List of practice Questions

A ladder of length 30 m is leaning against a wall making an angle of 30° with the horizontal. Find the distance between the foot of the ladder and the wall.

If \(A=\begin{bmatrix} x & 1 \\ 1 & 0 \end{bmatrix}\)and A = A^-1, then the value of x is :

If x, y, z are different and \(A=\begin{vmatrix} x & x^2 & 1+x^3 \\ y & y^2 & 1+y^3 \\ z & z^2 & 1+z^3 \end{vmatrix}=0\), then the value of xyz is :

If the function \(f(x)=\frac{k \sin x+2\cos x}{\sin x+\cos x}\) is increasing for all values of x, then

Which of the following are not the probability distribution of a random variable ?
A.

X	0	1	2
P(X)	0.4	0.4	0.2

X	0	1	2	3	4
P(X)	0.4	0.4	0.2	-0.1	0.3

Y	-1	0	1
P(Y)	0.6	0.1	0.2

Z	3	2	1	0	-1
P(Z)	0.3	0.2	0.4	0.1	0.05

X	0	1	2
P(X)	\(\frac{25}{36}\)	\(\frac{10}{36}\)	\(\frac{1}{36}\)

Choose the correct answer from the options given below :

A retailer has 900 kg of wheat, a part of which he sells at 10% loss and the remaining at a profit of 8%. Overall, he makes a profit of 6%, the quantity sold at profit is :

Consider the following statements with respect to probability distributions :
A. When mean (μ) = 1 and standard deviation (σ) = 0 for a data set, normal distribution is called standard normal distribution.
B. In a normal distribution of data, z is given by \(z=\frac{\mu-x}{\sigma}\)
C. P('t' success) is the (r + 1)^th term in the binomial expansion of (q + p)ⁿ.
D. In a random experiment, a collection of trials is called Bernoulli, if trials are department by nature.
E. When a random variable whose value is obtained by measuring and it takes many values between two values, it is called a continuous random variable.
Choose the correct answer from the options given below :

A shopkeeper marked his goods 40% higher than their cost price and allows 20% discount on every item. Find his net profit percentage.

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 ?

Figure with 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 :

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

A person takes a home loan of ₹1200000 from a bank at an interest rate of 12% per annum for 10 years. The EMI under flat rate system is.

If in a 200 m race. A beats B by 31 m and C by 18 m, then in a 350 m race. C will beat B by

The variance of the number obtained in a throw of an unbiased die is:

Heera purchased a bag for ₹4500 and sold it for ₹8,200. What is the profit percentage? (Correct to two places of decimal)

If the manufacturer gains 10%, the wholesale dealer gains 15% and the retailer gains 25%, then find the cost of production of a table, if the retails price of which is ₹1265?

A and B can do a work in 10 days and 15 days respectively. They worked together for 5 days, then B left the work and A alone did the remaining work. The whole work got completed in:

The domain of the function f(x) = log \((x^2-4)\) is:

The integrating factor of \(sinx \frac{dy}{dx}+2ycosx=4\) is:

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 value of the integral \(\int e^x (logx + \frac{1}{x})dx\) is:

If A is a skew-symmetric matrix of order n. then

If A = \(\begin{bmatrix}2a & 0& 0\\[0.3em]0& 2a& 0\\[0.3em]0&0 & 2a\\[0.3em] \end{bmatrix}\), then the value of \(|adj A|\)is:

Match List I with List II

List I	List II
A. The region represented by \(x \geq 0, y \geq 0\)	I. no feasible region
B. The region represented by the inequalities \(2x + y \geq 3, x + 2y \geq 6, x,y \geq 0\)	II. 1st quadrant
C. The region represented by the inequalities \(x + 2y \leq 8, 3x + 2y \leq 12, x,y \geq 0\)	III. unbounded
D. The region represented by the inequalities \(x + y \leq 2, 3x + 5y \geq 15, x,y \geq 0\)	IV. bounded

Choose the correct answer from the options given below:

\(2\tan^{-1} \frac12+\tan^{-1}\frac 17=\tan^{-1}x\), then the value of \(x\) is: