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Delhi University MCA Previous Year Questions (PYQs)

Delhi University MCA 2021 PYQ

Delhi University MCA PYQ 2021

If $$ f(x) = \begin{cases} \dfrac{1}{|x|}, & |x| > 2 \\ A + Bx^2, & |x| \leq 2 \end{cases} $$ Then $f(x)$ is differentiable at $x = -2$ for

(a) A = $\tfrac{3}{4}$ ,B = $-\tfrac{1}{16}$
(b) A = $-\tfrac{3}{4}$ , B = $\tfrac{1}{16}$
(c) A = $-\tfrac{3}{4}$ ,B = $-\tfrac{1}{16}$
(d) A = $\tfrac{3}{4}$, B = $\tfrac{1}{16}$






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Delhi University MCA Previous Year PYQ Delhi University MCA DU MCA 2021 PYQ

Solution

Delhi University MCA PYQ 2021
The equation $e^{x-8}+2x-17=0$ has _____real root(s),





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Delhi University MCA PYQ 2021
$$ S_n = \left[ (n+1)(n+2)\cdots(n+n)\cdot \frac{1}{n^n} \right]^{\tfrac{1}{n}} $$ $$ \lim_{n \to \infty} S_n = \; ? $$ $$ (a)\;\tfrac{1}{e} \qquad (b)\;\tfrac{2}{e} \qquad (c)\;\tfrac{4}{e} \qquad (d)\;1 $$





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Delhi University MCA PYQ 2021
Which of the following is false: 
(a) Every convergent positive series is convergent. 
(b) Every absolutely convergent series is convergent. 
(c) If the series $Σ S_n$ converges and $Σ |S_n|$ diverges, then $Σ S_n$ is conditionally convergent. 
(d) The series $1 − 2^{-2} + 3^{-2} − 4^{-2} + …$ is a divergent series.





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Delhi University MCA PYQ 2021

$G = U(98) = \{k \in \mathbb{N} : k \leq 98,\ \gcd(k,98)=1 \}$ be a group, where $\mathbb{N}$ is the set of all natural numbers.

The number of generators of the largest cyclic subgroup of $G$ is

(a) 12
(b) 32
(c) 42
(d) 49






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Delhi University MCA PYQ 2021
Let $Re(z)$ and $Im(z)$ be the real and imaginary parts of any complex number $z$, and $\arg(z)$ denotes the principal argument of $z$. Let $z_1$ and $z_2$ be two distinct complex numbers such that $\operatorname{Re}(z_1) = |z_1 - 2| \quad \text{and} \quad \operatorname{Re}(z_2) = |z_2 - 2|.$ If $\arg(z_1 - z_2) = \frac{\pi}{6},$ then
(a) $\operatorname{Im}(z_1 + z_2) = 4\sqrt{3}$ 
(b) $\operatorname{Im}(z_1 + z_2) = \dfrac{4}{\sqrt{3}}$ 
(c) $\operatorname{Re}(z_1 - z_2) = 8$ 
(d) $\operatorname{Re}(z_1 - z_2) = 9$ 





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Delhi University MCA PYQ 2021
Which one of the following statements is NOT correct in the ring $ R = \mathbb{Z}_4 \oplus \mathbb{Z}_6? $ 





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Delhi University MCA PYQ 2021
Given that $3^x$=656. The value of $5^{x-5}$ is ...
(a) 81
(b) 125
(c) 225
(d) 1/125





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Delhi University MCA PYQ 2021
What is the next term in the series 6, 20, 42, 72, 110, ... is
(a) 156
(b) 210
(c) 110
(d) 119





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Solution

Given series: $6,\,20,\,42,\,72,\,110,\,\_\_$

First differences: $14,\,22,\,30,\,38$

Second differences: $8,\,8,\,8$ (constant)

Next first difference $= 38 + 8 = 46$

Next term $= 110 + 46 = 156$

Answer: $\boxed{156}$ ✅

Delhi University MCA PYQ 2021
Next term in the series zaa, yeb, xic, wod, vue, ...
is
(a) uaf
(b) uef
(c) teg
(d) tag





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Delhi University MCA Previous Year PYQ Delhi University MCA DU MCA 2021 PYQ

Solution

Reasoning: 1st letters go backward: z, y, x, w, v, u 2nd letters are vowels forward: a, e, i, o, u, then wrap to a 3rd letters go forward: a, b, c, d, e, f So the next term is uaf.
Delhi University MCA PYQ 2021
Age of a child is half of the age of father. Twenty years ago the age of father was 10 times the age of son. What is the age of father?
(a) 60 years
(b) 55 years
(c) 50 years
(d) 45 years





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Solution

Let father's age be $F$ and child's age be $C$.

Given $C = \dfrac{F}{2}$

Twenty years ago: $F - 20 = 10(C - 20)$

Substitute $C = \dfrac{F}{2}$:

$F - 20 = 10\left(\dfrac{F}{2} - 20\right)$

$F - 20 = 5F - 200$

$180 = 4F \Rightarrow F = 45$

Answer: $\boxed{45\text{ years}}$ ✅ (Option d)

Delhi University MCA PYQ 2021
In a race of 1 Kilometer, athlete A beats athlete B by 50 meters, in another race of 500 meters, athlete B beats athlete C by 50 meters. By how many meters (Approximately) can athlete A beat athlete C in a race of 400 meters?
(a) 50 meters
(b) 58 meters
(c) 62 meters
(d) 72 meters





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Solution

$\dfrac{v_A}{v_B}=\dfrac{1000}{950}=\dfrac{20}{19}$,   $\dfrac{v_B}{v_C}=\dfrac{500}{450}=\dfrac{10}{9}$

$\Rightarrow \dfrac{v_A}{v_C}=\dfrac{200}{171}$

When A runs $400$ m, C runs $400\times\dfrac{171}{200}=342$ m.

Difference $=400-342=58$ m.

Answer: 58 meters ✅

Delhi University MCA PYQ 2021
Persons A, B, and C can finish a work in 15, 10, and 12 days respectively. Person B and person C start the work together but are asked to leave after 4 days. In how many days will the remaining work be done by person A?





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Solution

Rates: $A=\frac{1}{15},\; B=\frac{1}{10},\; C=\frac{1}{12}$ (work/day)

Work done by $B+C$ in 4 days: $4\!\left(\frac{1}{10}+\frac{1}{12}\right)=4\cdot\frac{11}{60}=\frac{11}{15}$

Remaining work: $1-\frac{11}{15}=\frac{4}{15}$

Time for $A$: $\dfrac{\frac{4}{15}}{\frac{1}{15}}=4$ days

Answer: $\boxed{4\text{ days}}$ ✅


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