List of top Mathematics Questions

Let $ \alpha $ and $ \beta $ be the distinct roots of $ ax^2 + bx + c = 0 $, then $ \lim_{x \to \alpha} \frac{1 - \cos(ax^2 + bx + c)}{(x - \alpha)^2} $ is equal to:
The distance of the point \( (2, 3) \) from the line \( 2x - 3y + 28 = 0 \), measured parallel to the line \( \sqrt{3}x - y + 1 = 0 \), is equal to
The equation \( x^2 + ax + 1 = 0 \) has no real roots. Which one of the following is correct?
The cross product of vector \( \vec{A} \) and vector \( \vec{B} \) has a magnitude of 50 units, where vector \( \vec{A} \) has a magnitude of 10. The angle between vector \( \vec{A} \) and \( \vec{B} \) is 60 degrees. What is the magnitude of vector \( \mathbf{B} \)?

Let \[ A = \begin{pmatrix} 2 & -1 & 1 \\ -1 & 0 & 2 \\ 1 & -2 & -1 \end{pmatrix} \] and let \( B = \frac{1}{|A|} A \). Then the value of \( |B| \) is equal to:

The slope of a line L passing through the point \((-2, -3)\) is not defined. If the angle between the lines L and \( ax - 2y + 3 = 0 \) (where \( a>0 \)) is 45°, then the angle made by the line \( x + ay - 4 = 0 \) with positive X-axis in the anticlockwise direction is:
The HCF of 306 and 657 is
The statement \( [(p \rightarrow q) \wedge \sim q] \rightarrow r \) is a tautology when \( r \) is equivalent to:
The numbers \(1, 2, 3, \ldots, m\) are arranged in random order. The number of ways this can be done, so that the numbers \(1, 2, \ldots, r \, (r < m)\) appear as neighbours is:
The domain of the real-valued function \( f(x) = \sqrt{9 - \sqrt{x^2 - 144}} \) is
Which of the following is a geometric progression?
If \(α,β,γ\) are the roots of \(4x^3-6x^2+7x+3=0\), then the value of \(αβ+βγ+γα\) is
In the following figure, if DE || BC, then x =
In the following figure, if DE || BC, then x
In the given figure, PA and PB are the tangents to the circle with centre at O. If ∠APB = 36°, then ∠AOB =
In the given figure, PA and PB are the tangents to the circle with centre at O
In the given figure, the radius of each outer circle is a, then the radius of the inner circle is
In the given figure, the radius of each outer circle is a, then the radius of the inner circle is
The 12th term of the geometric progression (G.P.) \(2,1,\frac 12, \frac 14, \frac 18,…….\) is
If a sin 45°= b cosec 30°, then the value of \(\frac {a^4}{b^4}\) is
The modal class of the following frequency distribution is
Class Interval0-2020-4040-6060-8080-100
Number of Students1518212917
If the slope of the line joining the points (4,2) and (3,-k) is -2, then the value of k is
If A and B are the two sets containing 3 and 6 elements respectively, then what can be the maximum number of elements in A∪B?
If secθ+tanθ=k, then secθ-tanθ=?
If sin2 θ+ cosec2 θ = 6, then sin θ + cosec θ =
In what ratio, Y-axis divides the line segment joining the points P(-4, 2) and Q(8, 3)?
If the probability of guessing the correct answer to a question is \(\frac {x}{12}\) and the probability of not guessing the correct answer is \(\frac 58\), the value of \(x\) is
If the mode and mean of a data are 24 and 60 respectively, then the median of the data is