Maths NCERT Exemplar Solutions Class 12th Chapter Eleven

If the equation of a plane $P$ , passing through the intersection of the planes, $x+4y-z+7$ $=0$ and $3x+y+5z=8$ is $ax+by+6z=15$ for some $a,b\in R$ , then the distance of the point $(\mathrm{3,2},-1)$ from the plane $P$ is

Let $P\left(\mathrm{3,3}\right)$ be a point on the hyperbola, $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ . If the normal to it at $P$ intersects the $x$ -axis at $\left(\mathrm{9,0}\right)$ and $e$ is its eccentricity, then the ordered pair $\left(a^2,e^2\right)$ is equal to:

Let $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1(ab)$ be given ellipse, length of whose latus rectum is 10 . If its eccentricity is the maximum value of the function, $?\left(t\right)=\frac{5}{12}+t-t^2$ , then $a^2+b^2$ is equal to:

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 $\mathcal{l}$  be a line which is normal to the curve y = 2x² + x + 2 at a point P on the curve. If the point Q(6, 4) lies on the line $\mathcal{l}$  and O is origin, then the area of the triangle OPQ 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

Let the eccentricity of the hyperbola $H:\frac{x^2}{a^2}-\frac{y^2}{b^2}=1be\sqrt[]{\frac{5}{2}}$ and length of its latus rectum be $6\sqrt[]{2},ify=2x+c$ is a tangent to the hyperbola H, then the value of c² is equal to

Let a line with direction ratios a, 4a, 7 be perpendicular to the lines with direction ratios 3, 1, 2b and b, a, 2. If the point of intersection of the line $\frac{x+1}{a^2+b^2}=\frac{y-2}{a^2-b^2}=\frac{z}{1}$ and the plane x – y + z = 0 is $\left(\alpha ,\beta ,\gamma \right),then\alpha +\beta +\gamma$ is equal to………

IF the foot of the perpendicular from the point A(1, 4, 3) on the plane P : 2x + my + nz = 4, is $\left(-2,\frac{7}{2},\frac{3}{2}\right),$ then the distance of the point A form the plane P, measured parallel to a line with direction ratios 3, 1, 4, is equal to:

Let $x=4$ be a directrix to an ellipse whose centre is at the origin and its eccentricity is $\frac{1}{2}$ . If $P(1,\beta ),\beta >0$ is a point on this ellipse, then the equation of the normal to it at $P$ is: