List of top Mathematics Questions asked in CUET (PG)

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 ___.

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

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:

Given below are two statements :
Statement I: \(\int\limits_{-a}^af(x)dx=\int\limits_{0}^a[f(x)+f(-x)]dx\)
Statement II : \(\int\limits_{0}^1\sqrt{(1+x)(1+x^3)}dx\) is less than or equal to \(\frac{15}{8}\).
In the light of the above statements, choose the most appropriate answer from the options given below :

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

Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: An elevator starts with m passengers and stops at n floors (m \(\leq\) n). The probability that no two passengers alight at the same floor is \(\frac{^np_m}{m_n}\)
Reason R: If (n + 1) p is an integer, say m, then\(p(x=r)= ^nC_rp^Ω(1-p)^{n-Ω} \)is maximum when r = m or r = m -1
In the light of the above statements, choose the most appropriate answer from the options given below :

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?

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

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

A straight line has equation y=-x+6 which of the following line is parallel to it?

Match List-I and List-II

LIST I		LIST II
A.	Value of\(\lim\limits_{x\rightarrow0}\left(\frac{sinx}{x}\right)^{\frac{sinx}{x-sinx}}\)	I.	e3
B.	Value of \(\lim\limits_{x\rightarrow0}\int\limits_0^x\frac{sint^2dt}{x^2}\)is	II.	0
C.	Value of \(\lim\limits_{x\rightarrow0}(e^{2x}+x)^{\frac{1}{x}}\)is	III.	1
D.	Value \(\lim\limits_{x\rightarrow a}\frac{log(x-a)}{log(e^x-e^a)}\)of	IV.	e-1

Choose the correct answer from the options given below:

The line integral per unit area along the boundary of small area around a point in vector field \(\overrightarrow A\) is called

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

Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: If dot product and cross product of \(\vec{A}\;and\;\vec{B}\)are zero, it implies that one of the vector \(\vec{A}\;and\;\vec{B}\) must be null vector
Reason R: Null vector is a vector with a zero magnitude.
In the light of the above statements, choose the correct answer from the options given below:

Which of the following is true :
A. Two vectors are said to be identical if their difference is zero.
B. Velocity is not a vector quantity.
C. Projection of one vector on another is not an application of dot product.
D. The maximum space rate of change of the function which is increasing direction of line function is known as gradient of scalar function.
Choose the most appropriate answer from the options given below :

If y = x²+x²+x+1, then y________

Given below are two statements:
Statement I: The angle between the vectors \(2\hat{i}+3\hat{j}+\hat{k}\) and \(2\hat{i}-\hat{j}-\hat{k}\) is \(\pi/2\)
Statement II: The vector \(\hat{a}\times(\hat{b}\times \hat{c})\) is coplanar with \(\hat{a}\) and \(\hat{b}\)
In the light of the above statements, choose the correct answer from the options given below:

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

Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R.
3 Assertion A: \(\int\limits_{-x}^{3}(x^3+5)dx=30\)
Reason R: f(x) = x³ +5 is an odd function
In the light of the above statements, choose the correct answer from the options given below:

The tangent to the hyperbola x² - y² = 3 are parallel to the straight line 2x + y +8 = 0 at the following points:

Given below are two statements: One is lebelled as Assertion A and the other is labelled as Reason R.
Assertion A: f(x) = tan²x is continuous at x = π/2
Reason R: g(x) = x² is continuous at x = π/2
In the light of the above statements, choose the correct answer from the options given below:

A. If (12 P)₃ = (123)_p, then value of P is infeasible.
B. The simplified sum of product form of the Boolean expression is \((P+\vec{Q}+\vec{R}).(P+\vec{Q}+R). (P+Q+\vec{R}) \;is\; (P+\vec{Q}.\vec{R})\).
C. The minimum number of D flip-flops needed to design a mod(258) counter is 8.
Choose the correct answer from the options given below :

If the unit vectors \(\vec{a}\) and \(\vec{b}\) are inclined at an angle 2θ such that \(|\vec{a}-\vec{b}|\lt 1\) and \(0 \leq \theta \leq \pi\), then θ lies in the interval.