Ncert Solutions Maths class 11th

Let f be a real valued continuous function on [0, 1] and f(x) = $x+{\displaystyle \underset{0}{\overset{1}{\int }}\left(x-t\right)f\left(t\right)dt.}$  Then, which of the following points (x, y) lies on the curve y = f(x)?

The sum of the infinite series $1+\frac{5}{6}+\frac{12}{6^2}+\frac{22}{6^3}+\frac{35}{6^4}+\frac{51}{6^5}+\frac{70}{6^6}+....$  is equal to:

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:

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…………….

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……….

The mean and standard deviation of 15 observations are found to be 8 and 3 respectively. On rechecking it was found that, in the observations, 20 was misread as 5. Then, the correct variance 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?

Let AB and PQ be two vertical poles, 160m apart from each other. Let C be the middle points of B and Q, which are feet of these two poles. Let $\frac{\pi }{8}$  and q 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 tan²q is equal to

If the tangents drawn at the points O(0, 0) and $P\left(1+\sqrt[]{5},2\right)$  on the circle x² + y² – 2x – 4y = 0 intersect at the point Q, then the area of the triangle OPQ is equal to