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AMU MCA Previous Year Questions (PYQs)

AMU MCA Function PYQ

AMU MCA PYQ
Let $f(x,y,z) = e^{\sqrt{1 - x^2 - y^2}}$. Then the range of $f$ is






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AMU MCA Previous Year PYQ AMU MCA AMU MCA 2020 PYQ

Solution

For real values:

$1 - x^2 - y^2 \ge 0$

$x^2 + y^2 \le 1$

Minimum value of $\sqrt{1 - x^2 - y^2}$ is $0$ (when $x^2+y^2=1$)

Maximum value is $1$ (when $x=y=0$)

So exponent varies from $0$ to $1$

$e^0 = 1$

$e^1 = e$

Hence range is $[1, e]$

AMU MCA PYQ
Let $f(x,y) = x^3 + y^3$ for all $(x,y) \in \mathbb{R}^2$. Then





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AMU MCA Previous Year PYQ AMU MCA AMU MCA 2021 PYQ

Solution

$f_x = 3x^2$ $f_y = 3y^2$ At (0,0) → critical point Second derivatives: $f_{xx} = 6x$, $f_{yy} = 6y$ At (0,0) → 0 Function changes sign around origin → saddle point
AMU MCA PYQ
If $S$ is the set of all real numbers except $-1$ and $*$ is defined by $a * b = a + b + ab$, then the inverse of $2 * 3$ is






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AMU MCA Previous Year PYQ AMU MCA AMU MCA 2020 PYQ

Solution

First compute:

$2 * 3 = 2 + 3 + (2)(3) = 11$

Inverse element $x$ satisfies:

$11 * x = 0$ (identity element is $0$)

$11 + x + 11x = 0$

$x(12) = -11$

$x = -\frac{11}{12}$


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