List of top Mathematics Questions

The set of all values of \(\lambda\) for which the system of linear equations 
\(2x_1-2x_2+x_3=\lambda x_1\)
 \(2x_1-3x_2+2x_3=\lambda x_2\)
\(-x_1+2x_2=\lambda x_3\) has a non-trivial solution

Let $A$ and $B$ be two sets containing four and two elements respectively. Then the number of subsets of the set $A \times B$, each having at least three elements is :

The number of ways of selecting $15$ teams from $15$ men and $15$ women, such that each team consists of a man and a woman. is :

If the angles of elevation of the top of a tower from three collinear points $A , B$ and $C$ on a line leading to the foot of the tower are $ 30^\circ, \, 45^\circ$ and $ 60^\circ$ respectively, then the ratio $AB : BC$ is

Let k be a non-zero real number. If $f(x) = \begin{cases} \frac{\left(e^x-1\right)^2}{sin\left(\frac{x}{k}\right)log\left(1+\frac{x}{4}\right)}, & \text{x $\ne$ 0} \\[2ex] 12, & \text{x = 0} \end{cases}$ is a continuous function, then the value of $k$ is :

At $t = 0$, the function $f \left(t\right) = \frac{sin\,t}{t}$ has

If $N$ is a set of natural numbers, then under binary operation $a ?b =a + b, (N, ?)$ is

The normal at the point $(at_1^2 ,\, 2at_1)$ on the parabola meets the parabola again in the point $(at_1^2 ,\, 2at_2)$ , then

If $|z| \ge 3$, then the least value of $\left|z+\frac{1}{4}\right|$ is

On the interval $[0, 1]$, the function $x^{25}(1 - x)^{75}$ takes its maximum value at the point

The area bounded by the curves $y = cos\, x$ and $y = sin \,x$ between the ordinates $x = 0$ and $x = \frac{3\pi}{2}$ is

If $(2, 7, 3)$ is one end of a diameter of the sphere $x^2 + y^2 + z^2 - 6\,x -12\,y -2\,z + 20 = 0$, then the coordinates of the other end of the diameter are

The two lines $x = my + n, z = py + q$ and $x = m'y + n',\, z = p'y + q'$ are perpendicular to each other, if

If a line segment OP makes angles of $ \frac{\pi}{4}$ and $\frac{\pi }{3}$ with X-axis and Y-axis, respectively. Then, the direction cosines are

If p : It rains today, q : I go to school, r : I shall meet my friends and s : I shall go for a movie, then which of the following is the proportion? If it does not rain or if I do not go to school, then I shall meet my friend and go for a movie.

If p, q, r are simple propositions with truth values T, F, T, then the truth value of $\left(\sim p \vee q\right) \wedge \sim r \Rightarrow p $ is

The value of $ \displaystyle \sum^{30}_{r = 16} (r + 2)(r - 3)$ is equal to :

If $y + 3x = 0$ is the equation of a chord of the circle, $x^2 + y^2 - 30x = 0$, then the equation of the circle with this chord as diameter is :

The solution of the differential equation $ydx - (x + 2y^2)dy = 0$ is $x = f(y)$. If $f(- 1) = 1$, then $f(1)$ is equal to :

A complex number $z$ is the said to be unimodular if $|z|=1 .$ Suppose $z_{1}$ and $z_{2}$ are complex number such that $\frac{z_{1}-2 z_{2}}{2-z_{1} z_{2}}$ is unimodular and $z _{2}$ is not unimodular. Then the point $z_{1}$ lies on a :

If $\begin{vmatrix}x^{2}+x&x+1&x-2\\ 2x^{2}+3x-1&3x&3x-3\\ x^{2}+2x+3&2x-1&2x-1\end{vmatrix}=ax-12,$ then 'a' is equal to :

The term independent of $x$ in the binomial expansion of $\left(1-\frac{1}{x}+3x^{5}\right)\left(2x^{2}-\frac{1}{x}\right)^{8}$ is :

The number of integers greater than $6,000$ that can be formed using the digits $3, 5, 6, 7$ and $ 8$ without repetition is

The mean of the data set comprising of $16$ observations is $16$. If one of the observatio $d$ three new observations valued $3,4$ and $5$ added to the data, then the mean of the resultant data is

The number of common tangents to the circles $x^2+y^2-4x-6y-12=0$ and $x^2+y^2+6x+18y+26=0$