List of top Questions asked in CUET (PG)

Match List-I and List-II

LIST I		LIST II
A.	\(\lim\limits_{x\rightarrow0}(1+sinx)^{2\cot x}\)	I.	e-1/6
B.	\(\lim\limits_{x\rightarrow0}e^x-(1+x)/x^2\)	II.	e
C.	\(\lim\limits_{x\rightarrow0}(\frac{sinx}{x})^{1/x^2}\)	III.	e2
D.	\(\lim\limits_{x\rightarrow\infty}(\frac{x+2}{x+1})^{x+3}\)	IV.	½

Choose the correct answer from the options given below:

Given below are two statements:
Statement I: For n ≥1, we have \(\frac{1}{1·2}+\frac{1}{2·3}+\frac{1}{3·4}+.....+\frac{1}{n(n+1)}=\frac{n^2}{n+1}\)
Statement II: (1+x)ⁿ ≥ (1+nx) for all natural number n, where x > -1.
In the light of the above Statements, choose the most appropriate answer from the options given below :

Match List-I and List-II

LIST I		LIST II
A.	ABC : FGJ :: KNO : ?	I.	CLL
B.	CAT : DDY :: BIG : ?	II.	AKB
C.	AKJ : GNM :: EMD : ?	III.	PJG
D.	HNP : PDA :: DLP : ?	IV.	PQT

Choose the correct answer from the options given below:

Given below are two statements: One is labelled as Assertion (A) and the other is labelled as Reason (R):
Assertion (A): Sum of n terms of series 1²+3²+5²+... to n terms is \(\frac{n}{3}(4n^2-1)\).
Reasons (R): Sum of the squares of first a natural numbers 1², 2², 3²,....,n² is \(\frac{n(n+1)(2n+1)}6\).
In the light of the above Statements, choose the correct answer from the options given below:

Given below are two statements:
Statement I: The sum of the series 2{7^-1+3^-17^-3 +5^-1.7^-5 +....} is log_e(\(\frac{4}{3}\)).
Statement II: The value of e always lies between 2 and 3.
In the light of the above Statements, choose the most appropriate answer from the options given below :

In a memory mapped I/O system, which of the following will not be there?

If the mean of 18, 19, x, 25 and 26 is 21, then find the mean of 5, 11, 13, 19 and (3x-1)

If \(\frac{\sin{\theta} + \cos{\theta}}{\sin{\theta} + \cos{\theta}} = \frac{1}{77}\), then find the value of \(\sin^4{\theta} - \cos^4{\theta}\):

Identify which of the given conclusions follows from the given statements:
Statement I: No perfume is a fragrance.
Some perfumes are deodorants.
All deodorants are cologne.
Statement II I. At least some perfumes are colognes.
II. No fragrance is deodorant.

Read the following information carefully and answer the question given below:
A is the son of B. C, B's Sister, has a son D and a daughter E. F is the maternal uncle of D. How is E related to F? 

Figure (x) is embedded in which one of the four alternatives

Choose the group of letters which is different from others:
POCG, BUDX, ATRG, ZIKL, FQMV

National Development Council was constituted on____.

If a=cos2α+isin2α and b=cos2β+isin2β then _______

If y = x²+x²+x+1, then y________

The mean of 50 items is 100. At the time of calculations, two items 80 and 190 were wrongly taken as 90 and 20. What is the correct value of the mean?

If f: R→R is defined by f(x)=3x²-5 and g: R→R by g(x)=\(\frac{x}{x+1}\) then gof(x) is

The number of vectors of unit length perpendicular to vectors \(\vec{a}\) = (1,1,0) and \(\vec{b}\) = (0,1,1) is

Let A(3, 0, - 1) , B(2, 10, 6) and C(1, 2, 1) be the vertices of a triangle and M be the mid-point of AC. If G divides BM in the ratio 2:1, then cos( ∠GOA ) (O being the origin) is equal to______.

If A = 26, SUN = 27 then CAT = ?

If A, G, H be respectively, the A.M., G.M., and H.M. of three positive numbers a, b, c; then the equation whose roots are these numbers is given by

If \(\vec{a},\vec{b},\vec{c}\) are non-coplanar unit vectors such that \(\vec{a}\times(\vec{b}\times \vec{c})=\frac{(\vec{b}+\vec{c})}{\sqrt2}\) then the angle between a and b is

The equation of the bisector of the acute angle between the lines 3x-4y+7=0 and 12x+5y-2=0

Given below are two statements: One is labelled as Assertion (A) and the other is labelled as Reason (R):
Assertion (A): Equation 5x-7y+z=11, 6x-8y-z=15 and 3x+2y-6z=7, then the system is consistent and has infinitely many solutions.
Reasons (R): If D=0 then the 3 linear equations is consistent and has infinitely many solutions if D₁ = D₂ = D₃=0.
In the light of the above Statements, choose the correct answer from the options given below :

if \(\vec{a}\), \(\vec{b}\) and \(\vec{c}\) are three non-coplanar vectors, then \((\vec{a}+\vec{b}+\vec{c}) [(\vec{a}+\vec{b})\times(\vec{a}+\vec{c})]\) equal to