List of top Mathematics Questions

A circle passing through the point P\(( \alpha , \beta )\) in the first quadrant touches the two coordinate axes at the points A and B. The point P is above the line AB. The point Q on the line segment AB is the foot of perpendicular from P on AB. If PQ is equal to 11 units, then value of \(( \alpha \beta )\)  is ___

A pair of dice is rolled 5 times. let getting a total of 5 in a single throw is considered as success. If probability of getting atleast four success is \(\frac{x}{3}\) then x is equal to

\(I(x) = \int \frac{x^2(xsec^2x + tanx)}{(xtanx+1)^2} dx\). If \(I(0)=1\) then \(I(\frac{\pi}{4})\) is equal to
Let the line passing through the points P (2, –1, 2) and Q (5, 3, 4) meet the plane x – y + z = 4 at the point R. Then the distance of the point R from the plane x + 2y + 3z + 2 = 0 measured parallel to the line \(\frac{x-7}{2}=\frac{y+3}{2}=\frac{z-2}{1}\) is equal to

The sum of all values of \( \alpha \), for which the points whose position vectors are:

\[ \mathbf{r_1} = \hat{i} - 2\hat{j} + 3\hat{k}, \quad \mathbf{r_2} = 2\hat{i} - 3\hat{j} + 4\hat{k}, \quad \mathbf{r_3} = (\alpha+1)\hat{i} + 2\hat{k}, \quad \mathbf{r_4} = \hat{j} + 2\hat{k} \]

are coplanar, is equal to:

If \(a ≠ ±b\) and are purely real, z ϵ complex number, \(Re(az^{2}+bz)=a\) and \(Re(bz^{2}+az)=b\) then number of value of z possible is
If gcd \( (m, n) = 1 \) and \[ 1^2 - 2^2 + 3^2 - 4^2 + \cdots + (2022)^2 - (2023)^2 = 1012 \, m^2 n \] then \( m^2 - n^2 \) is equal to:
Among the statements:
The system of the equations
\(x + y + z = 6\)
\(x + 2y +   \alpha  z = 5 \)
\(x + 2y + 6z = \)\( \beta\) has
The area enclosed by \(y = |x-1| + |x-2|\) and \(y = 3\)
Find all the four letter words with two vowels and 2 consonants from the word UNIVERSE?
If \(f(x) + f(\pi-x) = \pi^{2}\) then \(_{0}\int^{\pi}f(x) sinx dx\) ?
Rank of the word PUBLIC is?
Find the sum of series: \(2*2^2 - 2*3^2 + 2*4^2 +\) \(….(20 \,terms)\)

The number of seven-digit positive integers formed using the digits 1, 2, 3, and 4 only, and whose sum of the digits is 12, is         

If \(\frac{dy}{dx}\) = y+7 and y(0) = 0, then the value of y(1) is?
The integral \(∫^∞_0  \frac{6}{(e^{3x} + 6e^{2x} + 11e{x} + 6)}dx\)
Find area bounded by the curves \(y\) = \(max\{sin x, cos x\}\) and \(x-axis\) between \(x = -  \pi  \)and \(x =   \pi\)
Plane P3 is passing through (1,1,1) and line of intersection of P1 and P2 where \(P_{1}: 2x - y + z = 5\) and \(P_{2}: x + 3y + 2z + 2 = 0\). Then distance of (1,1,10) from P3 is:
Let the number of matrices of order 3 x 3 are possible using the digits [0, 1, 2, 3, … , 10) is mn, then (m + n) is ___. (where m is a prime number)

The fractional part of the number \(\tfrac{4^{2022}}{15}\) is equal to:

 For \(x \in \mathbb{R}\), two real‐valued functions \(f(x)\) and \(g(x)\) are such that

If \(sin^{-1}x=2\,tan^{-1}x\) , then the number of integral values of x is equal to:
\((2x^3-\frac{1}{3}x^8)^5\) → coefficient of \(x^4\)

Find out the rank of MONDAY in English dictionary if all alphabets are arranged in order?