List of practice Questions

For a discrete random variable X, whose probability distribution is defined as :
\(P(x)=\begin{cases} 2k(x+1) ;& x = 0,1 \\ 3kx; &  x=2 \\ k(5-x) & x=3 \end{cases}\)
The value of mean will be

A borrowed Rs 10000 each from his friends B and C for 2 years. He was supposed to pay compound interest at 10% per annum to B and simple interest 11% per annum to C. Who charged more interest at the end of 2 years and how much more ?

Match LIST I with LIST II

List-I		List-II
A	If the corner points of the feasible region For an LPP are (0, 4), (5, 0), (7, 9), then the minimum value of the objective function Z =5x+y is.	I	27
B	If the corner points of the feasible region for an LPP are (0, 0), (0, 2), (3, 4), (5, 3). then the maximum value of the objective function Z=3x+4y	II	60
C	The comer points of the feasible region for an LPP are (0, 2), (1, 2), (4,3), (7, 0). The objective function is Z = x+5y. Then (Max Z+Min Z) is	III	25
D	If the corner points of the feasible region for an LPP are (0, 4), (3, 0), (3, 2), (6,9) The objective function is Z=2x+6y. Then (Max Z-Min Z)	IV	26

Choose the correct answer from the options given below

A sum of money triples it self in 3 years at compound interest. In how many years will it becomes 9 times

Two unbiased coins are tossed. What is the probability of getting one head and one tail?

Which three of the given can be added to get a rectangular figure?

Choose the correct mirror image of the following:

The ratio between length and breadth of a rectangle is \(3:2\). If area of the rectangle is \( 96cm^2\), then length of the rectangle is

If\( cos 6\theta= sin 3\theta\), then the value of \(\theta\) is:

₹800 becomes ₹956 in 3 years at a certain rate of simple interest. If the rate of interest is increased by 4%, what will ₹ 800 amount to in 3 years:

The diameter of the driving wheel of a bus is 140 m. How many revolutions per minute must the wheel make in order to keep a speed of 66 km/h?

The absolute maximum value of the function f(x)=sinx + cosx, x \(\in\)[0, \(\pi\)] is:

The feasible region of an LPP is shown in the figure below.
If \( z=3x+9y\), then the minimum value of \(z\) occurs at :

The function \(f(x)=sinx+cosx,0\leq x\leq 2\pi \) is :

The value of C in Rolles's theorem for the function \(f(x)=e^xsinx,x\epsilon[0,\pi]\),is :

Objective function \(z=30x-30y \) is subject to which combination of constraints, with feasible solution shown in the figure.

(A)\(x \geq 0, \quad y \geq 0, \quad x \leq 15\)
(B)\(y \leq 20, \quad x + y \leq 30\)
(C)\(x + y \leq 30, \quad x + y \leq 15, \quad 2x - y \leq 5\)
(D)\(2x + y \leq 30, \quad x + y \leq 15, \quad x > 15\)
(E)\(3x + y \leq 30, \quad x + 3y \leq 15, \quad y \geq 20\)
Choose the correct answer from the options given below:
 

The area of the region \(\{(x, y) : x^2 + y^2 \leq 2ax, y^2 > ax, x \geq 0, y \geq 0\} \text{ where } a > 0\) , is :

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

Then P(x≤2) is:

Let \(\begin{vmatrix}3x&-7\\1&4\end{vmatrix}=\begin{vmatrix}3&2\\ 4&x\end{vmatrix}\), then value of x is:

The interval in which the \(f(x) = sinx-cosx, 0 ≤ x ≤ 2π\) is strictly decreasing is :

The equation of plane which cuts equal intercepts of unit length on the coordinate axes is:

The integral \(\int_0^1x(1-x)^n dx\) is equal to :

Match List I with List II

Choose the correct answer from the options given below:

A 10 m long, 4 m high and 24 cm thick wall is to be built using bricks having dimensions 25 cm × 12 cm × 8 cm. Number of bricks required is :

The order and the degree of the differential equation
\(\frac{d^2y}{dx^2}=(1+\frac{dy}{dx})^{\frac{1}{2}}\)
respectively are :