CAT Higher Order Equations Practice Questions With Solutions | Download Free PDF

For a sequence of real numbers $x_{1},x_{2},...x_{n}$, If $x_{1}-x_{2}+x_{3}-....+(-1)^{n+1}x_{n}=n^{2}+2n$ for all natural numbers n, then the sum $x_{49}+x_{50}$ equals

Consider the pair of equations: $x^{2}-xy-x=22$ and $y^{2}-xy+y=34$. If $x>y$, then $x-y$ equals

The number of real-valued solutions of the equation $2^{x}+2^{-x}=2-(x-2)^{2}$ is:

How many disticnt positive integer-valued solutions exist to the equation $(x^{2}-7x+11)^{(x^{2}-13x+42)}=1$ ?

If $x=(4096)^{7+4\sqrt{3}}$, then which of the following equals to 64?

For real x, the maximum possible value of $\frac{x}{\sqrt{1+x^{4}}}$ is

In how many ways can a pair of integers (x , a) be chosen such that $x^{2}-2\mid x\mid+\mid a-2\mid=0$ ?

If $x_1=-1$ and $x_m=x_{m+1}+(m+1)$ for every positive integer m, then $X_{100}$ equals

If the population of a town is p in the beginning of any year then it becomes 3 + 2p in the beginning of the next year. If the population in the beginning of 2019 is 1000, then the population in the beginning of 2034 will be

The product of two positive numbers is 616. If the ratio of the difference of their cubes to the cube of their difference is 157:3, then the sum of the two numbers is