CGL MAINS SCORE BOOSTER QUANT QUIZ-1

If $a^{2}+b^{2}+c^{2}=(a b+b c+c a)$ then find the value of $\frac{11 a^{2} b-3 a b^{2}}{2 a b c}$.

If $\frac{1}{a+\frac{1}{b+\frac{1}{c}}}=\frac{9}{26}$ then find the value of $(a+$ $b+c)$

Daniel is painting the walls and ceiling of a cuboidal hall with length, breadth and height of $15 \mathrm{~m}, 10 \mathrm{~m}$ and $7 \mathrm{~m}$ respectively. From each can of paint $100 \mathrm{~m}^{2}$ of area is painted. How many cans of paint will she need to paint the room.

The graphs of the equation $2 x+ y-6=0$ and $3x+2y-10=0$ Intersect at $\mathrm{P}(\mathrm{a}, \mathrm{b})$. What is the value of $\frac{a^{2}+b^{2}-a b}{a^{2}-b^{2}+a b}$ ?

If $a+b+c=3, \frac{1}{a}+\frac{1}{b}+\frac{1}{c}=0, \quad a c=\frac{4}{b}$ and $a^{3}+b^{3}+c^{3}=25$, then find the value of $a^{2}+b^{2}+c^{2}$?

Find the value

$\left(1-2 \sin ^{2} \theta\right)\left(\frac{1+\tan \theta}{1-\tan \theta}+\frac{1-\tan \theta}{1+\tan \theta}\right) \text { where, } 0 \leq \theta \leq 90$

Find the value.

$\frac{\tan 5 \theta+\tan 3 \theta}{4 \cos 4 \theta(\tan 5 \theta-\tan 3 \theta)}$

A metallic hemispherical bowl is made up of steel. The total steel used in making the bowl is $342 \pi \mathrm{cm}^{3}$. The bowl can hold $144 \pi \mathrm{cm}^{3}$ water then what is the total surface area of outer side metallic hemisphere ?

In the given figure, O is the center of the circle, and $\angle A O B=100^{\circ}$. Find $\angle A C B$? 

$A B C D$ is a Cyclic quardrilateral. The side $A B$ is extended to $E$ in such a way that $B E=B C$, If $\angle A D C=70^{\circ}, \angle B A D=105^{\circ}$ then $\angle D C E$ is equal to?