Recent questions tagged easy

Compute the following $ (iii)\;\begin{bmatrix}-1 & 4 & -6\\8 & 5 &16\\2 & 8 &5\end{bmatrix}+\begin{bmatrix}12 & 7 & 6\\8 & 0 & 5\\3 & 2 & 4\end{bmatrix}$

asked Feb 27, 2013 by balaji.thirumalai

1 answer

Compute the following $(i)\;\begin{bmatrix}a & b\\-b & a\end{bmatrix}+\begin{bmatrix}a & b\\b & a\end{bmatrix}$

asked Feb 27, 2013 by balaji.thirumalai

1 answer

Let $ A\;=\begin{bmatrix}2 & 4\\3 & 2\end{bmatrix}, B\;=\begin{bmatrix}1 & 3\\-2 & 5\end{bmatrix}, C\;=\begin{bmatrix}-2 & 5\\3 & 4\end{bmatrix}$. Find $ (v)\;BA\qquad$

asked Feb 27, 2013 by balaji.thirumalai

1 answer

Let $ A\;=\begin{bmatrix}2 & 4\\3 & 2\end{bmatrix}, B\;=\begin{bmatrix}1 & 3\\-2 & 5\end{bmatrix}, C\;=\begin{bmatrix}-2 & 5\\3 & 4\end{bmatrix}$. Find $ AB\qquad$

asked Feb 27, 2013 by balaji.thirumalai

1 answer

Let $ A\;=\begin{bmatrix}2 & 4\\3 & 2\end{bmatrix}, B\;=\begin{bmatrix}1 & 3\\-2 & 5\end{bmatrix}, C\;=\begin{bmatrix}-2 & 5\\3 & 4\end{bmatrix}$. Find $ 3A-C$

asked Feb 27, 2013 by balaji.thirumalai

1 answer

Let $ A\;=\begin{bmatrix}2 & 4\\3 & 2\end{bmatrix}, B\;=\begin{bmatrix}1 & 3\\-2 & 5\end{bmatrix}, C\;=\begin{bmatrix}-2 & 5\\3 & 4\end{bmatrix}$ Find: $(ii) (A-B)\qquad$

asked Feb 27, 2013 by balaji.thirumalai

1 answer

Let $ A\;=\begin{bmatrix}2 & 4\\3 & 2\end{bmatrix}, B\;=\begin{bmatrix}1 & 3\\-2 & 5\end{bmatrix}, C\;=\begin{bmatrix}-2 & 5\\3 & 4\end{bmatrix}$. Find $\;A+B\qquad$

asked Feb 27, 2013 by balaji.thirumalai

1 answer

Find the values of x,y and z from the following equations: $(iii)\;\begin{bmatrix}x+y+z\\x+z\\y+z\end{bmatrix}=\begin{bmatrix}9\\5\\7\end{bmatrix}$

asked Feb 27, 2013 by balaji.thirumalai

1 answer

Find the values of x,y and z from the following equations:$ (ii)\;\begin{bmatrix}x+y & z\\5+z & xy\end{bmatrix}=\begin{bmatrix}6 & 2\\5 & 8\end{bmatrix}\qquad$

asked Feb 27, 2013 by balaji.thirumalai

1 answer

Find the values of x,y and z from the following equations:$(i)\begin{bmatrix}4 & 3\\x & 5\end{bmatrix}=\begin{bmatrix}y & z\\1 & 5\end{bmatrix}\qquad$

asked Feb 27, 2013 by balaji.thirumalai

1 answer

Construct a 3 x 4 matrix,whose elements are given by:$(i)\;a_{ij}=\frac{1}{2}| -3i+j\;| \qquad$

asked Feb 27, 2013 by balaji.thirumalai

1 answer

Construct a 2 x 2 matrix, $A=[a_{ij}],$whose elements are given by:$ (ii) a_{ij}=\frac{i}{j}\qquad$

asked Feb 27, 2013 by balaji.thirumalai

1 answer

Construct a $2 \times 2$ matrix, $A=[a_{ij}],$whose elements are given by: $a_{ij}=\frac{(i+j)^2}{2}\qquad$

asked Feb 27, 2013 by balaji.thirumalai

1 answer

If a matrix has 5 elements,what are the possible orders can it have?

asked Feb 27, 2013 by balaji.thirumalai

1 answer

If a matrix has 18 elements,what are the possible orders it can have?

asked Feb 27, 2013 by balaji.thirumalai

1 answer

If a matrix has 13 elements,what are the possible orders it can have? (Note: This question has been split into 2 questions)

asked Feb 27, 2013 by balaji.thirumalai

1 answer

If a matrix has 24 elements,what are the possible orders it can have? (Note: This question has been split into 2 questions)

asked Feb 27, 2013 by balaji.thirumalai

1 answer

In the matrix $A=\begin{bmatrix}2 & 5 & 19 & -7\\35 & -2 & \frac{5}{2} & 12\\\sqrt 3 & 1 & -5& 17\end{bmatrix},$ write the elements $\;a_{13},a_{21},a_{33},a_{24},a_{23}$ \[\]

asked Feb 27, 2013 by balaji.thirumalai

1 answer

In the matrix $A=\begin{bmatrix}2 & 5 & 19 & -7\\35 & -2 & \frac{5}{2} & 12\\\sqrt 3 & 1 & -5& 17\end{bmatrix},$ write The number of elements

asked Feb 27, 2013 by balaji.thirumalai

1 answer

In the matrix $A=\begin{bmatrix}2 & 5 & 19 & -7\\35 & -2 & \frac{5}{2} & 12\\\sqrt 3 & 1 & -5& 17\end{bmatrix},$ write The order of the matrix.

asked Feb 27, 2013 by balaji.thirumalai

1 answer

Find area of the triangle with vertices at the point given in each of the following (-2, -3), (3, 2), (-1, -8)

asked Feb 23, 2013 by pady_1

1 answer

Find area of the triangle with vertices at the point given in each of the following (2, 7), (1, 1), (10, 8)

asked Feb 23, 2013 by pady_1

1 answer

Find equation of line joining (3, 1) and (9, 3) using determinants.

asked Feb 23, 2013 by pady_1

1 answer

Find values of $k$ if area of triangle is $4\; sq. units$ and vertices are $(-2, 0), (0, 4), (0, k)$

asked Feb 23, 2013 by pady_1

1 answer

Find the value of $tan^{-1}\frac{-1}{\sqrt 3}+cot^{-1}\frac{1}{\sqrt 3}-tan^{-1}sin\frac{\pi}{2}$

asked Feb 19, 2013 by sreemathi.v

1 answer

Evaluate $cos\bigg(cos^{-1}\bigg(\frac{-\sqrt{3}}{2}\bigg)+\frac{\pi}{6}\bigg)$

asked Feb 19, 2013 by sreemathi.v

1 answer

If $A=\begin{bmatrix}\alpha & \beta\\\gamma & -\alpha\end{bmatrix}$ is such that $A^2=I,$ then which of the following is true:

asked Feb 19, 2013 by sreemathi.v

1 answer

Write a unit vector in the direction of $ \overrightarrow a = 2\hat i - 6\hat j + 3\hat k.$

asked Feb 17, 2013 by thanvigandhi_1

1 answer

Find the projection of $ \overrightarrow a \: on \: \overrightarrow b\: if \: \overrightarrow a.\overrightarrow b=8\: and \: \overrightarrow b = 2\hat i + 6\hat j + 3\hat k$

asked Feb 17, 2013 by thanvigandhi_1

1 answer

Find the direction cosines of the line passing through the points $(-2,4,-5)$ and $(1,2,3)$

asked Feb 17, 2013 by thanvigandhi_1

1 answer

If matrix A = (1,2,3), write AA' where A' is the transpose of matrix A.

asked Feb 17, 2013 by thanvigandhi_1

1 answer

Write the value of the determinants \[ \begin{vmatrix} 2 & 3 & 4 \\ 5 & 6 & 8 \\ 6x & 9x & 12x \end{vmatrix} \]

asked Feb 17, 2013 by thanvigandhi_1

1 answer

Using principal value, evaluate the following : \[ sin^{-1} \bigg( sin \frac{3\pi}{5} \bigg) \]

