List of top Mathematics Questions asked in CUET (PG)

A circle S passes through the point (0, 1) and is orthogonal to the circles (x-1)² + y² = 16 and x² + y² = 1. Then
A. Radius of S is 8
B. Radius of S is 7
C. Centre of S is (-7, 1)
D. Centre of S is (-8, 1)

Given below are two statements: One is lebelled as Assertion A and the other is labelled as Reason R.
Assertion A: If two circles interesect at two points, then the line joining their centres is prependicular to the common chord.
Reason R: The perpendicular bisectors of two chords of a circle intersect at its centre.
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: The number of parallelograms in a chess board is 1296.
Reason R: The number of parallelograms when a set of m parallel lines is intersected by another set of n parallel lines is ^mC₂.ⁿC₂
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?

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 :

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 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:

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:

Match List-I and List-II

LIST I		LIST II
A.	Addition Theorem on probability	I.	\(P(Ei/A)=\frac{p(Ei)P(A/Ei)}{\displaystyle\sum_{l=1}^nP(Ei)P(A/Ei)},i=1,2\)
B.	Binomial distribution	II.	\(P(A\cap B)=P(A)P(B/A),if P(A)\neq0\)
C.	Baye's rule	III.	\(P(A\cup B)=P(A)+P(A)+P(B)-P(A\cap B)\)
D.	Multiplication theorem on prob	IV.	\(P(x=r)=^nC_rp^rq^{n-r},r=0,1,.....,n\)

Choose the correct answer from the options given below:

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

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:

The two adjacent sides of a cyclic QUADRILATERAL are 2 and 5 and the angle between them is 60°. If the third side is 3, the remaining fourth side is -

If A, B and C are acute positive angles such that A + B + C = π and cot A cot B cot c = K, then

The top of a hill observed from the top and bottom of a building of height h is at angles of elevation p and q respectively. The height of the hill is -

The mean deviation from the mean of the AP a, a+d, a+2d,..... a + 2nd is

An athlete takes as much time in running 200 m as a car takes in covering 500m. The distance covered by the athlete during the time the car covers 2 km is:

If \(cot^2 45\degree-sin^2 45\degree = K sin^2 30\degree x tan^2 45\degree xsec^2 45\), then the value of K is

The monthly income and expenditure of a person were ₹10,000 and ₹6,000 respectively. Next year, his income increased by 15% and his expenditure increased by 8%. Then the percentage increase in his savings is:

The area of a rhombus is 120 cm² and length of its one diagonal is 24 cm. Find the perimeter of the rhombus (in cm).

A sum of money doubles itself on simple interest in 10 years. Find the rate of interest per annum.

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