Maths NCERT Exemplar Solutions Class 12th Chapter Nine

Let ${\left(2x^2+3x+4\right)}^{10}={\sum }_{r=0}^{20}?a_r{x}^r$ . Then $\frac{a_7}{a_{13}}$ is equal to

Let $y=y\left(x\right)$ be the solution of the differential equation, $x{y}^{\mathrm{\text{'}}}-y=x^2(x\mathrm{c}\mathrm{o}\mathrm{s}x+\mathrm{s}\mathrm{i}\mathrm{n}x),x>0$ . If $y\left(\pi \right)=\pi$ , then $y^{\mathrm{\text{'}}\mathrm{\text{'}}}\left(\frac{\pi }{2}\right)+y\left(\frac{\pi }{2}\right)$ is equal to:

If $1+\left(1-2^2\cdot 1\right)+\left(1-4^2\cdot 3\right)+\left(1-6^2\cdot 5\right)+\dots \dots .+\left(1-{20}^2\cdot 19\right)=\alpha -220\beta$ , then an ordered pair $(\alpha ,\beta )$ 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, b). Then the value of 7a + 3b is equal to……….

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

Let y = y(x) be the solution of the differential equation $x\left(1-x^2\right)\frac{dy}{dx}+\left(3x^{2}y-y-4x^3\right)=0,x>1,withy\left(2\right)=-2.$ Then y(3) is equal to$$

Let the solution curve y = y(x) of the differential equation $\left[\frac{x}{\sqrt[]{x^2-y^2}}+e^{\frac{y}{x}}\right]x\frac{dy}{dx}=x+\left[\frac{x}{\sqrt[]{x^2-y^2}}+e^{\frac{y}{x}}\right]y$ pass through the points (1, 0) and (2α, α), α > 0. Then a is equal to

Le aa₁, a₂, a₃,…… be an A.P. If ${\displaystyle \sum _{r=1}^{\infty }\frac{a_r}{2^r}=4,}$ then 4a₂ is equal to……

Let the mean and the variance of 20 observations x1, x2,…….x20 be 15 and 9, respectively. For $\in R$ , if the mean of ${\left(x_1+\alpha \right)}^2,{\left(x_2+\alpha \right)}^2,....,{\left(x_{20}+\alpha \right)}^2$ is 178, then the square of the maximum value of is equal to………….

Let S = {1, 2, 3,…., 2022}. Then the probability, that a randomly chosen number n from the set S such that HCF (n, 2022) = 1, is: