List of top Mathematics Questions asked in CUET (PG)

If \(\overrightarrow r\) is the position vector of any point on a surface S that encloses the volume V, then find \(\iint\limits_S\overrightarrow r.d\overrightarrow S\)

If every pair from among the equation x² + px + qr = 0, x² + qx + rp = 0 and x² + rx + pq = 0 has a common root, then the product of three common roots is_______.

Given below are two statements :
Statement I: The number of different number each of 6 digits that can be formed by using all the digits 1, 2, 1, 0, 2, 2 is 50.
Statement II: These are 4536 possibilities of writing the four digit numbers which have all distinct digits.
In the light of the above statements, choose the correct answer from the options given below:

A boat goes 12 km in one hour along the stream and 6 km in one hour against the stream. The speed of the stream in km/h is:

Let \(a = cos\frac{2π}7 + isin\frac{2π}7\), a = a + a²+a⁴ and β = a³+ a⁵ +a⁶ then the equation whose root are α, β 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 f: R→R defined as of f(x) = x² + 1 then minimum value of f(x) is

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

For x = 3, find the value of \(x^5+x^4-x^3-x^2+x-1.\)

A triangle with vertices (4, 0), (-1,-1), (3, 5) is

If the curve ay + x² = 7 and x³ = y, cut orthogonally at (1, 1), then the value of a is -

Match List-I and List-II

LIST I		LIST II
A.	No. of triangles formed using 5 points in a line and 3 points on parallel line is	I.	20
B.	No. of diagonals drawn using the vertices of an octagon	II.	10
C.	The no. of diagonals in a regular polygon of 100 sides is	III.	45
D.	A polygon with 35 diagonals has sides	IV.	4850

Choose the correct answer from the options given below:

Sonu and Monu start together from point A to reach to B, with speeds, 5 km/h and 3 km/h respectively. If Sonu reaches B one hour before Monu, then the distance between A and B is:

Mohan invest a certain sum at the rate of Simple Interest 5% per annum. Find the number of years for which Mohan has to invest the the sum to double his sum

Ankit owes ₹ 42,580 on his credit cards, but he could pay only ₹ 12,580. If the annual rate of compound interest is 10%, then how much will he owe after 4 years?

Which of the following discount option in most beneficial for shop keeper?
(A) Successive discount of 20%, 30% and then pay 10% Service Tax. 
(B) Successive discount of 30%, 10% and then pay 10% Service Tax. 
(C) Pay Service Tax of 10% first, then successive discount of 20%, 30%. 
(D) Pay Service Tax of 10% first, then successive discount of 30%, 20%. 
Choose the most appropriate answer from the options given below

The percentage of loss when an article is sold at Rs. 50 is the same as that of the profit when it is sold at Rs. 70. Percentage of profit or loss on the article is ___.

If each observation of a Row data whose variance is σ² is multiplied by h, then the variance of the new set is

Given below are two statements: One is lebelled as Assertion A and the other is labelled as Reason R.
Assertion A: If the A.M. and G.M. between two numbers are in the ratio m : n, then the numbers are in the ratio \(m+\sqrt{m^2-n^2}:m-\sqrt{m^2-n^2}\)
Reason R: If each term of a G.P. be raised to the same power, the resulting sequence also forms a G.P.
In the light of the above statements, choose the correct answer from the options given below:

If a Chord which is normal to the parabola y² = 4ax at one end subtends a right angle at the vertex, then its slope is -

Renu speaks truth in 70% of the cases and Bina in 75% of the cases. The percentage of ceses they are likely to contradict each other in stating the same fact is

Which statistical method is best suitable for testing the goodness of fit between an observed and expected distribution?

Match List-I and List-II

LIST I		LIST II
A.	The angle between the straight lines, 2x2+ 3y2-7xy=0 is	I.	\(\tan^{-1}\frac{3}{5}\)
B.	The circles x2+y2+x+y=0 and x2+y2 +x-y=0 intersect at angle	II.	25π
C.	The area of circle centered at (1,2) and passing through (4,6) is	III.	π/4
D.	The parabola y2=4x and x2 =32y intersect at point (16,8) at angle	IV.	π/2

Choose the correct answer from the options given below:

The sum of two digits no. is 10, on reversing the digits of a number the number is decrease by 36. Find the number.

If each of n numbers x_i = i is replaced by (i + 1)x_i, then the new mean is