List of practice Questions

Match List I with List II

Choose the correct answer from the options given below:

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

Choose the correct answer from the options given below :

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

Choose the correct answer from the options given below:

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 ?

If \(A: B: C=1:4: 7 \) and \(B = (2x) % \)\(%\)\(\%\)of \((A+C)\), then \(x \) is :

The area of a circle is \(154 \text{ }cm^2\). Find the circumference of the circle. Take \(\pi=\frac{22}{7}\)

Principal value of \(\tan^{-1}(\sqrt3)+\tan^{-1}(1)\) is :