List of practice Questions

The mean of the numbers obtained on throwing a die having written 1 on three faces, 2 on two faces, and 5 on 1 face is :

If A is an invertible matrix, such that A² - A + I = 0, then the inverse of A is :

The slope of the normal to the curve y = 2x² + 3sinx at x = 0, is :

Match List I with List II

List I		List II
A.	\(\int\limits^{\frac{\pi}{2}}_0\frac{\sin^{\frac{7}{2}}x}{\sin^{\frac{7}{2}}+\cos^{\frac{7}{2}}}dx\)	I.	\(\frac{\pi}{4}-\frac{1}{2}\)
B.	\(\int\limits_0^{\pi}\frac{x\sin x}{1+\cos^2x}dx\)	II.	0
C.	\(\int\limits^{\frac{\pi}{2}}_{-\frac{\pi}{2}}x\cos x\ dx\)	III.	\(\frac{\pi}{4}\)
D.	\(\int\limits_{-\frac{\pi}{4}}^{\frac{\pi}{4}}\sin^2x\ dx\)	IV.	\(\frac{\pi^2}{4}\)

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Match List I with List II

LIST I		LIST II
A.	The solution set of the inequality \(5x-8\gt2x+3,x\in R\ is,\)	I.	\((-\infin,\frac{6}{5}]\)
B.	The solution set of the inequality \(3x-4\lt5x+7,x\in R\ is,\)	II.	\((\frac{6}{5},\infin)\)
C.	The solution set of the inequality \(4x+15\le3(1-2x)is,\)	III.	\([10,\infin)\)
D.	The solution set of the inequality \(7x-8\ge2(1+3x)is,\)	IV.	\((-\frac{11}{2},\infin)\)

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A person walks from his house to his office at a speed of x₁ km/hr and returns by the same route at a speed of x₂ km/hr. What is his average speed ?

From a well shuffled pack of 52 cards, three cards are drawn one by one. The probability that the three cards are Jack, Queen and King respectively?

In what ratio must a shopkeeper mix peas and soyabean of ₹16 and ₹25 per kg respectively, so as to obtain a mixture of ₹19 per kg?

The symbols that we use to represent number names are called a numerals. Children see numerals such as “6” in their everyday lives constantly. However, numerals are ---------- than quantities.

If \(f(x)=-3x^2\), then f(x) is:

The value of \(∫(5x-2)^3\) dx is:

The solution of the differential equation \(\frac{dy}{dx}=-\frac{x}{y}\) is:

If \(e^y(x+2)=10\), then \(\frac{d^2y}{dx^2}\) is equal to:

There are two values of a for which the determinant, \(\Delta =\begin{bmatrix}1& -2& 5\\[0.3em]0& a& 1\\[0.3em] 0& 4& 2a\\[0.3em] \end{bmatrix} = 86\), then the sum of these values of a is:

A particle is moving along the curve \(y=\frac34x^4+3\). The point on the curve at which y-coordinate is changing thrice as fast as the x coordinate, is :

Match List - I with List - II.

List - I	List -II
(A) \(P(\overline{A} \cap B)\)	(I)\(P(A)+P(B)\)
(B)\(P(A\cap \overline B)\)	(II)\(P(A)+P(B)-2P(A\cap B)\)
(C) \(P[(A\cap \overline B) \cup (\overline A \cap B)]\)	(III)\(P(B)-P(A\cap B)\)
(D)\(P(A\cup B)+ P(A\cap B)]\)	(IV)\(P(B)-P(A\cap B)\)

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The value of objective function is maximum under linear constraints is

The region R on the set \(A=\{x \in Z:0\leq x\leq 12\}\) , given by \(R=\{(a,b):|a-b|\)  is a multiple of 4 \(\}\)  is :

The ratio of areas under the curves \(y=sinx \) and \(y=sin2x\) ,from \(x=0\) to  \( x=\frac{\pi}{3}\) is

\((6:30+19:50), \)in 24 hours clock is :

The point estimate for the mean number of sales of cars for the following data 103, 140, 92, 115, 110, is:

The effective rate which is equivalent to stated rate of \(6\%\) compounded semiannually is:

Given relation R={(x, y): y=x+5, x < 4, x, y ∈ N}. Where N is a set of natural numbers then :

The prices and the quantities of three commodities are given are :

The Laspeyre's price index number for year 2009 with year 2006 as base is 200. The value of \(x\) is:

Which of the following statements are true ?
(A) Central limit theorem states that the sampling distribution of the mean (\(\bar x\)) approaches a normal distribution as the sample size increases.
(B) As per Central Limit Theorem, when the sample size increases, the mean (\(\bar x\)) for the data becomes closer to the mean of overall population.
(C) The shape of t-distribution does not depend on degree of freedom.
Choose the correct answer from the options given below :