List of top Questions asked in CUET (PG)

Which of the following statement is true:

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)

Match List-I with List-II and choose the correct option:

LIST-I	LIST-II
(A) The solution of an ordinary differential equation of order 'n' has	(III) 'n' arbitrary constants
(B) The solution of a differential equation which contains no arbitrary constant is	(IV) particular solution
(C) The solution of a differential equation which is not obtained from the general solution is	(I) singular solution
(D) The solution of a differential equation containing as many arbitrary constants as the order of a differential equation is	(II) complete primitive

Choose the correct answer from the options given below:

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})}

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 \( R \) be the planar region bounded by the lines \( x = 0 \), \( y = 0 \) and the curve \( x^2 + y^2 = 4 \) in the first quadrant. Let \( C \) be the boundary of \( R \), oriented counter clockwise. Then, the value of:

\[ \oint_C x(1 - y) \, dx + (x^2 - y^2) \, dy \] is equal to:

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:

If p is a prime number and a group G is of the order p2, then G is:

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?

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?

Which of the following offences may be considered a 'victimless crime'?

Match the LIST-I with LIST-II

Choose the correct answer from the options given below: