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Recent questions tagged true-or-false

True or False: The intercepts made by the plane $2x-3y+5z+4=0$ on the co-ordinate axis are $-2,\large\frac{4}{3},\frac{-4}{5}.$

asked Jan 7, 2013 by sreemathi.v

1 answer

True or False: The unit vector normal to the plane $x+2y+3z-6=0$ is $\large \frac{1}{\sqrt {14}}\hat i+\frac{2}{\sqrt {14}}\hat j+\frac{3}{\sqrt {14}}\hat k.$

asked Jan 6, 2013 by sreemathi.v

1 answer

True or False: If f.g is continuous at $x=a$,then f and g are separately continuous at $x=a.$

asked Jan 3, 2013 by sreemathi.v

1 answer

True or False: Trigonometric and inverse-trigonometric functions are differentiable in their respective domain.

asked Jan 3, 2013 by sreemathi.v

1 answer

True or False: The composition of two continuous functions is a continuous function.

asked Jan 3, 2013 by sreemathi.v

1 answer

True or False: If f is continuous on its domain D ,then | f | is also continuous on D.

asked Jan 3, 2013 by sreemathi.v

1 answer

True or False: Rolle's theorem is applicable for the function $f(x)=|x-1|$ in [0,2].

asked Jan 3, 2013 by sreemathi.v

1 answer

True or False: The maximum value of $\begin{vmatrix}1 & 1 & 1\\1 &(1-\sin x) & 1\\1 & 1 & 1-cos x\end{vmatrix}\;is\;\Large \frac{1}{2}$.

asked Dec 28, 2012 by sreemathi.v

1 answer

True or False: Let $\begin{vmatrix}a & p & x\\b & q & y\\c & r & z\end{vmatrix}$ = 16, then $\Delta_1=\begin{vmatrix}p+x & a+x & a+p\\q+y & b+y & b+q\\r+z & c+z & c+r\end{vmatrix}$ = 32

asked Dec 28, 2012 by sreemathi.v

1 answer

True or False: If the determinant $\small\begin{vmatrix}x+a & p+u & l+ f\\y+b & q+v & m +g\\z+c & r+w & n + h\end{vmatrix}$ splits into exactly $k$ determinants of order $3$, each element of which contains online term,then the value of $k$ is $8$.

asked Dec 28, 2012 by sreemathi.v

1 answer

True or False: The determinant $ \begin{vmatrix}\sin A & \cos A & \sin A+\cos B\\\sin B & \cos A & \sin B+\cos B\\\sin C & \cos A & \sin C+\cos B\end{vmatrix}$ is equal to zero

asked Dec 28, 2012 by sreemathi.v

1 answer

True or False: $\mid adj A\mid={\mid A\mid}^2$,where A is a square matrix of order two.

asked Dec 28, 2012 by sreemathi.v

1 answer

True or False: $\begin{vmatrix}x+1 & x+2 & x+a\\x+2 & x+3 & x+b\\x+3 & x+4 & x+c\end{vmatrix}=0,$where a,b,c are in A.P.

asked Dec 28, 2012 by sreemathi.v

1 answer

True or False: If the value of a third order determinant is 12,then the value of the determinant formed by replacing each element by its co-factor will be 144.

asked Dec 28, 2012 by sreemathi.v

1 answer

True or False: If A and B are matrices of order 3 and $\mid A\mid=5,\mid B \mid=3,then\mid 3AB\mid=27\times 5\times 3=405$

asked Dec 28, 2012 by sreemathi.v

1 answer

True or False: $|\;A^{-1}\;|\neq |\;A\;|^{-1}$,where A is non-singular matrix.

asked Dec 28, 2012 by sreemathi.v

1 answer

True or False: $(aA)^{-1}= \Large{ \frac{1}{a}}\normalsize A^{-1}$, where $a$ is a any real number and $A$ is a square matrix.

asked Dec 28, 2012 by sreemathi.v

1 answer

True or False: $(A^3)^{-1}=(A^{-1})^3$,where A is a square matrix and $|\;A\;|\neq 0$

asked Dec 28, 2012 by sreemathi.v

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: If $A =\begin{bmatrix} 2 & 3 & 1 \\ 1 &4 & 2 \end{bmatrix}\; and\; B=\begin{bmatrix}2 & 3 \\ 4& 5 \\ 2 & 1 \end{bmatrix},$ then AB and BA are defined and equal.

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: If A and B are two square matrices of the same order , then AB = BA.

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

1 answer

True or False: Matrix multiplication is commutative.

asked Dec 24, 2012 by sreemathi.v

1 answer

True or False: Matrix addition is associative as well as commutative.

asked Dec 24, 2012 by sreemathi.v

1 answer

True or False: Matrices of different order can not be subtracted.

asked Dec 24, 2012 by sreemathi.v

1 answer

True or False: Two matrices are equal if they have same number of rows and same number of columns.

asked Dec 24, 2012 by sreemathi.v

1 answer

True or False: Matrices of any order can be added.

asked Dec 24, 2012 by sreemathi.v

1 answer

True or False: The principal value of $\sin^{-1}\begin{bmatrix}\cos\bigg(\sin^{-1}\frac{1}{2}\bigg)\end{bmatrix}\;is\;\Large {\frac{\pi}{3}}$

asked Dec 21, 2012 by sreemathi.v

1 answer

True or False: The minimum value of n for which $\tan^{-1}\Large {\frac{n}{\pi}}\;>\Large {\frac{\pi}{4}},\normalsize\;n\in N,$ is valid is 5

asked Dec 21, 2012 by sreemathi.v

1 answer

True or False:The graph of inverse trigonometric function can be obtained from the graph of their corresponding trigonometric function by interchanging x and y axes.

asked Dec 21, 2012 by sreemathi.v

1 answer

True or False: The least numerical value, either positive or negative of angle $\theta$ is called principal value of the inverse trigonometric function.

asked Dec 21, 2012 by sreemathi.v

1 answer

True or False: The domain of trigonometric functions can be restricted to any one of their branch(not necessarily principal value) in order to obtain their inverse function.

asked Dec 21, 2012 by sreemathi.v

1 answer

True or False: The value of the expression $(\cos^{-1}x)^2$ is equal to $\sec^2x.$

asked Dec 21, 2012 by sreemathi.v

1 answer

True or False: All trigonometric functions have inverse over their respective domains.

asked Dec 21, 2012 by sreemathi.v

1 answer

True or False: A binary operation on a set has always the identity element.

asked Dec 20, 2012 by sreemathi.v

1 answer

True or False: Every function is invertible.

asked Dec 20, 2012 by sreemathi.v

1 answer

True or False: The composition of functions is associative

asked Dec 20, 2012 by sreemathi.v

1 answer

True or False: The composition of functions is commutative.

asked Dec 20, 2012 by sreemathi.v

1 answer

True or False: The relation R on the set A={1,2,3} defined as R={(1,1),(1,2),(2,1),(3,3)} is reflexive,symmetric and transitive.

asked Dec 20, 2012 by sreemathi.v

1 answer

True or False: Let A={0,1} and N be the set of natural numbers.Then the mapping $f:N \rightarrow A$ defined by f(2n-1)=0,f(2n)=1,$\quad n\in N$,is onto.

asked Dec 20, 2012 by sreemathi.v

1 answer

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