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Recent questions tagged easy

If a matrix has 5 elements, write all possible orders it can have.

asked Feb 5, 2013 by thanvigandhi_1

1 answer

Evaluate : $ \int (ax+b)^3 dx $

asked Feb 5, 2013 by thanvigandhi_1

1 answer

Evaluate : $ \int \large\frac{dx}{\sqrt{1-x^2} } $

asked Feb 5, 2013 by thanvigandhi_1

1 answer

Write the direction - cosines of the line joining the points (1,0,0) and (0,1,1).

asked Feb 5, 2013 by thanvigandhi_1

1 answer

Write the projection of the vector \( \hat i - \hat j \) on the vector \( \hat i + \hat j \)

asked Feb 5, 2013 by thanvigandhi_1

1 answer

Write the vector equation of the line given by $\large \frac{x-5}{3} = \frac{y+4}{7}=\frac{z-6}{2} $

asked Feb 5, 2013 by thanvigandhi_1

1 answer

Find the relationship between 'a' and 'b' so that the function 'f' defined by $ f(x) = \left\{ \begin{array}{l l}ax+1, & \quad if { x \leq 3} \\ bx+3, & \quad if { x > 3} \end{array} \right. $ is continuous at x = 3.

asked Feb 5, 2013 by thanvigandhi_1

1 answer

If \( x^y=e^{x-y}\), show that \( \large\frac{dy}{dx}=\frac{logx}{\{log(xe)\}^2} \)

asked Feb 5, 2013 by thanvigandhi_1

1 answer

Vectors $ 2\bar{i}-\bar{j}+2\bar{k}\;and\;\bar{i}+\bar{j}-3\bar{k}$ act along two adjacent sides of a parallelogram. Find the angle between the diagonals of the parallelogram.

asked Feb 4, 2013 by meena.p

1 answer

What is the area of the parallelogram having diagonals $ 3\bar{i}+\bar{j}-2\bar{k}\;and\;\bar{i}-3\bar{j}+4\bar{k}$?

asked Feb 4, 2013 by meena.p

1 answer

If $ \bar{a}\;and\;\bar{b}$ are vectors,prove that $ |\bar{a} \times \bar{b}|^2+(\bar{a}.\bar{b})^2=|\bar{a}|^2.|\bar{b}|^2$

asked Feb 4, 2013 by meena.p

1 answer

Form the differential equation of the family of parabolas having vertex at the origin and axis along positive y - axis.

asked Feb 4, 2013 by thanvigandhi_1

1 answer

Find a vector of magnitude 5 units, and parallel to the resultant of the vectors \( \overrightarrow a = 2\hat i + 3\hat j - \hat k \: and \: \overrightarrow b = \hat i - 2\hat j + \hat k\)

asked Feb 4, 2013 by thanvigandhi_1

1 answer

Evaluate:\[\int \limits _0 ^ \pi \Large\frac{e^{\cos x}}{[e^{\cos x}+e^{-\cos x}]}dx\]

asked Feb 4, 2013 by meena.p

1 answer

Write the value of $ \sin\bigg[ \large\frac{\pi}{3}$$-sin^{-1} \bigg( -\large\frac{1}{2} \bigg) \bigg]. $

asked Feb 4, 2013 by thanvigandhi_1

1 answer

For a 2 x 2 matrix, A = \( [a_{ij} ], \) whose elements are given by \( a_{ij}=\large\frac{i}{j},\) write the value of \( a_{12}.\)

asked Feb 4, 2013 by thanvigandhi_1

1 answer

For what value of x, the matrix $ \begin{bmatrix} 5-x & x+1 \\ 2 & 4 \end{bmatrix} $ is singular?

asked Feb 4, 2013 by thanvigandhi_1

1 answer

Evaluate:$\int \limits_{-\pi}^{\pi} x^{20} \sin ^9x dx $

asked Feb 4, 2013 by meena.p

1 answer

write \( A^{-1} \) for \( A = \begin{bmatrix} 2 & 5 \\ 1 & 3 \end{bmatrix} \)

asked Feb 4, 2013 by thanvigandhi_1

1 answer

Write the value of $ \int \sec\: x (\sec\: x+\tan \: x)dx $

asked Feb 4, 2013 by thanvigandhi_1

1 answer

Write the value of $ \int \large\frac{dx}{x^2+16} $

asked Feb 4, 2013 by thanvigandhi_1

1 answer

For what value of 'a' the vectors \( 2\hat i - 3\hat j + 4\hat k \) and \( a\hat i + 6\hat j - 8\hat k \) are collinear?

asked Feb 4, 2013 by thanvigandhi_1

1 answer

Write the direction cosines of the vector \( -2\hat i + \hat j - 5\hat k \).

asked Feb 4, 2013 by thanvigandhi_1

1 answer

Write the intercept cut off by the plane \( 2x+y-z=5\) on x - axis.

asked Feb 4, 2013 by thanvigandhi_1

1 answer

Find the value of y, if $\begin{bmatrix} x-y & 2 \\ x & 5 \end{bmatrix} = \begin{bmatrix} 2 & 2 \\ 3 & 5 \end{bmatrix} $

asked Feb 4, 2013 by thanvigandhi_1

1 answer

Using elements transformation find the inverse of $ \begin{bmatrix} 2 & -6 \\ 1 & -2 \end{bmatrix} $

asked Feb 4, 2013 by thanvigandhi_1

1 answer

Find x if \( \begin{bmatrix} 3 & 4 \\ -5 & 2 \end{bmatrix} = \begin{bmatrix} 2x & 4 \\ -5 & 3 \end{bmatrix} \)

asked Feb 3, 2013 by thanvigandhi_1

1 answer

Find the value of x, if : $ \begin{bmatrix} 1 & x & 1 \end{bmatrix} \; \begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 3 & 2 & 5 \end{bmatrix} \; \begin{bmatrix} 1 \\ -2 \\ 3 \end{bmatrix} = 0 $

asked Feb 3, 2013 by thanvigandhi_1

1 answer

Find the values of x, if $\begin{bmatrix} 2 & 4 \\ 5 & 1 \end{bmatrix} = \begin{bmatrix} 2x & 4 \\ 6 & x \end{bmatrix} $

asked Feb 3, 2013 by thanvigandhi_1

1 answer

If a matrix has 12 elements, what are the possible order it can have?

