List of practice Questions

The mean of \(n\) items is \(\bar{x}\). If each item is successively increased by \(3, 3^2, 3^3, \ldots, 3^n\), then the new mean will be:
There are two children in a family. The probability that both of them are boys is:
Let \(V\) be a vector space over a field \(F\) and \(a \in F\) and \(u \in V\). Which of the following statements is \textbf{not correct?}
\(\tan^{-1}(1) - \sec^{-1}2)\) is equal to:(
If the radius of a circle increases at a uniform rate of \(2\ \text{cm/s}\), then the rate of increase of area of the circle, at the approximate instant when the radius is \(20\ \text{cm}\), is:
The value of \(\displaystyle \int \frac{1}{(x-5)^2}\,dx\) is:
The order and degree of the differential equation \[ \left[1+\left(\frac{dy}{dx}\right)^2\right]^{\frac{3}{2}} = k\left(\frac{d^2y}{dx^2}\right) \] are respectively:
If the points \((1,1)\), \((-1,-1)\) are the vertices of a triangle, then this triangle is:
Find the centre and radius of the circle \(2x^2 + 2y^2 = 3x - 5y + 7\).
The total number of terms in the expansion of \((x + a)^{100} + (x - a)^{100}\) after simplification will be:
If \((x-2)\) is a common factor of the expressions \(x^2 + ax + b\) and \(x^2 + cx + d\), then \(\dfrac{b-d}{\,c-a\,}\) is equal to:
If \(-3x + 17<-13\), then
The determinant of an orthogonal matrix is:
If \(\cos x = \tan y,\ \cot y = \tan z\) and \(\cot z = \tan x\), then \(\sin x\) is equal to:
The elements of the set \(\{x : x \text{ is an integer},\; x^2 \le 4\}\) can be represented as \(\ldots Z \ldots\). Here, \(Z\) refers to:
If \(P = \{1, 2\}\), then \(P \times P \times P = \{(1,1,1), (1,1,2), (1,2,1), (2,1,2), (2,2,1), (2,2,2)\}\). The ordered triplet missing in \(P \times P \times P\) are:
\(a + ib>c + id\) can be explained only when:
If the sum of a certain \(n\) number of terms of the A.P. \(25, 22, 19, \ldots\) is \(116\), then the last term is:
In how many ways can the number \(7056\) be resolved into two factors?
How many 5-digit telephone numbers can be constructed using the digits 0 to 9, if each number starts with 67 and no digit appears more than once?
A sentence/a part of the sentence is underlined. Four alter natives are given to the underlined part which will improve the sentence. Choose the correct alternative and click the button corresponding to it. In case no im provement is needed, click the button corresponding to “No improvement”.
The young man was carried by the passionate appeal made by the social worker.
To leave a place suddenly secretly
In this question the rest of the passage is split into three parts and named P, Q and R. These three parts are not given in their proper order. Read the sentence and find out which of the four combinations is correct. Then find the correct answer:
However the major drawback

P. of this process is that
Q. there is no legally binding
R. outcome at the end of six years
Four words are given, out of which only one word is spelt correctly. Choose the correctly spelt word.
Find out which part of the sentence has an error and click the button corresponding to it. If the sentence is free from error, click the “No error” option.