CAT Linear Equations Practice Questions With Solutions | Download Free PDF

If $x$ and $y$ are positive real numbers such that $\log_{x}(x^2 + 12) = 4$ and $3 \log_{y} x = 1$, then $x + y$ equals

If $x$ and $y$ are real numbers such that $x^{2} + (x - 2y - 1)^{2} = -4y(x + y)$, then the value $x - 2y$ is

Any non-zero real numbers x,y such that $y\neq3$ and $\frac{x}{y}<\frac{x+3}{y-3}$, Will satisfy the condition.

Let both the series $a_{1},a_{2},a_{3}$... and $b_{1},b_{2},b_{3}$... be in arithmetic progression such that the common differences of both the series are prime numbers. If $a_{5}=b_{9},a_{19}=b_{19}$ and $b_{2}=0$, then $a_{11}$ equals

For some real numbers a and b, the system of equations $x + y = 4$ and $(a+5)x+(b^2-15)y=8b$ has infinitely many solutions for x and y. Then, the maximum possible value of ab is

For a real number x, if $\frac{1}{2}, \frac{\log_3(2^x - 9)}{\log_3 4}$, and $\frac{\log_5\left(2^x + \frac{17}{2}\right)}{\log_5 4}$ are in an arithmetic progression, then the common difference is

Let $a_n = 46 + 8n$ and $b_n = 98 + 4n$ be two sequences for natural numbers $n \leq 100$. Then, the sum of all terms common to both the sequences is

For any natural number n, suppose the sum of the first n terms of an arithmetic progression is $(n + 2n^2)$. If the $n^{th}$ term of the progression is divisible by 9, then the smallest possible value of n is

Let $0 \leq a \leq x \leq 100$ and $f(x) = \mid x - a \mid + \mid x - 100 \mid + \mid x - a - 50\mid$. Then the maximum value of f(x) becomes 100 when a is equal to

The largest real value of a for which the equation $\mid x + a \mid + \mid x - 1 \mid = 2$ has an infinite number of solutions for x is