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Delhi University MCA Previous Year Questions (PYQs)

Delhi University MCA DU Mathematics PYQ

Delhi University MCA PYQ
The system of linear equations  has





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Delhi University MCA PYQ
Let $z=\cos\!\left(\frac{2\pi}{7}\right)+i\sin\!\left(\frac{2\pi}{7}\right)$. Then the principal argument of $\overline{(1-z^{2}})$ is equal to





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Delhi University MCA PYQ
The set of all $\lambda\in R$ such that {an} where $a_n=\sqrt{\lambda^2n^2+n+1}-n, n\in N$, is





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Delhi University MCA PYQ
DU MCA Question 2019





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Delhi University MCA PYQ
The complex number  is the root of the quadratic equation with real coefficients





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Delhi University MCA PYQ
The locus of the point (α, β) such that the line y = αx + β, become a tangent to the hyperbola  9x2 - 4x2  = 36, is





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Delhi University MCA PYQ
Which of the following is not correct statement?





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Delhi University MCA PYQ
Let T = R3→R3 be a linear transformation defined by T(x,y,x) = (x-y, y-z, z-x). If rank(T) = ρ and nulity(T)=





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Delhi University MCA PYQ
If $\int \sin^2x\cos3xdx=\frac{\sin{x}}{a}+\frac{\sin{3x}}{b}-\frac{{\sin5x}}{c}$, then a+b+c=





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Delhi University MCA PYQ
The area (in squares units) of the quadrilateral formed by the tangent lines drawn to the ellipse  at the ends of its two latus rectums is





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Delhi University MCA PYQ
Let V=M2(R) denote the vector space 2x2 matrices with real entries over the field. Let T:V→V be defined by T(P) = Pt for any P∈V, where Pt is the transpose of P. If E is the matrix representation of T with respect to the standard basis of V the det(E) is equal to 





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Delhi University MCA PYQ
The equation 2x2 + y2 - 12x - 4y + 16 = 0 represents





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Delhi University MCA PYQ
If f(x) = ax3 + bx2 + x + 1 has a local maxima value 3 at the point of local maxima x = - 2, then f(2) is equal to :





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If the Newton-Raphson method is applied to find a real root of  f(x) = 2x2 + x - 2 = 0 with initial approximation x0 = 1. Then the second approximation x2 is





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Delhi University MCA PYQ
The equation of common tangent to the curve y2 = 8x and xy = - 1 is





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Solution:

Let the common tangent be: $$y = mx + c$$ For curve \( y^2 = 8x \):
Condition for tangency gives: $$mc = 2 \quad \text{(1)}$$ For curve \( xy = -1 \):
Condition for tangency gives: $$c^2 = 4m \quad \text{(2)}$$ Substitute \( c = \frac{2}{m} \) from (1) into (2): $$\left(\frac{2}{m}\right)^2 = 4m \Rightarrow \frac{4}{m^2} = 4m \Rightarrow m^3 = 1 \Rightarrow m = 1$$ Then, \( c = \frac{2}{1} = 2 \)

Final Answer:
$$\boxed{y = x + 2}$$
Delhi University MCA PYQ
The greatest value of the function  y = sin x . sin2x on (-∞, +∞)





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Delhi University MCA PYQ

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 PYQ
Let f(x) = sin8x + cos8x. Then the function f increases in the interval





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





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Delhi University MCA PYQ
The area of the plane region by the curves x + 2y2 = 0 and x + 3y2 = 1 above x axis is equal to 





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Delhi University MCA PYQ
The perimeter of the loop of the curve 9y2 = (x-y)(x-5)2





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





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Delhi University MCA PYQ
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

$G = U(98) = \{k \in \mathbb{N} : k \leq 98,\ \gcd(k,98)=1 \}$ 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
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
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
The series $$\sum_{n=3}^{\infty}\frac{1}{\,n(\log n)(\log\log n)^{c}\,} $$ converges if
(a) 0<c<1
(b) c>1
(c) -1<c<0
(d) c=1






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Delhi University MCA PYQ

If the following holds:

$ \lim_{n\to\infty}\frac{u_n}{v_n}=l,\quad u_n>0,\ v_n>0,\ l\ne 0 $ then choose the correct option:

(a) $\sum u_n$ and $\sum v_n$ converge together

(b) $\sum u_n$ diverges and $\sum v_n$ converges

(c) $\sum u_n$ converges and $\sum v_n$ diverges

(d) Neither $\sum u_n$ converges nor $\sum v_n$ diverges






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Let U and V be vector spaces. 
Then they are isomorphic iff there is a bijection from a basis of U to a basis of V. 
The isomorphism is the basis changer function.
This means that if U and V are finite-dimensional vector spaces, they are isomorphic iff dim(U)=dim(V).
Delhi University MCA PYQ
The condition for the line $x\cos\alpha+y\sin\alpha=p$ to touch the curve $\left(\dfrac{x}{a}\right)^3+\left(\dfrac{y}{b}\right)^3=1$ is $(a\cos\alpha)^t+(b\sin\alpha)^t=p^t$ where $t$ is equal to





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Delhi University MCA PYQ
If $g$ is Riemann integrable on $[a,b]$ and $f(x)=g(x)$ except for a finite number of points in $[a,b]$, then

 (a) $f$ is Riemann integrable and $\int_a^b f(x)\,dx=\int_a^b g(x)\,dx$

 (b) $f$ is Riemann integrable and $\int_a^b f(x)\,dx<\int_a^b g(x)\,dx$ 

 (c) $f$ is Riemann\text{-}integrable and $\int_a^b f(x)\,dx>\int_a^b g(x)\,dx$

 (d) $f$ is not Riemann\text{-}integrable 





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