List of practice Questions

If CE||DB, what is the value of x:

A man standing on the bank of a river observes that the angle subtended by a tree standing on the opposite bank is 60° on his side of Bank. When he moved away 24 m from the bank, he finds the angle to be 30°. Find the breadth of the river:

Which of the following statements are incorrect?
(A) Volume of a cone = \(\frac{1}{3} \pi r^3 h\)
(B) Volume of a cone = \(\frac{1}{3} \pi r^2 h\)  
(C) Volume of a hemisphere = \(\frac{2}{3} \pi r^2\)  
(D) Volume of a hemisphere = \(\frac{2}{3} \pi r^3\)  
(E) Volume of a cylinder = \(\frac{1}{3} \pi r^3 h\)  
Choose the correct answer from the options given below:

The difference between two numbers is 24. If one number is 2 times the second. Then the two numbers will be:

Which of the following statements are incorrect?(A) Volume of a cone = \(\frac{1}{3} \pi r^3 h\) (B) Volume of a cone = \(\frac{1}{3} \pi r^2 h\)  (C) Volume of a hemisphere = \(\frac{2}{3} \pi r^2\)  (D) Volume of a hemisphere = \(\frac{2}{3} \pi r^3\)  (E) Volume of a cylinder = \(\frac{1}{3} \pi r^3 h\)  Choose the correct answer from the options given below:

Which of the following is correct for standard deviation, where \(\bar{X}\) = mean 

A car costing ₹8,50,000 has scrap value of ₹1,25,000. If annual depreciation charge is ₹1,45,000, then useful life of the car is:

The following data are from a simple random sample: 1, 4, 7
The point estimate of the population standard deviation is:

A coin is tossed 5 times. The probability of getting atleast one head is:

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

A motor boat covers 16 km in 2 hours downstream and 14 km in 2 hours upstream. The speed of the motor boat is:

The maximum profit that a company can make if the profit function is given by
\(P(x)=32+24x-18x^2\) is:

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

For matrix \(A = \begin{bmatrix}3&1\\ 7&5\end{bmatrix}\), the values of x and y so that \(A^2+xI=yA\) are:

Let A and B be symmetric matrices of same order, then which of the following statement is true?

If \(x^{\frac{3}{4}}+y^{\frac{3}{4}}=a^{\frac{3}{4}}\) (a is a constant) then \(\frac{dy}{dx}\) is equal to :

If \(A = \begin{bmatrix} 4&5&2\\ 3&-1&7\end{bmatrix}\), then the sum of the elements of the matrix AA^T is:

If the mean of the probability distribution is 5, then the value of k is:

For the LPP Max Z=3x+4y, x+y≤40; x+2y≤ 60, x≥0, y≥0 the solution is:

The solution of \(7x ≡ 3(mod 5)\) is:

The region represented by the system of inequalities x, y≥0, y≤8, x + y≤4 is:

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

Choose the correct answer from the options given below:

The random variable X has a probability distribution P(X) of the following form, where k is some number.

Then P(x≤2) is:

Fisher's price index number is:

For the formula \(t= \frac{μ_1 - μ_2}{\sqrt {\frac{S_1^2}{n_1}+\frac{S_2^2}{n_2}}}\) consider of the following statements:
A. \(μ_1\) and \(μ_2\) are sample mean and population mean respectively.
B. \(n_1\) and \(n_2\) are sample sizes of two samples from same population.
C. \(S_1\) and \(S_2\) are sample means of two samples from same population.
D. \(S_1\) and \(S_2\) are standard error of two samples from same population.
E. \(n_1\) is the sample size and \(n_2\) is the population size.
Choose the correct answer from the options given below: