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MATHS 4

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Marks: 25

Q.   1

How much interest will be earned on ‘2000 at 6 % simple interest for 2 years?

 

Q.   2

Sonata deposited 50,000 in a bank for two years with the interest rate of 5.5% p.a. how much interest would she earn?

 

Q.   3

Rohika invested 70,000 in a bank at the rate of 6.5% p.a. simple interest rate. He received 85,925 after the end of term. Find out the period for which sum was invested by Rahul.

 

Q.   4

Kanti Devi deposited some amount in a bank for 7 ½ years at the rate of 6% p.a. simple interest. Kanti Devi received ‘1, 01,500 at the end of the term. Compute initial deposit of kanti Devi initial deposit of kanti Devi

 

Q.   5

Shila has a sum of 46,875 was lent out at simple interest at the end of 1 year 8 months the total amount was 50,000. Find the rate of interest percent per annum.                                                             

Q.   6

A sum amount to 1,331 at a principal of 1,000 at 10% compounded annually; Find the time.

 

Q.   7

If a sum triples in 15 years at simple rate of interest, the rate of interest per annum will be

Q.   8

In what time will a sum of money double its  at 6.25 Simple interest?

 

Q.   9

2000 is invested at annual rate of interest of 10%. What is the amount after two years if compounding is done monthly?

 

Q.   10

Which is a better investment 3% per year compounded monthly or 3.2% per year simple interest?  Given that (1+0.0025)12 = 1.0304

 

Q.   11

A builder borrows Rs. 2550 to be paid back with compound interest at the rate of 4% per annum by the end of 2 years in two equal yearly installments. How much will each installment be?

 

Q.   12

A man buys a scooter on making a cash down payment of Rs. 16224 and promises to pay two more yearly installment of equivalent amount in next two years. If the rate of interest is 4% per annum, compounded yearly, the cash value of the scooter, is

 

Q.   13

The populations of Chandigarh is increase at a rate of 1% for first year, it decrease at the rate of 4% for the second year and for third year it again increase at the rate of 5%. Then what will be the population of Chandigarh are 50000.

 

Q.   14

Simple interest on a sum at 5% per annum for 2 years is Rs. 60. The compound interest on the same sum for the same period is

 

Q.   15

Find an expression for y given 𝒅𝒚 ÷ 𝒅𝒙= 𝟕𝒙𝟓

Q.   16

dy = ∫ −𝟏𝟐𝐱−𝟒 dx solve it;

 

Q.   17

Given f ‘(x) = 𝟏 ÷ 𝟐 𝒙𝟏/𝟑 - 𝟏 ÷ 𝟒 𝒙¼+ π, find f (x)

 

Q.   18

Given f ‘(x) = ∫ ( 𝟐 ÷ 𝒙 + 𝟑 ÷ 𝒙𝟐 + 𝟏 ÷ 𝒙𝟓 ) dx

Q.   19

Find y as a function of x if 𝒅𝟐𝒚 ÷ 𝒅𝒙𝟐 = 2x when x = 2, y = 7 

 

Q.   20

Integrate ∫ (𝒘 + 𝟏÷𝒘 ) (𝒘 − 𝟏÷𝒘 ) dx

Q.   21

If 𝒅𝟐𝒚 ÷ 𝒅𝒙𝟐 = 10 – 3x, find 𝒅𝒚 ÷ 𝒅𝒙 + c

Q.   22

If f(x) = xk and f ‘(1) = 10, then the value of k is

Q.   23

The points of discontinuity of the function, f(x) = 𝒙𝟐+𝟐𝒙+𝟓 ÷ 𝒙𝟐−𝟑𝒙+𝟐 are

Q.   24

Necessary condition of Euler’s theorem is

Q.   25

If f(x, y) = 𝒙+𝒚÷𝒚 , x 𝒅𝒙÷𝒅𝒛 + y 𝒅𝒛÷𝒅𝒚=? 

Q.   26

Find the approximate value of [𝟎. 𝟗𝟖𝟐 + 𝟐. 𝟎𝟏𝟐 + 𝟏. 𝟗𝟒𝟐]½

Q.   27

f (x, y) = x3 + xy2 + 901 satisfies the Eulers theorem

Q.   28

Question 27 For a homogenous function if critical points exist the value at critical points is

Q.   29

The derivates of f(x) = ∫𝒙³𝒙² 𝟏÷𝒍𝒐𝒈𝒕 dt, (x>0) is  

Q.   30

The points of intersection of F1(x) =∫x2 (𝟐𝐭 − 𝟓)𝐝𝐭 𝐚𝐧𝐝 𝐟𝟐(x) =∫x0𝟐𝐭 𝐝𝐭, 𝐚𝐫𝐞

Q.   31

The solution of the equation 𝒙𝟐𝒅𝟐𝒚 ÷ 𝒅𝒙𝟐 = In x, when x=1, y=0 and 𝒅𝒚 ÷ 𝒅𝒙 = -1

Q.   32

The differential equation representing the family of curves y2 = 2c(x+√𝒄), where c is a positive perimeter, is of

Q.   33

The order and degree of the differentiate equations (𝟏 + 𝟑 𝒅𝒚÷𝒅𝒙)𝟐/𝟑 – 4 ( 𝒅𝟑𝒚÷𝒅𝒙𝟑 ) are

Q.   34

The cost function for the production of x unit of a commodity is given by C(x) = 2x3 +: 15x2 + 36x + 15

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