Verification of Truth of the Statement
Verification of Truth of the Statement
‘Verification of truth of the statement’ type questions are asked to check the perfect observation about statement, the object and its characteristics. Candidate should always check all the possibilities for the statement which is always true. The alternatives other than the correct answer also seem to bear a strong relationship with the thing mentioned. So, absolute truth is to be followed.
Example:
A camera always has______
(a) reels (b) flash
(c) photograph (d) lens
(e) stand
Ans. (d)
Explanation: Clearly, though all the alternatives may form part of the camera, the lens is the most vital part, without which camera cannot work. So the correct answer is D.
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Logical Sequence
Logical Sequence
In this type of question, a group of words/things/facts is given. You have to arrange these words in a meaningful order such as the sequence of occurrence of events, sequence of form of a part to whole, sequence of increasing/decreasing size, weight, value, intensity etc. and then choose the correct option accordingly.
Example:
Arrange the following in a meaningful sequence.
Sowing 2. Ploughing
Grain 4. Irrigation
Harvesting
(a) Sowing (b) Ploughing
(c) Grain (d) Irrigation
(a) 5, 1, 2, 3, 4 (b) 4, 2, 3, 1, 5
(c) 4, 3, 2, 5, 1 (d) 2, 1, 4, 5, 3
(e) None of these
Ans. (d)
Explanation: To produce the crop, first of all field more...
Decision Making
Decision Making
In this type of questions certain categories of information are given followed by certain criteria. The candidates are given a few cause that needs to be analysed. They are required to take the right decision, from the given options, after comparing the information in each c.se with the given information and criteria.
Example:
Directions: Read the following information to answer the given questions,
Following are the criteria for selecting candidates for Research Fellowship.
The candidate must-
Matrices
Matrices
In this type of questions a set of numbers or letters are given in a figure which is divided into different cells. These numbers or letters form a pattern by applying some logic - either row- wise or column-wise. One cell of the matrix is left empty. The candidate is required to analyse the matrix to find out the logic applied in the pattern and select one from the given options which will complete it.
Example:
Replace the question mark with the correct number.
Dot Situation
Dot Situation
The problems on Dot Situation involve a combination of three or more geometrical shapes usually triangle, square, rectangle or/and circle having one or more dots placed at any point inside the combination. This combination is followed by a set of four alternative figures each composed of a combination of same type of figures. Now, for each dot we have to observe the region in which it is enclosed, i.e. to which of the geometrical figures this region is common. Then, one has to look for such a region in the four alternatives. Once this is found, the procedure for other dots if any is repeated. The alternative figure which contains all such regions is the answer
Example:
1. Select the figure more...
Natural Numbers: Counting numbers \[1,\,\,2,\,\,3,\,\,4,\text{ }5,\text{ }6,....etc.\] are called Natural Numbers.
Whole Numbers: Counting numbers with 0 are whole numbers, i.e. \[0,1,2,3,4,....\] etc. are Whole numbers.
Integers: All natural numbers, the negatives of all natural numbers and zero are collectively known as integers, i.e. \[...-4,\text{ }-3,\text{ }-2,\text{ }-1,\text{ }0,\text{ }1,\text{ }2,\text{ }3,\text{ }4,...\] etc. are integers.
Rational Numbers: The numbers that can be expressed in the form \[\frac{p}{q}\], where p and q are integers are called rational numbers. Each rational number can be expressed either in a terminating or in a non-terminating repeating decimal form.
Irrational Numbers: The numbers which when expressed in decimal form are expressible as non-terminating and non-repeating decimals are known as irrational numbers.