asked Feb 17, 2013 by thanvigandhi_1

1 answer

Evaluate : $ \int \large\frac{\sec^2x}{3+\tan\:x}$$dx $

asked Feb 17, 2013 by thanvigandhi_1

1 answer

If $ \int_0^1 (3x^2+2x+k)dx=0,$ find the value of k

asked Feb 17, 2013 by thanvigandhi_1

1 answer

If the binary operation * on the set of integers Z, is defined by $ab=( a+3b^2)$ then find the value of $24$

asked Feb 17, 2013 by thanvigandhi_1

1 answer

If $ \overrightarrow a \times \overrightarrow b=\overrightarrow c \times \overrightarrow d\: and \: \overrightarrow a \times \overrightarrow c=\overrightarrow b \times \overrightarrow d$ show that $ \overrightarrow a-\overrightarrow d$ is parallel to $ \overrightarrow b-\overrightarrow c$ where $ \overrightarrow a \neq \overrightarrow d\: and \overrightarrow b \neq\overrightarrow c$

asked Feb 17, 2013 by thanvigandhi_1

1 answer

Prove that : $ \sin^{-1} \bigg(\large \frac{4}{5} \bigg)$$+\sin^{-1} \bigg(\large \frac{5}{13} \bigg) $$+ \sin^{-1} \bigg( \large\frac{16}{65} \bigg) = \large\frac{\pi}{2} $

asked Feb 17, 2013 by thanvigandhi_1

1 answer

Solve for x : $ \tan^{-1}3x+\tan^{-1}2x=\large\frac{\pi}{4} $

asked Feb 17, 2013 by thanvigandhi_1

1 answer

Find the value of $ \lambda $ so that the line $\large \frac{1-x}{3}=\frac{7y-14}{2\lambda}=\frac{5z-10}{11} $$\: and \; \large\frac{7-7x}{3\lambda}=\frac{y-5}{1}=\frac{6-z}{5}$ are perpendicular to each other.

asked Feb 17, 2013 by thanvigandhi_1

1 answer

Evaluate : $ \int \large\frac{(x-4)e^x}{(x-2)^3}$$dx $

asked Feb 15, 2013 by thanvigandhi_1

1 answer

If $ y=3\cos(\log\: x)+4\sin(\log\: x),$ then show that $ x^2.\large\frac{d^2y}{dx^2}$$+x\large\frac{dy}{dx}$$+y=0$

asked Feb 15, 2013 by thanvigandhi_1

1 answer

Find $\large \frac{dy}{dx}$ if $( (x^2+y^2)^2=xy)$

asked Feb 15, 2013 by thanvigandhi_1

1 answer

Find the intervals in which the function f given by $ f(x)=x^3+\frac{1}{x^3}, x \neq 0$ is (i) increasing (ii) decreasing.

asked Feb 15, 2013 by thanvigandhi_1

1 answer

Evaluate :$ \int_0^{\pi}\large \frac{e^{\large \cos x}}{e^{\large \cos x}+e^{\large-\cos x}}$$dx$

asked Feb 15, 2013 by thanvigandhi_1

1 answer

If $ \begin{bmatrix} x+3y & y \\ 7-x & 4 \end{bmatrix}=\begin{bmatrix} 4 & -1 \\ 0 & 4 \end{bmatrix} $, find the values of x and y.

asked Feb 15, 2013 by thanvigandhi_1

1 answer

If $ \begin{bmatrix} 2x & 5 \\ 8 & x \end{bmatrix}=\begin{bmatrix} 6 & 5 \\ 8 & 3 \end{bmatrix} $, then find x.

asked Feb 15, 2013 by thanvigandhi_1

1 answer

Find order and degree ( if defined ) of following differential equation : $ \bigg( \large\frac{d^2y}{dx^2} \bigg)^2$$+\cos \bigg( \large\frac{dy}{dx} \bigg)=0$

asked Feb 15, 2013 by thanvigandhi_1

1 answer

If $ |\overrightarrow a|=\sqrt 3, |\overrightarrow b|=2$ and the angle between $ \overrightarrow a \: and \: \overrightarrow b$ is $ 60^{\circ}$, find $ \overrightarrow a.\overrightarrow b$

asked Feb 15, 2013 by thanvigandhi_1

1 answer

Find a vector in the direction of vector $ \overrightarrow a = \hat i - 2\hat j$, whose magnitude is 7.

asked Feb 15, 2013 by thanvigandhi_1

1 answer

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