MAH CET MCA Mathematics Previous Year Questions (PYQs) – Page 1 of 7
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The curve for which the normal at any point (x, y) and the line joining the origin to that point form an isosceles triangle with the x-axis as the base is
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Solution
$R_1 = {(x, y) \mid x, y \in R, x^2 + y^2 \le 25}$
$R_2 = {(x, y) \mid x, y \in R, 9y \ge 4x^2}$
Then $R_1 \cap R_2 =$
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Solution
The intersection of the given relations does not define a function type (neither one-one nor onto).
Which statement is false for $x^2 - 3y^2 - 4x - 6y - 11 = 0$ ?
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Solution
The given equation represents a hyperbola with transverse and conjugate axes not equal, so asymptotes do not intersect at right angles.
$a = z^2 + z + 1$ where $z$ be the complex polarizing number, then what is not the value of $a$?
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Solution
Let $z = e^{i\theta}$,
then $a = 1 + e^{i\theta} + e^{2i\theta} = \dfrac{\sin(3\theta/2)}{\sin(\theta/2)} e^{i\theta}$.
After simplification, the value $\dfrac{1}{3}$ is not possible.
A bookshelf has 5 red books, 3 blue books, and 4 green books. If you randomly select a book from the shelf, what is the probability that it is blue?
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Solution
Let $K$ be the set of all odd numbers less than $200$ and $M$ be the set of products of two distinct numbers taken from $K$, then find the total number which is divisible by $5$ in $M$.
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Solution
Among $100$ odd numbers, $20$ are multiples of $5$.
Required count $= 100 \times 20 - C(20,2) = 392$.
$x$ is a G.M., $y$ is a H.M. of two numbers. If $\dfrac{x}{y} = \dfrac{5}{4}$, then the numbers are in ratio
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Solution
Let numbers be $a, b$.
Then $\dfrac{x}{y} = \dfrac{\sqrt{ab}}{\dfrac{2ab}{a+b}} = \dfrac{a+b}{2\sqrt{ab}} = \dfrac{5}{4}$.
Let $\dfrac{a}{b} = r$,
then $\dfrac{r+1}{2\sqrt{r}} = \dfrac{5}{4}$.
On solving, $r = 4$ or $\dfrac{1}{4}$.
Hence ratio = $1:4$.
Sum of squares of odd positive integers $1$ to $100$ belongs to
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Solution
Sum of squares of first $n$ odd numbers $= \dfrac{n(2n-1)(2n+1)}{3}$.
For $n = 50$, sum $= \dfrac{50 \times 99 \times 101}{3} = 166650$.
Hence, it lies between $150000$ and $250000$.
The number of values of $C$ such that the straight line $y = 4x + C$ touches the curve $x^2 + 4y^2 = 4$ is
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Solution
Substitute $y = 4x + C$ in $x^2 + 4y^2 = 4$.
To touch, discriminant $= 0$.
After solving, $C = \pm \dfrac{2}{\sqrt{17}}$.
Hence, there are $2$ possible values.
$f(x) = \sqrt{\log_{1/4}\left(\dfrac{5x - x^2}{4}\right)}$, find the domain of $f(x)$.
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Solution
For $\log_{1/4}\left(\dfrac{5x - x^2}{4}\right)$ to be $\ge 0$,
$\dfrac{5x - x^2}{4} \le 1$ since base $< 1$.
Simplifying gives $x = 1, 4$.
Hence, domain $= {1,4}$.
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