Recent questions tagged toolbox

What is the value of $sin^{-1}(-x)$?

asked Mar 12, 2013 by balaji.thirumalai

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What is the value of $tan^{-1} \frac{1}{x}$

asked Mar 12, 2013 by balaji.thirumalai

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What is the value of $cos^{-1}\frac{1}{x}$?

asked Mar 12, 2013 by balaji.thirumalai

1 answer

What is the value of $sin^{-1}\frac{1}{x}$

asked Mar 12, 2013 by balaji.thirumalai

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What is the value of $cos^{-1}$$cos(x)$?

asked Mar 12, 2013 by balaji.thirumalai

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What is the value of $sin^{-1}sinx$?

asked Mar 12, 2013 by balaji.thirumalai

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$sin^{-1}x = (sin x)^{-1}$. True or False?

asked Mar 12, 2013 by balaji.thirumalai

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What is the range of the principal value of $\; cot^{-1}x$?

asked Mar 12, 2013 by balaji.thirumalai

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What is the range of the principal value of $\; sec^{-1}x$?

asked Mar 12, 2013 by balaji.thirumalai

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What is the range of the principal value of $\; cosec^{-1}x$?

asked Mar 12, 2013 by balaji.thirumalai

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What is the range of the principal value of $\tan^{-1}x$?

asked Mar 12, 2013 by balaji.thirumalai

1 answer

What is the range of the principal value of $\sin^{-1}x$?

asked Mar 12, 2013 by balaji.thirumalai

1 answer

What is the range of the principal value of $\cos^{-1}x$?

asked Mar 12, 2013 by balaji.thirumalai

1 answer

True or False? Let $f : X \rightarrow Y$ and $g : Y \rightarrow Z$ be two invertible functions. Then $g\;o\; f$ is also invertible with $(g \;o\; f)^{-1} = g^{-1} \; o f^{-1}$.

asked Mar 12, 2013 by balaji.thirumalai

1 answer

Which of the following is true? A function f : X → Y is invertible if and only if:

asked Mar 12, 2013 by balaji.thirumalai

1 answer

A relation $R$ in $X$ given by $R = X \times X$ is called what?

asked Mar 12, 2013 by balaji.thirumalai

1 answer

Fill in the blank: Given a binary operation ∗ : A × A → A, an element e ∈ A, if it exists, is called ____ for the operation ∗, if a ∗ e = a = e ∗ a, ∀ a ∈ A.?

asked Mar 12, 2013 by balaji.thirumalai

1 answer

Given two functions f(x) and g(x), (g o f) implies which of the following?

asked Mar 12, 2013 by balaji.thirumalai

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If a * b = b* a ∀ a, b, ∈ A, then the binary operation * on A is said to be what?

asked Mar 12, 2013 by balaji.thirumalai

1 answer

If (a ∗ b) ∗ c = a ∗ (b ∗ c), ∀ a, b, c, ∈ A, then the binary operation * on A is said to be what?

asked Mar 12, 2013 by balaji.thirumalai

1 answer

Which of the following is true?

asked Mar 12, 2013 by balaji.thirumalai

1 answer

True or False: A Function can be both one-one and onto.

asked Mar 12, 2013 by balaji.thirumalai

1 answer

Fill in the blank: A function f : X → Y is said to be ______, if every element of Y is the image of some element of X under f, i.e., for every y ∈ Y, there exists an element x in X such that f (x) = y.

asked Mar 12, 2013 by balaji.thirumalai

1 answer

Fill in the blank: A function $f: A \rightarrow B$ is called _____ if there are two or more elements in A that have the same image in B.

asked Mar 12, 2013 by balaji.thirumalai

1 answer

Fill in the blank: A function $f: A \rightarrow B$ where for every $x1, x2 \in X, f (x1) = f (x2) \Rightarrow x1 = x2$, is called a ______ function?

asked Mar 12, 2013 by balaji.thirumalai

1 answer

Fill in the blank: A relation R in a set A is called ______ relation, if each element of A is related to every element of A, i.e., R = A × A.