Polynomials: If x is a variable, n be a positive integer and \[{{a}_{0}},\text{ }{{a}_{1}},\text{ }{{a}_{2}}\ldots .,\text{ }{{a}_{n}}\] are real number, then an expression of the form \[p\left( x \right)\text{ }=\text{ }{{a}_{0}}+\text{ }{{a}_{1}}x\text{ }+\text{ }{{a}_{2}}{{x}^{2}}+\text{ }{{a}_{n}}{{x}^{n}}\] is called polynomial, in the variable x. In a polynomial, \[p\left( x \right)\text{ }=\text{ }{{a}_{0}}+\text{ }{{a}_{1}}x+\text{ }{{a}_{2}}{{x}^{2}}+\text{ }\ldots \ldots .\text{ }+\text{ }{{a}_{n}}{{x}^{n}},\text{ }{{a}_{0}},\text{ }{{a}_{1}}x,\text{ }{{a}_{2}}{{x}^{2}},\ldots .,\text{ }{{a}_{n}}{{x}^{2}}\] are known as the terms of the polynomial and \[{{a}_{0}},\,\,{{a}_{1}},\text{ }{{a}_{2}}\ldots \ldots ..\], an are known as their coefficients
Degree of a polynomial: Let p(x) be a polynomial in x. Then, the highest power of x in p(x) is called the degree of the polynomial p(x). Thus, the degree of the polynomial, \[p\left( x \right)\text{ }=\text{ }{{a}_{0}}+\text{ }{{a}_{1}}x\text{ }+\text{ }{{a}_{2}}{{x}^{2}}+\text{ }\ldots \ldots more...
Pair of Linear Equations in Two Variables
Pair of Linear Equations in Two Variables
Linear equation in two variables: An equation which can be put in the form \[ax\text{ }+\text{ }by\text{ }+\text{ }c\text{ }=\text{ }0\], where a, b, c are real numbers \[(a~\,\,\ne \,\,0,\text{ }b\,\,\ne \,\,~0)\] is called a linear equation in two variables x and y.
Simultaneous linear equations in two variables: A pair of linear equations in two variables is said to form a system of simultaneous linear equation.
Solution of a given system of two simultaneous equations: A pair of value of the variable x and y satisfying each of the equations in a given system of two simultaneous equations more...
Quadratic Equation: An equation of the form \[a{{x}^{2}}+\text{ }bx\text{ }+\text{ }c\text{ }=\text{ }0\], where a, b, c real numbers and \[(a~\,\,\ne \,\,0)\], is called a quadratic equation in variable x or if p(x) is a quadratic polynomial then \[p\left( x \right)\text{ }=\text{ }0\] is called a quadratic equation.
Roots of a Quadratic Equation: A real number is called a root of the quadratic equation \[a{{x}^{2}}+\text{ }bx\text{ }+\text{ }c\text{ }=\text{ }0\text{ }(a\,\,\ne \,~0)\text{ }\] if \[a{{\alpha }^{2}}+\text{ }b\alpha \text{ }+\text{ }c\,\,=\text{ 0}\]
Note: If \[\alpha \] is a root of the quadratic equation \[\mathbf{a}{{\mathbf{x}}^{\mathbf{2}}}\mathbf{+ bx + c = 0}\], then \[\alpha \] is called a zero of the polynomial \[\mathbf{a}{{\mathbf{x}}^{\mathbf{2}}}\mathbf{+ bx +c}\mathbf{.}\]
Sequence: Certain numbers arranged in a definite order, according to a definite rule, are said to form a sequence.
e.g. (i) A rule defined as \[{{T}_{n}}\text{ }=\text{ }5n\text{ }+\text{ }1\] gives
\[{{T}_{1}}=\text{ }6,\text{ }{{T}_{2}}=\text{ }11,\text{ }{{T}_{3}}=\text{ }16,\text{ }{{T}_{4}}=\text{ }21\], .............
Thus, the numbers \[6,\text{ }11,\text{ }16,\text{ }21..........\] from a sequence.
Progressions: Sequences which follow a definite pattern are called progressions.
Arithmetic Progression (A.P.): An arithmetic progression is a list of numbers in which each term is obtained by adding a fixed number d to the proceeding term, except the first term. The fixed number d is called the common difference.
The general form of an AP is; \[a,\text{ }a\text{ }+\text{ }d,\text{ }a\text{ }+\text{ }2d,\text{ }a\text{ more...
