List of top Questions asked in CUET (UG)- 2023

Let f: R→R defined by f(x)=2x³-7 for x∈R. Then:
(A) f is one-one function
(B) f is many to one function
(C) f is bijective function
(D) f is into function
Choose the correct answer from the options given below:

A product costs the manufacturer ₹20 per unit. The demand function is given by p(x) = 1000-20x, then the quantity for maximum profit is:

The equation of the normal to the curve y = 2sinx at (0, 0) is:

Mr. Dileep Rao has set up a sinking fund so that he can accumulate \(₹ 10,00,000\) in \(10 \)years for his children's higher education. How much amount should Dileep Rao deposit at the beginning of each year to accumulate this amount at the end of\( 10\) years. If the interest rate is  compounded annually? Given that \((1.12)^{11}=3.477\) (Rounded off to the nearest paise)

With reference to time series, match List I with List II

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The angle at which the normal to the plane 4x - 8y + z = 7 is inclined to y-axis is :

For the given five values 17, 26, 20, 35, 44, the three years moving averages are :

The total cost of a firm is given by c(x)=\(\frac{2x^3}{3}-4x^2+8x+7. \) The level of output at which marginal cost is minimum is

Match List I with List II

Choose the correct answer from the options given below:

The equation of the curve whose slope is given by \(\frac{dy}{dx}=\frac{4x}{y}\), x>0,y>0 and which passes through the point (2, 2) is: 

The general solution of the differential equation ydx + xdy = 0 is:

Match List I with List II

List I		List II
A.	\(\frac{d^2y}{dx^2}+(\frac{dy}{dx})^{\frac{1}{2}}+x^{\frac{1}{2}}\)	I.	order 2, degree 1
B.	\(\frac{dy}{dx}=\frac{x^{\frac{1}{2}}}{y^{\frac{1}{2}}(1+x)^{\frac{1}{2}}}\)	II.	order 2, degree not defined
C.	\(\frac{d^2y}{dx^2}=\cos3x+\sin3x\)	III.	order 2, degree 4
D.	\(\frac{d^2y}{dx^2}+2\frac{dy}{dx}+y=\log(\frac{dy}{dx})\)	IV.	order 1, degree 2

Choose the correct answer from the options given below :

Area of the region bounded by the curve |x|+|y|=1 and x-axis is :

The function \(f(x)= \frac{x^4}{4}-\frac{x^2}{2}\) has

A sum of money triples itself in 3 years at simple interest. In how many years will it become 9 times of itself?

A doll making small-scale unit calculates the variable cost of making x number of dolls per day as three times the square of \(x\). The fixed cost of packaging x dolls is  \(₹ 2800\). The marginal cost of producing 120 dolls:

Which of the following is correct ?

A student goes to school from his residence at a speed of \(2\frac{1}{2}\) km/h and reaches school 6 minutes late. If he travels at a speed of 3 km/h, he reaches 10 minutes before time. What is the distance of his school from his residence ?

The vectors \(3\hat{i}-\hat{j}+2\hat{k},2\hat{i}+\hat{j}+3\hat{k}\) and \(\hat{i}+λ\hat{j}-\hat{k}\) are coplanar if λ is :

Principal value of \(\tan^{-1}(\sqrt3)+\tan^{-1}(1)\) is :

If the selling price is doubled, the profit triples. Find the profit % :

A tank can be filled by two pipes A and B in 18 minutes and 24 respectively. Another tap C can empty the full tank in 36 mintues. If the tap C is opened 6 minutes after the pipes A and B are opened, the tank will become full in a total of :

If \(A: B: C=1:4: 7 \) and \(B = (2x) % \)\(%\)\(\%\)of \((A+C)\), then \(x \) is :

The slope of normal to the curve \(y = 3x^2-6x\) at x = 0 is:

The rate of change of the area of a circular disc with respect to its circumference when radius is 3 is: