Jamia Millia Islamia MCA 2024 Previous Year Questions (PYQs) – Page 4 of 10
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Which word does NOT belong with the others?
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Solution
$\text{Milk}$ (others are milk products).
Play is to actor as concert is to —
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Solution
A concert is performed by a $,\text{musician}$.
A man walks $5,\text{km}$ south, turns right and walks $3,\text{km}$, then turns left and walks $5,\text{km}$. In which direction is he from the starting place?
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Solution
Coordinates: $(0,0)!\to!(0,-5)!\to!(-3,-5)!\to!(-3,-10)$, which is to the south-west of the start.
Find the number of triangles in the figure given below.
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Solution
On careful counting of all the small, medium, and large triangles in the figure,
the total number of triangles = $14$.
A and B are brothers. C and D are sisters. A’s son is D’s brother.
How is B related to C?
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Solution
If A’s son is D’s brother → D is A’s daughter.
So, C and D are sisters → both daughters of A’s brother (B).
Hence, B is the uncle of C.
Let A={1,2,3} and R={(1,1),(2,2),(3,3),(1,2),(2,3),(1,3)}. Then R is
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Solution
$A={1,2,3},; R={(1,1),(2,2),(3,3),(1,2),(2,3),(1,3)}$
Reflexive: $(1,1),(2,2),(3,3)\in R\Rightarrow$ reflexive.
Symmetric: $(1,2)\in R$ but $(2,1)\notin R\Rightarrow$ not symmetric.
Transitive: check the only nontrivial chain: $(1,2)$ and $(2,3)\Rightarrow (1,3)$, which is in $R$.
Pairs with $(x,x)$ keep the second pair; $(1,3)$ can only compose with $(3,3)$ giving $(1,3)$; $(2,3)$ with $(3,3)$ gives $(2,3)$. All required compositions are in $R$.
$\boxed{\text{$R$ is reflexive and transitive, but not symmetric.}}$
On A={1,2,3} let R={(1,2)}. Then R is
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Solution
Not reflexive (missing $(1,1),(2,2),(3,3)$). Not symmetric (since $(2,1)\notin R$). Transitive holds vacuously because there is no pair starting at $2$ to trigger $(1,2)$∘$(2,\cdot)$.
A={1,2,3}. Which $f:A\to A$ does not have an inverse?
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Solution
A, C, and D are bijections (permutations), hence invertible. In B, both $2$ and $3$ map to $1$ (not one-to-one), so not bijective $\Rightarrow$ no inverse.
The maximum number of equivalence relations on the set $A = {1, 2, 3}$ are
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Solution
Number of equivalence relations = Number of partitions of the set = Bell number $B_3 = 5$.
If $f : \mathbb{R} \to \mathbb{R}$ such that $f(x) = 3x$, then what type of function is $f$?
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Solution
Number of equivalence relations = Number of partitions of the set = Bell number $B_3 = 5$.
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