List of practice Questions

For real numbers a and b, define aRb if b-a+√5 is an irrational number. Then the relation R is:

The equation of the normal to the curve y = 2sinx at (0, 0) is:

The function \(f(x)= \frac{x^4}{4}-\frac{x^2}{2}\) has

With reference to time series, match List I with List II

Choose the correct answer from the options given below:

The value of x given by \(cos (tan ^{-1}x) = sin (cot^{-1} \ \frac{3}{4})\)is:

The general solution of the differential equation ydx + xdy = 0 is:

A doll making small-scale unit calculates the variable cost of making x number of dolls per day as three times the square of \(x\). The fixed cost of packaging x dolls is  \(₹ 2800\). The marginal cost of producing 120 dolls:

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

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