28/11/24
1) y= (x -1)eˣ then dy/dx at x=1
a) e b) 2e c) 1 d) 0
2) Which one of the following is the value of ∫3ᵃˣ dx ?
a) 3ᵃˣ⁺¹ b)3ᵃˣ c) 3ᵃˣ. logₑ3ᵃ d) 3ᵃˣ/alogₑ3
3) Solve by cramer's rule: x + y-3=0; x + 2y- 5=0.
4) What are the order and degree of d³y/dx³= 4 √(x² dy/dx +7).
5) For what value of x will (x -1)(3- x) have its maximum.
6) Find the area bounded by y= 4x -3, y= 0, x=1 and x=3.
7) The effective rate of interest corresponding a nominal rate of 7% p.a convertible quarterly is
a) 7% b) 7.5% c) 5% d) 7.18%
8) A boat sails a distance of 44km in 4 hours with the current. It takes 4 hours 48 minutes longer to cover the same distance against the current. Find the speed of the boat in still water and the speed of the current.
9) Ravi invested Rs4800 in 6% Rs100 shares quoted at Rs120. Calculate
a) number of shares held by him.
b) Ravi's income from the investment.
Ravi sold these shares, when they were quoted at Rs140 and invested the proceeds in 5% Rs10 shares quoted at Rs8. Calculate Ravi's income now (from the newly bought shares) and his percentage return now on his initial investment. 40, 240, 350, 175/24%
10) Ravi invested Rs6840 in buying shares of nominal value Rs30 which are being sold at 20% premium. The dividend on the shares is 12% per annum. Calculate
a) the market value of shares.
b) the number of shares bought by Ravi.
c) the dividend Ravi would receive at the end of the year. 36,190,684
1) The probability that a leap year will have 52 Tuesday or Saturday is
a) 2/7 b) 3/7 c) 4/7 d) 1/7
2) If A= 2 -1
-1 2 and I is the unit matrix of order 2, then find A².
3) Find dy/dx of x³ w.r.t. x³.
4) If 2ˣ + 2ʸ = 2ˣ⁺ʸ, then the value of dy/dx at x= y= 1.
a) 0 b) -1 c) 1 d) 2
5) The maximum value of xy when x + 2y = 8 is
a) 20 b) 16 c) 8 d) 24
6) 1) The fixed cost of new product is ₹18000 and the variable cost per unit is ₹550. If the demand function is p(r)= 4000 - 15x, find the break-even points.
7) 5) A man cover a certain distance from house to office, if he travel at 30 km per hour, then he is late by 10 mins, but if he travels at 40 km/hr then he reaches his office his 5 minutes earlier. Find his distance from home to office.
8) The value of a machine depreciated by 10% per year during the first two years and 15% per year during the third year. Express the total depreciation of the machine, as percent during 3 years.
9) Find the value(s) of which y=(x²-2x)² is an increasing function.
10) ∫ (e⁵ˣ + e³ˣ)/eˣ dx
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