List of top Mathematics Questions asked in CUET (PG)

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 -
If 3x+4y = 60 and 4x+3y= 59, then the value of x+y is:
Two pipes A and B can fill a tank in 18h and 12h respectively. If both the pipes are opened simultaneously, then how much time will be taken to fill the tank
Twelve men can do a work in 8 days and 16 women can do the same work in 12 days. Eight men and 8 women worked together for 6 days. How many additional men need to be employed to complete the remaining work in one day?
Evaluate
\(\frac{tan 55°}{cot 35°}+\frac{sin 33°}{cos 57°}+\frac{sec 49°}{cosec 41°}\)
An article is marked for ₹200. A shopkeeper earns 25% profit even after allowing \(12\frac{1}{2}\)% discount on it. What is the cost price of the article (in ₹)?
What is the median of the given data?
2, 3, 5, 0, 8, 13, 4
A sum is to be distributed among 4 persons in the proportion of 3:3:2:5. If second person gets ₹ 500 more than the third person them what is the share of the fourth person
The value of \(e^{\log10 \tan1\degree+\log10 \tan2\degree+\log10 \tan3\degree+.........+\log10 \tan89\degree}\)is
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 :
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
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 (AT)-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 :
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 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)
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
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:
Which of the following functions is differentiable at x = 0?
If f and g are differentiable functions in (0, 1) satisfying f(0) = 2 = g(1), g(0) = 0 and f(1) = 6, then for some c ∈]0, 1[
If A1, A2 be two AM's and G1, G2 be two GM's between a and b, then \(\frac{A1+A2}{G1G2}\) is equal to
The H.P. of two numbers is 4 and the arithmatic mean A and geometric mean G satisfy the relation 2A + G2 = 27, the numbers 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_______.
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:
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