Delhi University MCA DU Mathematics Previous Year Question Paper and Solution with PDF

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Delhi University MCA
Previous Year Questions

Delhi University MCA
Previous Year Questions
Delhi University MCA

Delhi University MCA Previous Year Questions (PYQs)

Delhi University MCA DU Mathematics PYQ

Qus : 1

The system of linear equations

has

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Qus : 6

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Qus : 7

The complex number

is the root of the quadratic equation with real coefficients

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Qus : 8

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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Qus : 9

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Qus : 10

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Qus : 11

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Qus : 12

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Qus : 13

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Qus : 14

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Qus : 15

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Qus : 16

Which of the following is not correct statement?

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Qus : 17

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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Qus : 18

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Qus : 19

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Qus : 20

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Qus : 21

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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Qus : 22

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) = P^t 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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Qus : 23

The equation 2x² + y² - 12x - 4y + 16 = 0 represents

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Qus : 24

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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Qus : 25

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 x₂is

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Qus : 26

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:

$\boxed{y = x + 2}$

Qus : 27

The greatest value of the function y = sin x . sin2x on (-∞, +∞)

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Qus : 28

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Qus : 29

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

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Qus : 30

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Qus : 31

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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Qus : 32

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Qus : 33

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

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Qus : 34

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Qus : 35

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Qus : 36

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Qus : 37

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Qus : 38

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Qus : 39

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Qus : 40

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Qus : 41

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Qus : 42

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Qus : 47

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Qus : 48

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Qus : 49

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Qus : 74

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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).

Qus : 75

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Qus : 78

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Qus : 80

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Qus : 85

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Delhi University MCA Previous Year Questions (PYQs)

Delhi University MCA DU Mathematics PYQ

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