Kiran Expert Team Solutions for Chapter: Mock Test Model Practice Set, Exercise 55: Quantitative Aptitude

If $\mathrm{tan\theta }=\frac{1}{\sqrt{11}}$ and $0<\mathrm{\theta }<\frac{\mathrm{\pi }}{2}$, then the value of $\frac{{\mathrm{cosec}}^2\mathrm{\theta }-{\text{sec}}^2\mathrm{\theta }}{{\text{cosec}}^2\mathrm{\theta }+{\text{sec}}^2\mathrm{\theta }}=?$

If each angle of a triangle is less than the sum of the other two, then the triangle is :

$A, B$ and $C$ are three points on the circumference of a circle, and if $\stackrel{\rightharpoonup }{AB}=\stackrel{\rightharpoonup }{AC}=5\sqrt{2} cm$ and $\angle BAC={90}^o$, Find Radius.

Find the unit's digit in $\frac{{12}^{55}}{3^{11}}+\frac{8^{48}}{{16}^{18}}$

$2$ vessels have spirit and water in the ratio of $8:3$ and $5:1$ respectively. From these $2$ vessels, a third vessels of $35$ litres has to be filled in such a way that the new ratio of sprit and water becomes $4:1$. How many litres has been taken from first vessel?

A sum of money is taken at the rate of $6\%$ p.a. on simple interest. After $1$ year, $Rs.6800$ is paid as fine and the remaining money is paid with $5\%$ of simple interest. if the interest paid in the second year is $\frac{11}{20}$ times the interest paid in first year. Find the sum of money.

Mohit takes certain sum of money from a bank at $10\%$ p.a. compound interest. He clears his debt by paying two equal installments of $Rs.1000$ each at the end of first and second year. Find the money he borrowed?

A dog after seeing a cat finds that the cat is $25$ leaps away. Cat after seeing the dog starts running and the dog chases the cat. If in every minute dog takes $5$ leaps while cat takes $6$ leaps and $6$ leap of dog is equal to two leaps of cat. In how many minutes will the dog catch the cat?