List of top Mathematics Questions

Which is true ?

Let $A=\begin{vmatrix} 5& 5\alpha & \alpha \\[0.3em] 0 &\alpha &5\alpha \\[0.3em] 0 &0& 5 \end{vmatrix}$ , If $\left|\,A^2\,\right|=25$,then $\left|\,\alpha\,\right|$ equals

The equation of a tangent to the parabola $y^2 = 8x$ is $y = x + 2$. The point on this line from which the other tangent to the parabola is perpendicular to the given tangent is

A tower stands at the centre of a circular park. $A$ and $B$ are two points on the boundary of the park such that $AB (= a)$ subtends an angle of $60^\circ$ at the foot of the tower, and the angle of elevation of the top of the tower from $A$ or $B$ is $30^??. The height of the tower is

Consider a family of circles which are passing through the point (-1, 1) and are tangent to xaxis. If (h, k) are the co-ordinates of the centre of the circles, then the set of values of k is given by the interval

The largest interval lying in $\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$ for which the function $f \left(x\right)=4^{-x^2}+cos^{-1}\left(\frac{x}{2}-1\right)+log\left(cos\,x\right)$ is defined, is

The set $S=\left\{1, 2, 3, \dots, 12\right\}$ is to be partitioned into three sets $A, B, C$ of equal size. Thus, $A\cup B\cup C=S, A\cap B = B\cap C = A \cap C=\phi.$ The number of ways to partition $S$ is

If $sin^{-1}\left(\frac{x}{5}\right)+cos\,ec^{-1}\left(\frac{5}{4}\right)=\frac{\pi}{2} $ then a value of $x$ is

In a geometric progression consisting of positive terms, each term equals the sum of the next two terms. Then the common ratio of this progression equals

In the binomial expansion of $(a - b)^n, n \geq 5,$ a the sum of $5^{th}$ and $6^{th}$ terms is zero, then $\frac{a}{b}$ equals

The sum of the series ${^{20}C_0} - {^{20}C_1} + {^{20}C_2} - {^{20}C_3} + ..... - .... + {^{20}C_{10}}$ is

A pair of fair dice is thrown independently three times. The probability of getting a score of exactly $9$ twice is

If one of the lines of $my^2 + (1 - m^2)xy - mx^2 = 0$ is a bisector of the angle between the lines $xy = 0$, then $m$ is

Let $A$ be the square of natural numbers and $x$, $y$ are any two elements of $A$. Then

If $2\,sin\,x=\sqrt{\frac{p}{q}}+\sqrt{\frac{q}{p}}$, then

One Indian and four American men and their wives are to be seated randomly around a circular table. Then, the conditional probability that Indian m an is seated adjacent to his wife given that each American man is seated adjacent to his wife, is

Let $0(0, 0), P(3, 4)$ and $Q(6, 0)$ be the vertices of a $\Delta$ OP The point R inside the $\Delta OPQ$ is such th at the triangles $OPR, PQR$ and $OQR $ are of equal area. The coordinates of R are

Let $E^c$ denotes the complement of an event $E$. If $E, F, G$ are pairwise independent events with $P (G) > 0$ and $P(E \cap F \cap G)=0$ then , $P(E^c \cap F^c|G) equals$

Let $\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$ be unit vectors such that $\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}=\overrightarrow{0}.$ Which one of the following is correct?

The number of distinct real values of $\lambda$, for which the vectors $-\lambda^2\widehat{i}+\widehat{j}+\widehat{k}, \widehat{i}-\lambda^2\widehat{j}+\widehat{k}$ and $\widehat{i}+\widehat{j}-\lambda^2\widehat{k}$ are coplanar, is

A man walks a distance of 3 units from the origin towards the North-East (N 45$^{\circ}$ E) direction. From there, he walks a distance of 4 units towards the North-West (N 45$^\circ$ W) direction to reach a point P. Then, the position of P in the Arg and plane is

Let $ABCD$ be a quadrilateral with area 18, with side AB parallel to the side $CD$ and $AB = 2 CD$. Let $AD$ be perpendicular to $AB$ and $CD$. If a circle is drawn inside the quadrilateral $ABCD$ touching all the sides, then its radius is