List of top Questions asked in CUET (PG)

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

Match List I with List II

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:

Let E be the ellipse\(\frac{x^2}{9}+\frac{y^2}{4}=1\) and C be the circle x² + y² = 9. Let P and Q be the points (1, 2) and (2, 1) respectively. Then

The point(s) at which function f is given by \(f(x)={\begin{Bmatrix}\frac{x}{|x|};x\lt0  \\ -1; x\geq0\end{Bmatrix}}\) is continuous is/are

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_______.

If f: R→R defined as of f(x) = x² + 1 then minimum value of f(x) is

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 -

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 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 :

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 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.

Each of the angle between vectors \(\vec{a},\vec{b}\) and \(\vec{c}\) is equal to 60°. If \(|\vec{a}|= 4,|\vec{b}| = 2\; and\; |\vec{c}|=6\) then the modulus of \(\vec{a}+\vec{b}+\vec{c}\) is

If \(\vec{a}=2\vec{i}+2\vec{j}+3\vec{k},\vec{b}=\vec{i}+2\vec{j}+\vec{k}\;and\;\vec{c}=3\vec{i}+\vec{j}\) are such that \(\vec{a}+\gamma\vec{b}\) is perpendicular to \(\vec{c}\) then determine the value of \(\gamma\)?

Match List-I and List-II

LIST I		LIST II
A.	\(|\vec{A}+\vec{B}|=|\vec{A}-\vec{B}|\)	I.	45°
B.	\(|\vec{A}\times\vec{B}|=\vec{A}.\vec{B}\)	II.	30°
C.	\(|\vec{A}.\vec{B}|=\frac{AB}{2}\)	III.	90°
D.	\(|\vec{A}\times\vec{B}|=\frac{AB}{2}\)	IV.	60°

Choose the correct answer from the options given below:

Given below are two statements :
Statement I: If the roots of the quadratic equation \(x^2-4x-log_3a=0\) are real, then the least value of a is 1/81.
Statement II: The harmonic mean of the roots of the equation \((5+ \sqrt2)x^2 - (4+\sqrt5)x + (8+2\sqrt5) = 0\) is 2.
In the light of the above statements, choose the correct answer from the options given below:

If A, B and C are any three sets, then
A. A-(B∩C) = (A ∩ B) - (A∩C)
B. A-(B∪C) = (A - B) ∩ (A-C)
C. n (A-B) = n(A) -n (A ∩ B)
D. A∩(B - C) = (A∩B) ∩ (A-C)
Choose the most appropriate answer from the options given below :

Choose the correct sequence of the four statements given below, so that the phrase makes a complete sense:
A. Then the sets of equations connecting both are known as transformation of co-ordinates.
B. We can associate a unique set of co-ordinates.
C. Given a point P in rectangular co-ordinates.
D. Called the curvilinear co-ordinates of P.
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 :

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

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

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