List of practice Questions

Which one of the following is more useful and effective for a quick visualization of a limited amount of information?

In the equation \(y_i = β_0+β_1.X_1+ε_1, \ β_0\) stands for

Given below are two statements about a normally distributed data.
Statement I : 95.45% of the occurrences will lie between \(\bar {X}±3σ\).
Statement II : 68.27% of the occurrences will lie between \(\bar {X}±1σ\).
In the light of the above statements, choose the correct answer from the options given below:

Read the given statements about correlation carefully and identify the correct statements.
A. A positive relation means that the variables vary in the same direction.
B. If two or more variables are related in a statistical way, is sufficient to conclude that a cause and effect relation exists.
C. A negative relation means that the two variables vary in the opposite direction.
D. Pearson's Product-Moment Method is a method used to calculate r.
Choose the correct answer from the options given below:

Match List I with List II :

List I (Method)		List II (Characteristic)
(A)	Mean	(I)	Identify what is most common
(B)	Median	(II)	Based on sound mathematics
(C)	Mode	(III)	Square-root of the variance
(D)	Standard deviation	(IV)	Divides into 2 equal parts

Choose the correct answer from the options given below:

Ravi invested certain sum on simple interest. He invested two-third of his sum at 7% p.a and the remaining at 8% p.a. In 3 years he earned ₹1320 as interest. Find the sum invested by him (in ₹).

In what ratio must a grocer mix tea leaves costing Rs.600/kg and rs.650/kg. So that by selling the mixture at Rs.682/kg, he gains 10%?

If sec 5 A = Cosec A, then the value of A is

Given below are two statements: One is labelled as Assertion (A) and the other is labelled as Reason (R)
Assertion (A): If volumes of two spheres are in the ratio 125:64, then their surface areas will be in the ratio 25:16.
Reason (R): If volumes of two spheres are V1, V2 and their respective surface areas are S1, S2, then
\(\frac{S_1}{S_2} =(\frac{V_1}{V_2})^\frac{2}{3}\)
In the light of the above statements, choose the most appropriate answer from the options given below:

Which one of the following options is considered as the relative measure of dispersion?

Direction: Read the following scenario and answer the TWO questions that follow.
The CEO of the Jamshedpur Tea Factory (JTF) was in a quandary over employees skipping work. It was becoming increasingly difficult for him to identify employees who faked illness to skip work. The work of the employees was complex and intricate, and they had to report to eight supervisors. “Faking illness” made it difficult for JTF to judiciously decide on “Promotion” and “Training” of employees. An employee could only be promoted on the completion of a multi-skilling training program. Further, to be nominated for the training program, an employee must be recommended by a minimum of six supervisors. JTF wanted to promote only sincere and deserving employees.
The CEO was thinking of changing the policy regarding leave, training & promotion.
Which of the following will be the MOST efficient course of action for JTF and yet be fair to the employees?

Let T₁ and T₂ be two distinct common tangents to the ellipse \(E:  \frac{x^2}{6} + \frac{y^2}{3} = 1\) and the parabola \(P: y^2 = 12x\). Suppose that the tangent T₁ touches P and E at the points A₁ and A₂, respectively and the tangent T₂ touches P and E at the points A₄ and A₃, respectively. Then which of the following statements is(are) true?

Identify the statement which is not correct regarding consumer behaviour and demand.

A system of ideal gas undergoes a thermodynamic process in which the initial pressure and volume are equal to the final pressure and volume. Let △Q is the heat supplied to the system,△W is the work done by the system and △U is the change in internal energy. The correct option is: 

The coefficient of x5 in the expansion of \((2x^3 - \frac{1}{3x^2})^5\) is

For a given pair of transparent media, the critical angle for which colour is maximum?

The correct stability order of the following carbocations is : (I)H₂C⨁-CH=CH-CH₃, (II)⨁CH₂-CH=CH-BMe₂, (III)H₂C⨁-CH=CH-NMe₂, (IV)H₂C⨁-CH=CH-OMe

Suppose P is the point on the line joining  \((-9,4,5)\) and \((11,0,-1)\) that lies closest to the origin O. Then \(|OP|^2\) equals to?

The portion of the tangent to the curve x\(^{\frac{2}{3}}\)+y\(^{\frac{2}{3}}\)=a\(^{\frac{2}{3}}\), a>0 at any point of it, intercepted between the axes

Suppose the line joining distinct points P and Q on \((x-2)^{2}+(y-1)^{2}=r^{2}\) is the diameter of \( (x-1)^2+(y-3)^2=4\).The value of r is 

A thin glass rod is bent in a semicircle of radius R.A charge is non-uniformly distributed along the rod with a linear charge density \(\lambda=\lambda_0sin\theta\) (\(\lambda_0\) is a positive constant). The electric field at the center P of the semicircle is