Ncert Solutions Maths class 11th

Let a circle C : ${\left(x-h\right)}^2+{\left(y-k\right)}^2=r^2,k>0,$ touch the axis (1,0). If the line x + y = 0 intersects the circle C at P and Q such that the length of the chord PQ is 2, then the value of h + k + r is equal to

The area (in sq. units) of region enclosed between the parabola y² = 2x and the line x + y = 4 is

The sum of all elements of the set $\left\{\alpha \in \left\{1,2,...,100\right\}:HFC\left(\alpha ,24\right)=1\right\}$ is

The number of 7-digit numbers which are multiples of 1 and are formed using all the digits 1, 2, 3, 4, 5, 7 and 9 is

Let $S=\left\{\left(\begin{array}{cc}\hfill -1\hfill & \hfill a\hfill \\ \hfill 0\hfill & \hfill b\hfill \end{array}\right)a,b\in \left\{1,2,3,...100\right\}\right\};$ and let Tn = $\left\{A\in S:A^{n\left(n+1\right)}=I\right\}.$ Then the number of elements in ${\displaystyle \underset{n=1}{\overset{100}{\cap }}{T}_n}is............$

Consider the following statements:

A : Rishi is a judge.

B : Rishi is honest.

C : Rishi is not arrogant.

The negation of the statement “if Rishi is a judge and he is not arrogant, then he is honest” is

The number of solutions of the equation $cos\left(x+\frac{\pi }{3}\right)cos\left(\frac{\pi }{3}-x\right)=\frac{1}{4}co{s}^{2}2x,x\in \left[-3\pi ,3\pi \right]is:$

Let the area of the triangle with vertices A $\left(1,\alpha \right),B\left(\alpha ,0\right)C(0,\alpha )$ be 4 sq. units. If the points $\left(\alpha ,-\alpha \right),\left(-\alpha ,\alpha \right)and\left({\alpha }^2,\beta \right)$ are collinear, then $\beta$ is equal to

Let the maximum area of the triangle that can be inscribed in the ellipse $\frac{x^2}{a^2}+\frac{y^2}{4}=1,a>2,$ having one of its vertices at one end of the major axis of the ellipse and one of its sides parallel to the y-axis, be $6\sqrt[]{3}$ . Then the eccentricity of the ellipse is

A particle is moving in the xy-plane along a curve C passing through the point (3, 3). The tangent to the curve C at the point P meets the x-axis at Q. If the y-axis bisects the segment PQ, then C is a parabola with