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Given that (1<sup>2</sup> + 2<sup>2</sup> + 3<sup>2</sup> + ..... + 20<sup>2</sup>) = 2870, the value of (2<sup>2</sup> + 4<sup>2</sup> + 6<sup>2</sup> + ... + 40<sup>2</sup> ) is :

Correct Answer: 11480
= (22 +42 +62 + ..... + 402)
= (1 × 2)2 +(2 × 2)2 +(2 × 3)2 + ..... + (2 × 20)2
= 22 × (12 + 22 + 32 + ..... + 202)
= (4 × 2870)
= 11480

A machine depreciates in value each year at the rate of 10% of its previous value. However, every second year there is some maintenance work so that in that particular year, depreciation is only 5% of its previous value. If at the end of the fourth year, the value of the machine stands at Rs 1,46,205, then find the value of machine at the start of the first year.

The average value of property of Agil, Mugilan and Anithais Rs. 130cr. The Property of Agil is 20cr greater than the property value of Mugilan and Anitha property value is 50cr greater than the Agil property value. The value ofproperty of Anitha is

With respect to the numerical evaluation of the definite integral $${\text{K}} = \int_{\text{a}}^{\text{b}} {{{\text{x}}^2}{\text{dx,}}} $$   where a and b are given, which of the following statements is/are TRUE?
I. The value of K obtained using the trapezoidal rule is always greater than or equal to the exact value of the definite integral.
II. The value of K obtained using the Simpson's rule is always equal to the exact value of the definite integral.

The assessed value of a house is $72,000. The assessed value is 60% of the market value of the house. If taxes are $3 for every $1,000 of the market value of the house, how much are the taxes on the house?

Arrange the series of step involved in designing a filter for first order low pass filter Step 1: Select a value of C less than or equal to 1µF Step 2: Choose a value of high cut-off frequency fH Step 3: Select a value of R1C and RF depending on the desired pass band gain Step 4: Calculate the value of R

What is the value of higher heating value if the value of lower heating value is 10 J and the product has 5 moles of H2O and Enthalpy of vaporization is 4 J/mole at standard conditions?

The face value of a share is 60% of its market value. The selling price of the share is 20% less than its market value. Find the face value if the selling price is 24.32 rupees.

The market value of the share is 100% more than the face value. Find the relation between face value and discount if the selling price is 50% less than the market value.

The market value of a share is 80% of the face value. If the selling price = the market value, what percentage of the selling price is the face value.

The market value of the share is 88% more than the face value. Find the relation between face value and discount if the selling price is 12% less than the market value.