asked Mar 12, 2013 by balaji.thirumalai

1 answer

Fill in the Blank: A relation $R$ in a set $A$ is called ______ relation, if no element of $A$ is related to any element of $A$, i.e., $R = \phi \subset A \times A.$

asked Mar 12, 2013 by balaji.thirumalai

1 answer

We can multiply two matrices if and only if which of the following is true?

asked Mar 9, 2013 by balaji.thirumalai

1 answer

If a matrix A is of the order $m$ x $n$. Then what is the order of the matrix kA, where k is a scalar constant?

asked Mar 9, 2013 by balaji.thirumalai

1 answer

If the order of two matrices are equal, then which of the following is true?

asked Mar 9, 2013 by balaji.thirumalai

1 answer

Which of the following is true in a square matrix, given that $m$ is the number of rows and $n$ is the number of columns?

asked Mar 9, 2013 by balaji.thirumalai

1 answer

Which of the following is true about the number of elements in a $m$x$n$ matrix with $m$ rows and $n$ columns?

asked Mar 9, 2013 by balaji.thirumalai

1 answer

For a relation R in a set A to be called $\mathbf{symmetric}$, if $(a_1,a_2) \in R$, which of the following must also be true

asked Mar 8, 2013 by balaji.thirumalai

1 answer

A relation R in a set A is called $\mathbf{transitive},$ if $(a_1,a_2) \in R$ and $(a_2,a_3) \in R$ and which of the following conditions must also hold true?

asked Mar 8, 2013 by balaji.thirumalai

1 answer

Given $(a_1,a_2) \in R$ and $(a_2,a_3) \in R \; \Rightarrow \;(a_1,a_3)\in R$ for all$\; a_1,a_2,a_3 \in A$. Then the relation $R$ is called what?

asked Mar 8, 2013 by balaji.thirumalai

1 answer

In a set $A$, if $(a_1,a_2) \in R\;\Rightarrow\; (a_2,a_1)\in R \; for \;a_1,a_2 \in A$, then what is the relation $R$ called?

asked Mar 8, 2013 by balaji.thirumalai

1 answer

If $(a,a) \in R\;$ for every $\; a\in\;A$, then what is the relation $R$ in the set $A$ is called?

asked Mar 8, 2013 by balaji.thirumalai

1 answer

A relation R is an equivalance relation if it satisifes which of the following properties?

asked Mar 8, 2013 by balaji.thirumalai

1 answer

True or False: $(AB)^{-1}=A^{-1}B^{-1},$ where A and B are invertible matrices satisfying commutative property with respect to multiplication.

asked Dec 24, 2012 by sreemathi.v

1 answer

True or False: If A is skew symmetric matrix, then $A^2$ is a symmetric matrix.

asked Dec 24, 2012 by sreemathi.v

1 answer

True or False: AA' is always a symmetric matrix for any matrix A.

asked Dec 24, 2012 by sreemathi.v

1 answer

True or False: If A,B and C are square matrices of same order, then AB = AC always implies that B=C.

asked Dec 24, 2012 by sreemathi.v

1 answer

True or False: If (AB)' = B'A', where A and B are not square matrices, then number of rows in A is equal to number of columns in B and number of columns in A is equal to number of rows in B.

asked Dec 24, 2012 by sreemathi.v

1 answer

True or False: If A and B are any two matrices of the same order, then (AB)' = A'B'.

asked Dec 24, 2012 by sreemathi.v

1 answer

True or False: If each of the three matrices of the same order are symmetric matrix.

asked Dec 24, 2012 by sreemathi.v

1 answer

True or False: Transpose of a column matrix is a column matrix.

asked Dec 24, 2012 by sreemathi.v

1 answer

True or False: If a matrix AB = 0, then A=0 or B=0 or both A and B are null matrices.

asked Dec 24, 2012 by sreemathi.v

1 answer

True or False: If A and B are two matrices of the same order, then A-B = B-A.

asked Dec 24, 2012 by sreemathi.v

1 answer

True or False: If A and B are two square matrices of the same order , then A+B = B+A.

asked Dec 24, 2012 by sreemathi.v

1 answer

True or False: A square matrix where every element is unity is called an identify matrix.

asked Dec 24, 2012 by sreemathi.v

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