List of top Questions asked in CUET (UG)

Match List I with List II

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The value of x given by \(cos (tan ^{-1}x) = sin (cot^{-1} \ \frac{3}{4})\)is:

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

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

The marked price of a chair is \(150%\)\(\%\) of its cost price. A discount of \(30\%\) is given while selling the chair. What is the profit percentage?

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)

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:

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

Find the missing term
1, 4, 27, 16, ?, 36, 343

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

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

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

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 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

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: 

Two friends A and B invest in a business in partnership, B borrows 20% of A's salary, combines it with 60% of his salary and invest with A, who puts all of his remaining salary. One year later the ratio of profit A and B is 5:3 respectively and B returns Rs. 21000 to A which he borrowed from him. What is the difference between salary of A and B ?

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

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For x+y=8, the maximum value of xy is:

The maximum value of Z=5x+3y subject to the constraints \(2x+4y \leq16,\) \(3x+y\leq9\). \(x,y\geq0\) is:

If \(f(x)=e^x\) and \(g(x)=log_{e}{x}=lnx  \) then \((gof)(x) \) is

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 :

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 ?

Match List I with List II

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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 :