List of top Mathematics Questions

$\sim q$ can be deduced from $\sim(p \supset (q \lor r))$ by using rules of propositional logic in the following sequence(s):
(i) $p \supset (q \cdot r)$ (ii) $\sim(p \supset s)$
Taking (i) and (ii) as premises, which of the following can be deduced?
Given a fair six-faced dice where the faces are labelled '1', '2', '3', '4', '5', and '6', what is the probability of getting a '1' on the first roll of the dice and a '4' on the second roll?
If \(\vec{a}+2\vec{b}+3\vec{c}=\vec{0}\) and
\((\vec{a}\times\vec{b})+(\vec{b}\times\vec{c})+(\vec{c}\times\vec{a})=\lambda(\vec{b}\times\vec{c})\)
then the value of λ is equal to
Let f be a non-negative function defined on [\(0,\frac{\pi}{2}\)]. If \(\int_{0}^{x}(f'(t)-sin\,2t)dt=\int_{0}^{x}f(t)tan\,t\,dt\). \(f(0)=1\), then \(\int_{0}^{\frac{\pi}{2}}f(x)dx\) is
If the sum of all the solutions of $\tan ^{-1}\left(\frac{2 x}{1-x^2}\right)+\cot ^{-1}\left(\frac{1-x^2}{2 x}\right)=\frac{\pi}{3},-1 < x < 1, x \neq 0$, is $\alpha-\frac{4}{\sqrt{3}}$, then $\alpha$ is equal to ___
The tangent to the parabola, x2 = 2y at the point \((1,\frac{1}{2})\) makes with the x-axis an angle of :
For a given vector \( \mathbf{w} = [1 \; 2 \; 3]^T \), the vector normal to the plane defined by \( \mathbf{w}^T \mathbf{x} = 1 \) is:
Which one of the following options represents the given graph? \begin{center} \includegraphics[width=0.5\textwidth]{02.jpeg} \end{center}
Let $x, y, z>1$ and $A=\begin{bmatrix}1 & \log _x y & \log _x z \\ \log _y x & 2 & \log _y z \\ \log _z x & \log _z y & 3\end{bmatrix}$ Then ∣adj(adjA2)∣ is equal to
The converse of ((~ p) ∧ q) ⇒ r is

Let \( R = \{a, b, c, d, e\} \) and \( S = \{1, 2, 3, 4\} \). Total number of onto functions \( f: R \to S \) such that \( f(a) \neq 1 \), is equal to:

If $a_r$ is the coefficient of $x^{10-r}$ in the Binomial expansion of $(1+x)^{10}$, then $\displaystyle\sum_{r=1}^{10} r^3\left(\frac{a_r}{a_{r-1}}\right)^2$ is equal to
Let A be the point (0,4) in the xy-plane and B be the point (2t,0). Let L be AB's midpoint and let AB's perpendicular bisector meet the y-axis M. Let N be the midpoint of LM. The locus of N is
\(\text{The value of    } cosec20°tan60°-sec20° \text{is }\)
The sum of the first 20 terms of the series 5 + 11 + 19 + 29 + 41 + ... is
If \(\frac{1}{6}\)sinθ.cosθ.tanθ are in G.P, then the solution set θ is
$\displaystyle\lim _{x \rightarrow \infty} \frac{(\sqrt{3 x+1}+\sqrt{3 x-1})^6+(\sqrt{3 x+1}-\sqrt{3 x-1})^6}{\left(x+\sqrt{x^2-1}\right)^6+\left(x-\sqrt{x^2-1}\right)^6} x^3$

Area of the Region bounded by the curve y=√49-x2 and x-axis is .

Let g(x) = f(x) + f(1 - x) and f''(x) > 0, x ∈ (0,1). If g is decreasing in the interval (0, α) and increasing in the interval (α, 1), then tan-1 (2α) + tan-1 (\(\frac{1}{α}\)) + tan-1\((\frac{α+1}{α})\) is equal to

If (h,k) is the image of the point (3,4) with respect to the line 2x - 3y -5 = 0 and (l,m) is the foot of the perpendicular from (h,k) on the line 3x + 2y + 12 = 0, then lh + mk + 1 = 2x - 3y - 5 = 0.

If a curve passes through the point (1, 1) at any point (x, y) on the curve, the product of the slope of its tangent and x co-ordinate of the point is equal to the y co-ordinate of the point, then the curve also passes through the point
The sum $\displaystyle\sum_{n=1}^{21} \frac{3}{(4 n-1)(4 n+3)}$ is equal to
Let \(f(x)\) be a quadratic polynomial with leading coefficient 1 such that \(f(0) = p, p≠0\) and \(f(1)=\frac{1}{3}\). If the equation \(f(x) = 0\) and \(fofofof(x) = 0\) have a common real root, then \(f(–3)\) is equal to.......................
The length of the common chord of two intersecting circles is 24 cm. If the diameter of the circles are 30 cm and 26 cm, then the distance between the center (in cm) is