List of top Mathematics Questions

Let the locus of the centre $(\alpha, \beta), $ $\beta>0$, of the circle which touches the circle $x ^2+( y -1)^2=1$ externally and also touches the x-axis be L Then the area bounded by L and the line y=4 is :

If the sum and the product of mean and variance of a binomial distribution are 24 and 128 respectively, then the probability of one or two successes is :

If the numbers appeared on the two throws of a fair six faced die are $\alpha$ and $\beta$, then the probability that $x^2+\alpha x+\beta>0$, for all $x \in R$, is :

The number of solutions of $|\cos x |=\sin x$, such that $-4 \pi \leq x \leq 4 \pi$ is :

For any real number x, let [ x ] denote the largest integer less than equal to x Let f be a real valued function defined on the interval [-10,10] by $f(x)=\begin{cases} x-[x], & \text { if }(x) \text { is odd } \\ 1+[x]-x & \text { if }(x) \text { is even }\end{cases}$Then the value of$ \frac{\pi^2}{10} \int\limits_{-10}^{10} f(x) \cos \pi x d x$ is :

Which of the following statements is a tautology?

The total number of functions, $f :\{1,2,3,4\} \rightarrow\{1,2,3,4,5,6\}$ such that $f (1)+ f (2)= f (3)$, is equal to :

The general solution of the differential equation $\left(x-y^2\right) d x+y\left(5 x+y^2\right) d y=0$ is :

The value of 2 sin(12°) – sin(72°) is

The negation of the Boolean expression ((~ q) ∧ p) ⇒ ((~ p) ∨ q) is logically equivalent to:

If $\alpha, \beta, \gamma, \delta$ are the roots of the equation $x ^4+ x ^3+ x ^2+ x +1=0$, then $\alpha^{2021}+\beta^{2021}+\gamma^{2021}+\delta^{2021}$ is equal to

Let l be a line which is normal to the curve $y = 2x^2 + x + 2$ at a point P on the curve. If the point Q(6, 4) lies on the line l and O is origin, then the area of the triangle OPQ is equal to _________ .

Let the lines
$y + 2x = \sqrt {11} + 7\sqrt 7$ and $2y + x = 2\sqrt {11} + 6\sqrt 7$
be normal to a circle $C : (x – h)^2 + (y – k)^2 = r^2$. If the line
$\sqrt {11}y - 3x =\frac { 5\sqrt {17}}{3} + 11$
is tangent to the circle C, then the value of $(5h – 8k)^2 + 5r^2$ is equal to _______.

Let R₁ and R₂ be relations on the set {1, 2, ….., 50} such that R₁ ={(p, pⁿ) : p is a prime and n≥ 0 is an integer} and R₂ = {(p, pⁿ) : p is a prime and n = 0 or 1}. Then, the number of elements in R₁ – R₂ is ______.

If the tangents drawn at the points O(0, 0) and P(1 + √5, 2) on the circle x² + y² – 2x – 4y = 0 intersect at the point Q, then the area of the triangle OPQ is equal to

The number of elements in the set { $z = a + ib ∈ C : a,b ∈ Z$ and $1 < | z - 3 + 2i | < 4$ } is _______ .

Let O be the origin and A be the point $z_1 = 1 + 2i$. If B is the point $z_2, Re(z_2) < 0$, such that OAB is a right angled isosceles triangle with OB as hypotenuse, then which of the following is NOT true?

Let the eccentricity of the hyperbola
$H : \frac{x²}{a²} - \frac{y²}{b²} = 1$
be √(5/2) and length of its latus rectum be 6√2, If y = 2x + c is a tangent to the hyperbola H. then the value of c² is equal to

Let AB and PQ be two vertical poles, 160 m apart from each other. Let C be the middle point of B and Q, which are feet of these two poles. Let $\frac \pi 8$ and $θ$ be the angles of elevation from C to P and A, respectively. If the height of pole PQ is twice the height of pole AB, then $tan^2θ$ is equal to

If $\vec a= 2\hat i +\hat j + 3\hat k$, $\vec b = 3\hat i + 3\hat j + \hat k$ and $\vec c = c_1\hat i + c_2\hat j + c_3\hat k$ are coplanar vectors and $\vec a.\vec c = 5$, $\vec b⊥\vec c$ then $122( c_1 + c_2 + c_3 )$ is equal to _____ .

If two distinct points Q, R lie on the line of intersection of the planes –x + 2y – z = 0 and 3x – 5y + 2z = 0 and
$PQ = PR = \sqrt{18}$
where the point P is (1, –2, 3), then the area of the triangle PQR is equal to

The acute angle between the planes P₁ and P₂, when P₁ and P₂ are the planes passing through the intersection of the planes 5x + 8y + 13z – 29 = 0 and 8x – 7y + z – 20 = 0 and the points (2, 1, 3) and (0, 1, 2), respectively, is

Let the plane
$P : \stackrel{→}{r} . \stackrel{→}{a} = d$
contain the line of intersection of two planes
$\stackrel{→}{r} . ( \hat{i} + 3\hat{j} - \hat{k} ) = 6$
and
$\stackrel{→}{r} . ( -6\hat{i} + 5\hat{j} - \hat{k} ) = 7$
. If the plane P passes through the point (2, 3, 1/2),
then the value of $\frac{| 13a→|² }{d²}$ is equal to

The number of positive integers k such that the constant term in the binomial expansion of $( 2x^3 + \frac {3}{x^k} )^{12}, x ≠ 0$ is $2^8$ . l, where l is an odd integer, is______.