The following data shows the percentage of urban Indian households who have a high speed 5G internet connection

Year(x)	2020	2021	2022	2023	2024
Urban housue hold(y)	9%	18%	21%	29%	38%

If a straight line trend by the method of least squares is \(y=23+6.9(x-2022)\)
then the forecast for the year 2025 is

If \(x=2 a t, y=a t^2\), where ' a ' is a constant, then \(\frac{d^2 y}{d x^2}\) at \(x=2\) is :

There are 4 bulbs out of which 2 are defective. Each bulb is tested in random order till both the defective bulbs are identified. The probability that only two tests are required to identify the defective bulbs is:

An insect moves along the ellipse \(\frac{x^2}{16}+\frac{y^2}{4}=1\), when the rate of change of abscissa is 4 times that of ordinate, then the insect lies in the quadrant:
A. \(I or II\)
B. \(III or IV\)
C. \(II or III\)
D. \(II or IV\)
Choose the correct answer from the options given below:

In a linear programming problem (LPP), the maximum value of the objective function \(Z=2 x+5 y\) subjected to the constraints :
\(\begin{array}{l}2 x+3 y \leq 6 \\2 x+y \leq 4 \\x, y \geq 0\end{array}\)
is

From the below-mentioned graph of shaded feasible region of a linear programming problem (LPP) with objective function
\(z=1.50 x+1.00 y\), the maximum value of \(z\) will be;-

The equation of normal at the point (1, 1) on the curve \(2y + x^3 = 3\) is:

The total cost \(C(x)\) associated with the production of \(x\) units of an item is given by
\(\ C(x)=0.001 x^3+0.06 x^2+20 x+500\).
The marginal cost when 10 units are produced is:

A sofa set costing ₹ \(36000\) has a useful life of \(10\) years. If the annual depreciation is ₹ \(3000\) , then the scrap value by linear method is:

Match List-l with List-II

List-l (Compound/Elements)	List-II (Uses)
(A) Magnesium based alloy is constituent of	(I) Bullets
(B) Lanthanoid oxide	(II) Petroleum cracking
(C) Mixed oxides of Lanthanoids are employed in	(III) Television screen
(D) Misch metal	(IV) Lanthanoid metal and iron

Choose the correct answer from the options given below :

Identify the incorrect statement(s) among the following:
(A) Two electric field lines of force never intersect.
(B) Two opposite charges, each of \( 10 \times 10^{-9} \, \text{C} \), separated by 5 mm. The magnitude of the dipole moment is \( 5 \times 10^{-11} \, \text{C-m} \).
(C) Electric field intensity due to a single charge varies as the square of the distance from the charge, whereas electric field intensity due to an electric dipole varies inversely as the cube of the distance of the point.
(D) Electric field intensity due to an electric dipole has spherical symmetry around it in space.
Choose the correct answer from the options given below:

A capacitor of capacitance C is first charged by a battery of V volts. It is disconnected from the battery and is filled with a dielectric of dielectric constant K. The ratio of energy stored in the two cases, respectively will be

The solution of a LPP with basic feasible solutions (0,0), (10,0), (0,20), (10, 15) and objective function Max Z = 2x + 3y is: