Delhi University MCA 2019 Previous Year Questions (PYQs) – Page 3 of 5
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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
at the ends of its two latus rectums is1
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Solution
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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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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The equation of common tangent to the curve y2 = 8x and xy = - 1 is
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Solution
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:
$$\boxed{y = x + 2}$$
The greatest value of the function y = sin x . sin2x on (-∞, +∞)
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Let f(x) = sin8x + cos8x. Then the function f increases in the interval
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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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Solution
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