 6\beta = 0 \), then \( \alpha + \beta + \gamma + \delta = \) ?
If \( \omega_1 \) and \( \omega_2 \) are two non-zero complex numbers and \( a, b \) are non-zero real numbers such that \[ |a\omega_1 + b\omega_2| = |a\omega_1 - b\omega_2|, \] then \( \dfrac{\omega_1}{\omega_2} \) is:
If \( f : \mathbb{R} \to A \), defined by \( f(x) = \cos x + \sqrt{3}\sin x - 1 \), is an onto function, then \( A = \)
If the system of equations \( 2x + py + 6z = 8 \), \( x + 2y + qz = 5 \) and \( x + y + 3z = 4 \) has infinitely many solutions, then \( p = \)?
The roots of the quadratic equation \( x^2 - 16 = 0 \) are:
What quantity of water (in ml) should be added to reduce glycerin content from 60% to 50% in a 320ml body lotion?
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
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?
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'?
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
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?
Probability of getting a rotten apple from a lot of 480 apples is 0.125. Find the number of good apples.
A jug was full of juice. A person draws out \( \frac{1}{6} \) of the juice from the jug and replaces it with water. He repeated this process 3 times and thus there was only 1250 ml of juice left in the jug. What was the initial quantity of juice in the jug?
Evaluate the integral: \[ I = \int_{\pi/6}^{\pi/3} \cos^{-4} x \, dx \]
Evaluate the integral: \[ I = \int_0^{3\pi/2} \frac{\cos^5 x}{\cos^3 x+\sin^3 x}dx \]
The differential equation for which \( y^2 = 4a(x + a) \) (where \( a \) is a parameter) is the general solution is:
Evaluate the integral: \[ \int \frac{\sec^2 x}{(\sec x+\tan x)^{5/2}}dx \]
Evaluate the integral: \[ \int \operatorname{Cos}^{-1} \left( \frac{1-x^2}{1+x^2} \right) dx \]
Evaluate the integral: \[ \int \frac{x+1}{x^3 - 1}dx \]
Evaluate the integral: \[ \int \frac{x^4-16x^2+2x+8}{x^3-4x^2+2}dx \]
If the lengths of the tangent, subtangent, normal, and subnormal for the curve \( y = x^2 + x - 1 \) at the point \( (1,1) \) are \( a, b, c, \) and \( d \) respectively, then their increasing order is:
If \( y = \log(\sec(\tan^{-1}x)) \) for \( x>0 \), then \( \frac{dy}{dx} \) at \( x = 1 \) is:
If \( x = \sqrt{2}e^t(\sin t - \cos t) \) and \( y = \sqrt{2}e^t(\sin t + \cos t) \), then \( \left[ \frac{d^2y}{dx^2} \right]_{t=\frac{\pi}{4}} \) is:
P and Q are the ends of a diameter of the circle \( x^2+y^2=a^2(a>\frac{1}{\sqrt{2}}) \). \( s \) and \( t \) are the lengths of the perpendiculars drawn from P and Q onto the line \( x+y=1 \) respectively. When the product \( st \) is maximum, the greater value among \( s, t \) is:
If \( A(2,-1,1) \), \( B(2,5,1) \) and \( C(0,-2,3) \) are the vertices of a triangle, and \( D \) is the point of intersection of the side \( BC \) and the internal angular bisector of angle \( A \), then \( AD = \):