List of top Questions asked in CUET (PG)

If C is the positively oriented circle represented by \( |z|=2 \), then \( \int_C \frac{e^{2z}}{z-4} dz \) is:
Let f be a continuous function on \(\mathbb{R}\) and \( F(x) = \int_{x-2^{x+2} f(t) dt \), then F'(x) is}
If C is a triangle with vertices (0,0), (1,0) and (1,1) which are oriented counter clockwise, then \( \oint_C 2xydx + (x^2+2x)dy \) is equal to:
For the function \( f(x, y) = x^3 + y^3 - 3x - 12y + 12 \), which of the following are correct:
A. minima at (1,2)
B. maxima at (-1,-2)
C. neither a maxima nor a minima at (1,-2) and (-1,2)
D. the saddle points are (-1,2) and (1,-2)
Which of the following statement is true:
Consider the following: Let f(z) be a complex valued function defined on a subset \( S \subset \mathbb{C} \) of complex numbers. Then which of the following are correct?
A. The order of a zero of a polynomial equals to the order of its first non-vanishing derivative at that zero of the polynomial
B. Zeros of non-zero analytic function are isolated
C. Zeros of f(z) are obtained by equating the numerator to zero if there is no common factor in the numerator and the denominator of f(z)
D. Limit points of zeros of an analytic function is an isolated essential singularity
If \( S = \lim_{n \to \infty} \left(1-\frac{1}{2^2}\right)\left(1-\frac{1}{3^2}\right) ... \left(1-\frac{1}{n^2}\right) \), then S is equal to:
Let [x] be the greatest integer function, where x is a real number, then \( \int_{0}^{1} \int_{0}^{1} \int_{0}^{1} ([x] + [y] + [z]) \, dx \, dy \, dz = \)
Let V(F) be a finite dimensional vector space and T: V \(\to\) V be a linear transformation. Let R(T) denote the range of T and N(T) denote the null space of T. If rank(T) = rank(T\textsuperscript{2}), then which of the following are correct?
A. N(T) = R(T)
B. N(T) = N(T\textsuperscript{2})
C. N(T) \(\cap\) R(T) = \{0\
D. R(T) = R(T\textsuperscript{2})}

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Which of the following offences may be considered a 'victimless crime'?
What are the five ordeals, treated as divine means of proof of the guilt or innocence of the accused in the traditional Indian governance system?
Noted socio-legal researchers Shaw and Mckay propounded, "traditions of delinquency are transmitted through successive generations of the same region in the same way as language, customs and attitudes are transmitted". How it is known as?
Under the Protection of Women from Domestic Violence Act, 2005, the definition of "domestic relationship" includes:
In the Juvenile Justice (Care & Protection of Children) Act, 2015, "children in need of care and protection" specifically excludes:
What is one of the salient features of the Scheduled Castes and Scheduled Tribes (Prevention of Atrocities) Act?
Which unique preventive measures is mandated under the POCSO Act?
Which remedy is uniquely provided under the Protection of Women from Domestic Violence Act, 2005, that goes beyond traditional legal recourse?
What are the three main sources of typically finding physical evidence according to Forensic Sciences?