Class 11th

Let arg(z) represent the principal argument of the complex number z. Then $\left|z\right|=3$ and art(z – 1) – arg(z + 1) = $\frac{\pi }{4}$  intersect

Let a be root of the equation 1 + x² + x⁴ = 0. Then the value of a¹⁰¹¹ + a²⁰²² - a³⁰³³ is equal to:

Which element is known to have the highest elastic moduli?

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 : ${\left(x-h\right)}^2+{\left(y-k\right)}^2=r^2.$ If the line $\sqrt[]{11}y-3x=\frac{5\sqrt[]{77}}{3}+11$ is tangent to the circle C, then the value of $\sqrt[]{11}y-3x=\frac{5\sqrt[]{77}}{3}+11$  is equal to…………….

The number of elements in the set $\left\{z=a+ib\in C:a,b\in Zand1<\left|z-3+2i\right|<4\right\}$  is……….

The number of elements in the set $\left\{z=a+ib\in C:a,b\in Zand1<\left|z-3+2i\right|<4\right\}$  is……….

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

Let A = $\left\{1,a_1,a_2....a_{18},77\right\}$  be a set of integers with 1 < a₁ < a₂ < … < a₁₈ < 77. Let the set A + A = $\left\{x+y:x,y\in A\right\}$  contains exactly 39 elements. Then, the value of a₁ + a₂ +…. + a₁₈ is equal to…………

A ray of light passing through the point P(2, 3) reflects on the x-axis at point A and the reflected ray passes through the point Q(5, 4). Let R be the point that divides the line segment AQ internally into the ration 2 : 1. Let the co-ordinates of the foot of the perpendicular M from R on the bisector of the angle PAQ be (a, β)). Then the value of 7a + 3β) is equal to……….

Let p, q, r be three logical statements. Consider the compound statements

  $S_1:\left(\left(\sim p\right)\vee q\right)\vee \left(\left(\sim p\right)\vee r\right)and$  

  $S_2:p\to \left(q\vee r\right)$  

 Then, which of the following is NOT true?