List of practice Questions

Suppose that a 95% confidence interval states that population mean is greater than 100 and less than 300. Then the value of sample mean \((\bar{x})\) and margin of error (E) respectively are :

A machine costing ₹ one lakh depreciates at constant rate 10%. Estimated useful life of machine is 8 years.
Match List I with List II

List I		List II
A.	Total depreciation in 2nd and 3rd year is	I.	₹81,000
B.	Value of machine after one year is	II.	₹17,100
C.	Value of machine after 2 year is	III.	₹43050
D.	Scrap value of machine is : given (1.1)3 - 2.144 & (0.9)3 - 0.4305	IV.	₹90,000

Choose the correct answer from the options given below :

A bond of face value ₹1000 matures in 10 years and interest is paid annually at 4% per annum. If the present value of the bond is ₹838, find the yield to maturity (1.04)^-10 ≈ 0.676.

Consider the following feasible region. Which of the following constraints represents the feasible region ?

A. 2x + 3y ≤ 6
B. x - 2y ≤ 2
C. 3x + 2y ≤ 12
D. 3x - 2y ≤ -3
E. x - 2y ≥ -1
Choose the correct answer from the options given below :

The graph of the inequality 3x - 2y > 6 is

An electric company has 300 Transistors, 400 Capacitors and 500 Inductors. The company wishes to make electronic goods using two circuits A and B. Requirement by circuit is as follows :

	Transistor	Capacitor	Inductor
A	175	300	200
B	125	100	300

The profit from circuit A and B is ₹2000 and ₹3000 respectively then constrains of the LLP based on this data are :

In a 1000 m race. A beats B by 50 meters or 10 seconds. The time taken by A to complete the race is :

If x = 4t², \(y=\frac{3}{t^3}\), then \(\frac{d^2y}{dx^2}\) at t = 1 is :

In a binomial distribution, the probability of getting a success is \(\frac{1}{3}\) and the standard deviation is 4. Then its mean is :

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

A vehicle whose cost is ₹7,00,000 will depreciate to scrap value of ₹1,50,000 in 5 years. Using linear method of depreciation, the book value of the vehicle at the end of the third year is :

The value of 28 mod 3 is.

A container is full of mango juice. One fifth of juice is taken out from this container and then an equal amount of water is poured into the bottle. This process is repeated 3 more times. The final ratio of juice and water in the container is:

Three partners A, B and C shared the profit in a business in the ratio 6:9:10 respectively. If A,B and C invested the money for 12 months, 7 months and 5 months respectively, then the ratio of their investment is:

A cistern is filled in 30 minutes by three pipes A, B and C. The pipe C is thrice as fast as pipe A and pipe B is twice as fast as A. The time taken by pipe A alone to fill the cistern is:

Match List I with List II

LIST I		LIST II
A.	The solution set of the inequality \(5x-8\gt2x+3,x\in R\ is,\)	I.	\((-\infin,\frac{6}{5}]\)
B.	The solution set of the inequality \(3x-4\lt5x+7,x\in R\ is,\)	II.	\((\frac{6}{5},\infin)\)
C.	The solution set of the inequality \(4x+15\le3(1-2x)is,\)	III.	\([10,\infin)\)
D.	The solution set of the inequality \(7x-8\ge2(1+3x)is,\)	IV.	\((-\frac{11}{2},\infin)\)

Choose the correct answer from the options given below:

If \(\begin{bmatrix} a+2&3b+2c\\c+3&7d+6 \end{bmatrix}=\begin{bmatrix} 2&-3\\3c&-8 \end{bmatrix}\), then the values of a,b,c and d are.

If \(3\begin{bmatrix} x&3\\2&1 \end{bmatrix}+4\begin{bmatrix} 1&2\\5&y \end{bmatrix}=\begin{bmatrix} 10&17\\26&11 \end{bmatrix}\)then the value of (3x+2y) is:

If the matrix \(A=\begin{bmatrix} 5&4a+6\\a+12&a+3 \end{bmatrix} \)is a symmetric matrix, then the value of a is:

If \(y=x^3\log x, then\ \frac{d^2y}{dx^2}\) is:

The maximum value of the function \(f(x)=x+\sqrt{1-x}\) on the interval [0,1] is, 

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

Match List I with List II

LIST I		LIST II
A.	The maximum value of the function \(f(x)=25x-\frac{5x^2}{2}+7\) in [-1,6] is	I.	24
B.	The minimum value of the function \(f(x)=2x^3-15x^2+36x+1\) in [1,5] is	II.	\(\frac{1}{16}\)
C.	The maximum value of the function \(f(x)=\frac{x}{2}-x^2\) in [0,1] is	III.	\(\frac{139}{2}\)
D.	The least value of the function \(f(x)=\frac{9}{x+3}+x\) in [-7,1], \(x\ne-3\) is	IV.	\(-\frac{37}{4}\)

Choose the correct answer from the options given below:

The probability distribution of a discrete random variable X is defined as:
\(P(X=x)=\begin{cases} 3kx & \text{for } x=1,2,3\\  5k(x+2) & \text{for } x=4,5 \\ 0& \text{otherwise}\end{cases}\)
The mean of the distribution is:

In a Binominal distribution, The probability of getting success is \(\frac{1}{5}\) and standard deviation is 4. then its mean is