List of top Mathematics Questions asked in CUET (PG)

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

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

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

A. If A and B are two invertible matrices, then (AB)^-1 = A^-1 B^-1
B. Every skew-symmetric matrix of odd order is invertible
C. If A is non-singular matrix, then (A^T)^-1 = (A^-1)^T
D. If A is an involutory matrix, then (I+A) (I-A) = 0
E. A diagonal matrix is both an upper triangular and a lower triangular
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 -

If x,y,z are all distinct and \(\begin{vmatrix} x & x^2 & 1+x^3\\ y & y^2 & 1+y^3 \\ z & z^2 & 1+z^3 \end{vmatrix}\)=0, then the value of xyz is

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

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: 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:

Match List-I and List-II

LIST I		LIST II
A.	8 : 81 :: 64 : ?	I.	290
B.	182 : ? :: 210 : 380	II.	132
C.	42 : 56 :: 110 : ?	III.	342
D.	48 : 122 :: 168 : ?	IV.	625

Choose the correct answer from the options given below:

Consider the adjoining diagram: What is the minimum number of different colours required to paint the figure such that no two adjacent regions have same colour?

If A = \(\begin{bmatrix}        2 & 3 & 1           \\[0.3em]        0 & -1           & 5 \end{bmatrix}\) and B = \(\begin{bmatrix} 1 & 2 & -1  \\[0.3em]  0 & -1  & 3 \end{bmatrix}\), what is the value of (2A-3B)?

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

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 ___.

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

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:

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:

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

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________

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______.

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