List of practice Questions

The straight line \[ \frac{x-3}{3} = \frac{y-2}{1} = \frac{z-1}{0} \] is:
If \( E \) and \( F \) are two independent events with \( P(E)=0.3 \) and \( P(E\cup F)=0.5 \), then \( P(E/F) - P(F/E) \) equals:
If \( g(f(x)) = |\sin x| \) and \( f(g(x)) = (\sin\sqrt{x})^2 \), then:
If \( {}^9P_5 + 5 \cdot {}^9P_4 = {}^{10}P_r \), then the value of \( r \) is:
The value of the expression \[ {}^{47}C_4 + \sum_{j=1}^{5} {}^{52-j}C_3 \] is:
The sum of the first four terms of an arithmetic progression is 56. The sum of the last four terms is 112. If its first term is 11, then the number of terms is:
If \[ x = \int_0^y \frac{1}{\sqrt{1+9t^2}} \, dt \quad \text{and} \quad \frac{d^2 y}{dx^2} = ay, \] then \( a \) is equal to:
The value of \[ \int_{-1}^{1} \frac{x^3 + |x| + 1}{x^2 + 2|x| + 1} \, dx is equal to: \]
A function \( f \) is defined by \( f(x) = 2 + (x-1)^{2/3 \) on \( [0,2] \). Which of the following statements is incorrect?}
Let \( f(x) \) be a second degree polynomial. If \( f(1)=f(-1) \) and \( p,q,r \) are in A.P., then \( f'(p), f'(q), f'(r) \) are:
Let \( \vec{a}, \vec{b}, \vec{c} \) be vectors of equal magnitude such that the angle between \( \vec{a} \) and \( \vec{b} \) is \( \alpha \), between \( \vec{b} \) and \( \vec{c} \) is \( \beta \), and between \( \vec{c} \) and \( \vec{a} \) is \( \gamma \). Then the minimum value of \( \cos\alpha + \cos\beta + \cos\gamma \) is:
If \( \vec{a}, \vec{b}, \vec{c} \) are non-coplanar vectors and \( \lambda \) is a real number, then the vectors \[ \vec{a} + 2\vec{b} + 3\vec{c}, \quad \lambda\vec{b} + 4\vec{c}, \quad (2\lambda - 1)\vec{c} \] are non-coplanar for:
The value of \[ \int_0^{1.5} [x^2] \, dx is equal to: \]
The function \( f(x) = 2x^3 - 3x^2 - 12x + 4, \, x \in \mathbb{R \) has:}
For what value of \( a \), the sum of the squares of the roots of the equation \[ x^2 - (a-2)x - a + 1 = 0 \] will have the least value?
Let \( p(x) \) be a real polynomial of least degree which has a local maximum at \( x = 1 \) and a local minimum at \( x = 3 \). If \( p(1) = 6 \) and \( p(3) = 2 \), then \( p'(0) \) is equal to:
An \( n \times n \) matrix is formed using \( 0, 1 \) and \( -1 \) as its elements. The number of such matrices which are skew symmetric is:
Mr. Prasanna, a General Manager in a multinational company, has been given two spreadsheets: an original billing file Bill.ods and a reviewed version of the same spreadsheet Rev Bill.ods. Both contain customer billing details prepared by different teams. Write the steps he should follow to compare these worksheets and identify the differences between them.
Which of the following is the correct typing posture?
Which of the following types of fire extinguishers should not be used to extinguish an electrical fire?
Arjun notices that his colleague frequently complains of neck pain and sore shoulders after long working hours. Which of the following is the most likely cause?
In ________ Data Model, the data is stored in the form of linked records, organized into a tree-like structure.
Which of the following best explains the use of a query in LibreOffice Base?
While forming a relationship between two tables in LibreOffice Base, the ________ of the common field must be ________.

Which of the following is an example of a DBMS?