asked Feb 2, 2013 by thanvigandhi_1

1 answer

Find the product of matrix \( A = \begin{bmatrix} 3 \\ 2 \\ -5 \end{bmatrix} \) and its transpose.

asked Feb 2, 2013 by thanvigandhi_1

1 answer

If \( A = \begin{bmatrix} \cos\theta & -\sin\theta \\ \sin\theta &\cos\theta \end{bmatrix} \) and $A + A'= I$, then find the value of \( \theta \).

asked Jan 29, 2013 by thanvigandhi_1

1 answer

If \( A = \begin{bmatrix} 2 & -2 \\ -3 & 4 \end{bmatrix} \), find \( -A^2+6A.\)

asked Jan 29, 2013 by thanvigandhi_1

1 answer

If $ \begin{bmatrix} 2 & 4 \\ 5 & 1 \end{bmatrix} = \begin{bmatrix} 2x & 4 \\ 6 & x \end{bmatrix} $, then find x.

asked Jan 29, 2013 by thanvigandhi_1

1 answer

Verify the Rolles Theorem for the function $ f(x)=\sin x- \cos x, $in the interval $ \bigg[\Large\frac{\pi}{4},\frac{5\pi}{4}\bigg]$

asked Jan 28, 2013 by meena.p

1 answer

Using LMV Theorem, find a point on the curve $ y=(x-3)^2,$ where the tangent is parallel to the chord joining (3,0) and (5,4).

asked Jan 28, 2013 by meena.p

1 answer

It is given that for the function $ f(x)=x^3-6x^2+px+q\;on\;[1,3].$Rolles theorem holds with $ c=2+\large\frac{1}{\sqrt 3}.$Find the values of p and q.

asked Jan 28, 2013 by meena.p

1 answer

Verify Rolles theorem for the function $ f(x)=\Large e^{1-x^2}$in the interval [-1,1]

asked Jan 28, 2013 by meena.p

1 answer

Find $\Large\frac{dy}{dx}$when$y=\tan^{-1}\bigg[\Large\frac{x^{\frac{1}{3}}+a^{\frac{1}{3}}}{1-x^{\frac{1}{3}}a^{\frac{1}{3}}}\bigg]$

asked Jan 28, 2013 by meena.p

1 answer

Find the values of x,y and z, if $ \begin{bmatrix} x+y+z \\ x+z \\ y+z \end{bmatrix} = \begin{bmatrix} 9 \\ 5 \\ 7 \end{bmatrix} $

asked Jan 28, 2013 by thanvigandhi_1

1 answer

Express $ \begin{bmatrix} 2 & -2 & -4 \\ -1 & 3 & 4 \\ 1 & -2 & -3 \end{bmatrix} $ as the sum of a symmetic and skew-symmetric matrix.

asked Jan 28, 2013 by thanvigandhi_1

1 answer

If \( A = \begin{bmatrix} 6 & -5 \\ 2 & 3 \end{bmatrix} \), then show that A-A' is skew matrix.

asked Jan 27, 2013 by thanvigandhi_1

1 answer

Find the value of x, such that \( A = \begin{bmatrix} x & 5 \\ 4 & 2x \end{bmatrix} = \begin{bmatrix} 2 & 5 \\ 16 & 4 \end{bmatrix} \)

asked Jan 27, 2013 by thanvigandhi_1

1 answer

If \( A = [ a_{ij}],\) where \( a_{ij}= \left\{ \begin{array}{l l}i+j, & \quad if\; { i \geq j}\\ i-j, & \quad if\; { i < j} \\ \end{array}. \right.\) construct a 3 x 2 matrix A.

asked Jan 25, 2013 by thanvigandhi_1

0 answers

If A is a matrix of order 3 x 4 and B is matrix of order 5 x 4, what is the order of matrix (AB)'.

asked Jan 25, 2013 by thanvigandhi_1

1 answer

If $y=\sin ^{-1}\big [x^2\sqrt{1-x^2}+x\sqrt {1-x^4}\big],$ prove that $ \Large\frac{dy}{dx}=\frac{2x}{\sqrt{1-x^4}}+\frac{1}{\sqrt{1-x^2}}$

asked Jan 25, 2013 by meena.p

1 answer

Find$ \Large\frac{dy}{dx}\;\normalsize when\;y=\sin ^{-1} \bigg[\Large\frac{5x+12 \sqrt{1-x^2}}{13}\bigg]$

asked Jan 25, 2013 by meena.p

1 answer

Find all the points of discontinuity of f defined by f(x) = | x | - | x+1|.

asked Jan 25, 2013 by meena.p

1 answer

Show that the function $ f(x)= \left\{ \begin{array}{1 1} x+\lambda, & \quad x< 1 \\ \lambda x^2+1, & \quad x\geq1 \end{array} \right. $ is continuous function, regardless of the choice of $ \lambda \in R $

asked Jan 25, 2013 by meena.p

1 answer

Show that Sin | x | is continuous.

asked Jan 25, 2013 by meena.p

1 answer

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