List of top Mathematics Questions

The equation of the plane passing through the point $(1, 1, 1)$ and perpendicular to the planes $2

Let $O$ be the origin and let $P Q R$ be an arbitrary triangle. The point $S$ is such that $\overrightarrow{O P} \cdot \overrightarrow{O Q}+\overrightarrow{O R} \cdot \overrightarrow{O S}=\overrightarrow{O R} \cdot \overrightarrow{O P}+\overrightarrow{O Q} \cdot \overrightarrow{O S}=\overrightarrow{O Q} \cdot \overrightarrow{O R}+\overrightarrow{O P} \cdot \overrightarrow{O S}$ Then the triangle $P Q R$ has $S$ as its

If $8\sqrt{x}\left(\sqrt{9+\sqrt{x}}\right)dy = \left(\sqrt{4+\sqrt{9+\sqrt{x}}}\right)^{-1}\,\,dx, \,\,\,\,x > 0$ and $

What will be the distance of $ (1, 0, 2) $ from the point of intersection of plane $ x - y + z = 16 $ and the line $ \left(\frac{x-2}{3}\right) = \left(\frac{y+1}{4}\right) = \left(\frac{z-2}{12}\right) $ ?

$ P $ speaks truth in $ 70\% $ cases and $ Q $ speaks in $ 80\% $ of the cases. In what percentage of cases are they likely to contradict each other in stating the same fact?

If = $\int x \log\left(1+ \frac{1}{x}\right)dx = f\left(x\right)\log\left(x+1\right)+g\left(x\right)x^{2}+Lx +C$, then

If the tangent at a point on the ellipse $\frac{x^2}{27} + \frac{y^2}{3} =1$ meets the coordinate axes at A and B, and O is the origin, them the minimum area (in s units) of the triangle OAB is:

$P$ and $Q$ are two distinct points on the parabola, $y^2 = 4x$, with parameters $t$ and $t_1$ respectively. If the normal at $P$ passes through $Q$, then the minimum value of $t^2_1$ is :

The logical expression \( X \), in its simplest form for the truth table \[ \begin{array}{|c|c|c|} \hline A & B & X \\ \hline 0 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \\ 1 & 1 & 1 \\ \hline \end{array} \] is

If \( f(a + b - x) = f(x), \) then \( \int_a^b f(x) \, dx \) is

If \( y = 2^x \), then \[ \frac{dy}{dx} \, \text{at} \, x = e \, \text{is} \]

The shortest distance between the lines \( x = y + 2 = 6z - 6 \) and \( x + 1 = 2y = -12z \) is

The domain and range of the function \( f(x) = 2 - |x - 5| \) is

The number of surjective functions from \( A \) to \( B \) where \( A = \{1,2,3,4\} \) and \( B = \{a, b\} \) is

\[ \int x^2 (x^4 + 1)^{3/4} \, dx \text{ is equal to } \]

If the letters of the word KRISNA are arranged in all possible ways and these words are written out as in a dictionary, then the rank of the word KRISNA is

The solution of the equation \[ \sin^2\theta + \cos^2\theta = 1 \] lies in the interval

If \( f(x) = (1 + x)^2 \) for \( x>0 \), then \( f(x) \) is

If \( a = 1 \), \( b = 2 \), \( c = 3 \), and \( d = 4 \), then \[ abc = d \]

While shuffling a pack of 52 playing cards, 2 are accidentally dropped. The probability that the missing cards to be of different colours is

Which of the following is INCORRECT for the hyperbola \( x^2 - 2y^2 + 2x + 8y - 1 = 0 \)?

A box contains 20 identical balls of which 10 are blue and 10 are green. The balls are drawn at random from the box one at a time with replacement. The probability that a blue ball is drawn 4th time on the 7th draw is

Number of ways of selecting three squares on a chessboard so that all the three be on a diagonal line of the board or parallel to it is

The foci of the ellipse \( \frac{x^2}{144} + \frac{y^2}{81} = 1 \) and the hyperbola \( \frac{x^2}{144} - \frac{y^2}{81} = 1 \) coincide then value of \( b^2 \) is

The number of common tangents to the circles \( x^2 + y^2 = 16 \) and \( x^2 + y^2 - 6x = 0 \) is