List of top Mathematics Questions

Let $z=1+i$ and $z_1=\frac{1+i \bar{z}}{\bar{z}(1-z)+\frac{1}{z}}$ Then $\frac{12}{\pi} \arg \left(z_1\right)$ is equal to________

Let the equation of the plane passing through the line $x-2 y-z-5=0=x+y+3 z-5$ and parallel to the line $x+y+2 z-7=0=2 x+3 y+z-2$ be $a x+b y+c z=65$ Then the distance of the point $(a, b, c)$ from the plane $2 x+2 y-z+16=0$ is _______

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

Let \(S=\left\{z∈C : \bar{z}=i(z^2+Re(\bar{z}))\right\}\). Then \(\sum\limits_{z∈S}|z|^2\) is equal to 

Let [α] denote the greatest integer ≤ α. Then \([\sqrt1] + [ \sqrt 2 ] + [ \sqrt3 ] + . . . + [ \sqrt120 ] [\sqrt1 ] + [ \sqrt2 ] + [ \sqrt3 ] + . . . + [ 120 ]\)  is equal to

Let S = \(\{z \in C-\{i,2i\}:\frac{z^2+8iz-15}{z^2-3iz-2}\in R\}\) if \(\alpha-\frac{13}{11}i\in S, a \in R-{0}\), then  \(242\alpha^2\) is equal to ____.

Let \(α=8−14𝑖\), \(𝐴=\{z∈C:\frac {αz−\bar α\bar z}{z^2−(\bar z)^2−112i }=1\}\) and \(𝐵={𝑧∈C:|𝑧+3𝑖|=4}\). Then \(∑_{𝑧∈𝐴∩𝐵 }(\text {𝑅𝑒}\ ⁡𝑧−\text {𝐼𝑚⁡}\ 𝑧)\) is equal to _____ .

Let \( z = 1 + i \) and \( z_1 = \frac{1 + \bar{z}}{z(1 - z) + 1} \), where \( \bar{z} \) denotes the conjugate of \( z \). Then\(\frac{12}{\pi} \arg(z_1)\) is equal to:

For \(a∈ C, let A = {z∈C : Re (a + z ) > Im ( a + z)}\) and \(B = {z∈C : Re (a + z ) < Im ( a + z)}.\) Then among the two statements: 
(S₁) : If \(Re (a), Im (a) > 0\), then the set A contains all the real numbers 
(S₂): If \(Re (a), Im (a) < 0,\) then the set B contains all the real numbers

Let \( w_1 \) be the point obtained by the rotation of \( z_1 = 5 + 4i \) about the origin through a right angle in the anticlockwise direction, and \( w_2 \) be the point obtained by the rotation of \( z_2 = 3 + 5i \) about the origin through a right angle in the clockwise direction. Then the principal argument of \( w_1 - w_2 \) is equal to:

If 5f ( x+y ) = f(x).f(y) and f(3) = 320, then the value of f(1) is

The domain of the function f(x) = \(\frac{1}{\sqrt{[x]^2-3[x]-10}}\) is (where [x] denotes the greatest integer less than or equal to x)

The number of points, where the curve \(f(x) = e^{8x} - e^{6x} - 3e^{4x} - e^{2x} + 1\), \(x ∈ R\) cuts x-axis, is equal to

Let A = {1, 2, 3, 4, 5} and B = {1, 2, 3, 4, 5, 6). Then the number of functions f: A→B satisfying f(1) + f(2) = f(4)-1 is equal to _________ .

\( Let f(x) = | x^2 - x | + |x|, \text{ where } x \in \mathbb{R} \text{ and } | t | \text{ denotes the greatest integer less than or equal to } t. \text{ Then, } f \text{ is:} \)

Suppose \( f: \mathbb{R} \to (0, \infty) \) be a differentiable function such that: \( 5f(x + y) = f(x) \cdot f(y), \quad \forall x, y \in \mathbb{R} \). If \( f(3) = 320 \), then the value of:\( \sum_{n=0}^{5} f(n) \) is equal to:

Let $𝑆={𝑤_1,𝑤_2,…….}$ be the sample space associated to a random experiment. Let $𝑃(𝑤_𝑛)= \frac{𝑃(𝑤_{𝑛−1})}{2} ,𝑛≥2.$ Let 𝐴=${(2𝑘+3𝑙:k,𝑙∈ℕ)}$ and $𝐵={𝑤_𝑛:𝑛∈𝐴}$. Then 𝑃( 𝐵) is equal to

The negation of the statement
(p v q) ∧ (q v(∼r)) is

A person forgets his 4-digit ATM pin code. But he remembers that in the code all the digits are different, the greatest digit is 7 and the sum of the first two digits is equal to the sum of the last two digits. Then the maximum number of trials necessary to obtain the correct code is

Fifteen football players of a club-team are given 15 T-shirts with their names written on the backside. If the players pick up the T-shirts randomly, then the probability that at least 3 players pick the correct T-shirt is

Let the probability of getting head for a biased coin be \(\frac{1}{4}\) . It is tossed repeatedly until a head appears. Let N be the number of tosses required. If the probability that the equation \(64x² + 5Nx + 1 = 0\) has no real root is \(\frac{p}{q}\) , where p and q are co-prime, then q – p is equal to _______.