List of practice Questions

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)

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

Let f: R→R defined by f(x)=2x³-7 for x∈R. Then:
(A) f is one-one function
(B) f is many to one function
(C) f is bijective function
(D) f is into function
Choose the correct answer from the options given below:

Match List I with List II

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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 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?

Which of the following is correct ?

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

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

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

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 ?

A sum of money triples itself in 3 years at simple interest. In how many years will it become 9 times of itself?

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

If the selling price is doubled, the profit triples. Find the profit % :

The slope of normal to the curve \(y = 3x^2-6x\) at x = 0 is:

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

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

If \(\frac{x+y}{x-y}+\frac{x-y}{x+y}=\frac{10}{3}\),then \(\frac xy=\)

Angle between tangents to the curve y=x²-5x+6 at the points (2, 0) and (3, 0) is:

The rate of change of the area of a circular disc with respect to its circumference when radius is 3 is:

The shortest distance between the lines \(\frac{x + 3}{1} = \frac{y-2}{2} = \frac{z+4}{3} \space and \space  \frac{x+3}{-3} = \frac{y+7}{2} = \frac{z-6}{4}\) is: =

Match List I with List II

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If Mr. Ravi borrows a sum of ₹1,50,000 at an interest rate of 10% (flat) for a tenure of 3 years, then his EMI based on above data is (approximately) ₹:

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 ?