List of practice Questions

If the order of a matrix A is 2 × 3, the order of matrix B is 3 × 4 and the order of matrix C is 3 × 4, then the order of the matrix (A, B).C^T is

The vectors \(3\hat{i}-\hat{j}+2\hat{k},2\hat{i}+\hat{j}+3\hat{k}\) and \(\hat{i}+λ\hat{j}-\hat{k}\) are coplanar if λ is :

A tank can be filled by two pipes A and B in 18 minutes and 24 respectively. Another tap C can empty the full tank in 36 mintues. If the tap C is opened 6 minutes after the pipes A and B are opened, the tank will become full in a total of :

The following data is taken from a simple random sample :
3, 7, 5, 9, 15, 11, 8, 4, 6, 2
The point estimate of the population standard deviation is :

For a certain data test statistic ‘t’ is calculated as : \(|t|=|\frac{65-68}{\frac{4}{\sqrt{15}}}|=2.90\), then select the correct option :

Shyam takes a loan of ₹5,00,000 with 8% annual interest rate for 10 years. The value of EMI under flat rate system is :

The maximum value of Z=5x+3y subject to the constraints \(2x+4y \leq16,\) \(3x+y\leq9\). \(x,y\geq0\) is:

Which of the following are propositions ?
(A) The sum of four angles of quadrilateral is 180°.
(B) A line segment has two end points.
(C) 7𝑥+3=14
(D) 3 X 9=21

Area bounded by y=|x-5| and x-axis between x = 2; and x = 4 is:

The value of \(\int\limits_{-1}^1x^2 [x] dx\) is:

The value of \(\int\limits_{-3}^2x^2 |2x| dx\) is:

The percent income of a year on 6% debentures of face value of ₹100 available in the market for ₹200 is:

A random variable X has the following probability distribution

then value of E(X) is:

The integrating factor of differential equation \(\frac{dy}{dx}+y=\frac{1+y}{x}\) is:

The interval in which the function \(f(x) = 10-6x-2x²\) is decreasing is:

The integral \(∫\frac{dx}{x^2(x^4+1)}^{\frac{3}{4}}\) equals_____.

Match List I with List II

Choose the correct answer from the options given below:

The cost price 15 articles is equal to the selling price of 20 articles. Find the loss percentage.

If point \(B(0, 1)\) is equidistant from points\( A(5, -3) \)and \(C(x, 6)\), then find the values of \( x\)

The heights of two right circular cones are in the ratio \(1 : 2\) and the circumferences of their bases are in the ratio \(3: 4.\) Find the ratio of their volumes.

The area of the region bounded by the line 2y = 5x +7, x-axis and the lines x - 1 and x -3 is :

If y = Asinx + Bcosx, Where A and B are constants, then \(\frac{d^2y}{dx^2}\) is equal to :

If xy = e^(x-y), then the value of \(\frac{dy}{dx}\) at (1, 1) is :

If f(x) is a function which is derivable in an interval 1 containing a point c, then match List I with List II.

List I		List II
A.	f(x) has second order derivate at x = c such that f'(c) = 0 and f'(c) < 0; then	I.	point of inflexion of f(x)
B.	Necessary condition for point x = c to be extreme point of f(x) is	II.	‘c’ is point of local minima of f(x)
C.	If f'(x) does not change its sign as x crosses the point x = c then it is called a	III.	c is a critical point of f(x)
D.	f(x) has second order derivate at x = c such that f'(c) and f'(c) > 0; then	IV.	‘c’ is point of local maxima of f(x)

Choose the correct answer from the options given below :

Which one of the following is not an Arithmetic progression ?