For the following questions answer them individually
Let A (1, 2) and C(- 3, -6) be two diagonally opposite vertices of a rhombus, whose sides AD and BC are parallel to the line $$7x - y = 14$$. If B ($$ \alpha, \beta $$) and D ($$ \gamma, \delta $$) are the other two vertices, then $$ \alpha+ \beta+\gamma+\delta $$ is equal to
Let $$ \frac{\pi}{2}<\theta< \pi $$ and $$\cot\theta=-\frac{1}{2\sqrt{2}}.$$ Then the value of $$\sin\left( \frac{150}{2}\right)\left(\cos 80 + \sin 80\right)+\cos\left( \frac{150}{2}\right)\left(\cos 80 - \sin 80\right)$$ is equal to
If the mean and the variance of the data
Table
are $$ \mu $$ and 19 respectively, then the value of $$\lambda $$+ \mu$$ is
Let $$I(x)=\int\frac{3dx}{\left(4x+6\right)\left(\sqrt{4x^{2}}+8x+3\right)}$$ and $$I(0)=\frac{{\sqrt{3}}}{4}+20.$$
If $$I\left( \frac{1}{2} \right)=\frac{a\sqrt{2}}{b}+c, \text { Where a,b,c } \in N,gcd(a,b)=1, \text{ a+b+c is equal to}$$
The area of the region enclosed between the circles $$x^{2}+y^{2}=4 \text{ and } x^{2}+(y-2)^{2}=4$$ is
Let $$\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$$ be three vectors such that $$\overrightarrow{a}\times\overrightarrow{b}=2(\overrightarrow{a}\times\overrightarrow{c}).$$ If $$ \mid \overrightarrow{a}\mid, \mid\overrightarrow{b}\mid = 4, \mid \overrightarrow{c}\mid = 2,$$ and the angle between \overrightarrow{b}$$ and $$ \overrightarrow{c} is 60^{o}$$, then $$\mid\overrightarrow{a}\cdot\overrightarrow{c}$$ is
The least value of $$(\cos^{2} \theta- 6\sin \theta \cos \theta + 3\sin^{2} \theta +2)$$ is
Let PQ be a chord of the hyperbola $$\frac{x^{4}}{cd}-\frac{y^{b^{2}}}{cd}=1$$, perpendicular to the x-axis
suck thet OPQ is an equilaterl triangle, O beging the center of the hyperbola. IF the eccentricity of the hyperbola is SS\sqrt{3}. $$ then the area of the triangle OPQ is
$$ \text{Let }\sum_{k=1}^n a_k=\alpha n ^2 +\beta n.$$ If $$a_{10}=59$$ and $$ a_6 = 7a_1,$$ then $$ \alpha+\beta $$ is equal to
The system of linear equations
$$x + y + z = 6$$
$$2x + 5y + az =36$$
$$x + 2y + 3z = b$$
