Recent questions tagged easy

The cartesian equation of a line is $\frac{\large x-5}{\large 3} = \frac{\large y+4}{\large 7} = \frac{\large z-6}{\large 2}$. Write its vector form.

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Find the equation of the line in vector and in cartesian form that passes through the point with position vector $2\hat{ i}- \hat{j} + 4\hat{k}$ and is in the direction$\hat{i} + 2\hat{j} - \hat{k}$.

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Find the equation of the line which passes through the point $(1, 2, 3)$ and is parallel to the vector $3\hat{i} + 2\hat{j} -2\hat{k}$. .

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Show that the line through the points $(4, 7, 8), (2, 3, 4)$ is parallel to the line through the points $(-1, -2, 1), (1, 2, 5)$

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Show that the line through the points (1, -1, 2), (3, 4, -2) is perpendicular to the line through the points (0, 3, 2) and (3, 5, 6).

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Show that the three lines with direction cosines $\large \frac{12}{13}, \frac{-3}{13}, \frac{-4}{13}; \;\; \frac{4}{13}, \frac{12}{13}, \frac{3}{13}; \;\; \frac{3}{13}, \frac{-4}{13}, \frac{12}{13}$ are mutually perpendicular.

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Show that the points (2, 3, 4), (-1, -2, 1), (5, 8, 7) are collinear.

asked Nov 29, 2012 by balaji.thirumalai

1 answer

If a line has the direction ratios $-18, 12, -4,$ then what are its direction cosines?

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Find the direction cosines of a line which makes equal angles with the coordinate axes.

asked Nov 29, 2012 by balaji.thirumalai

1 answer

If a line makes angles $90^\circ$,$135^\circ$, $45^\circ$ with the x, y and z-axes respectively, find its direction cosines.

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Find the equation of the plane passing through (a, b, c) and parallel to the plane $\hat{r}. (\hat{i}+\hat{j}+\hat{k}) = 2$.

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Let A = $\begin{bmatrix} 1 & sin\theta & 1 \\ -sin\theta & 1 & sin\theta \\ -1 & -sin\theta & 1 \end{bmatrix}$, where $0 \leq \theta \leq 2\pi$. Then: \[ \begin{array} ((A) \, Det(A) = 0 \quad& (B) \, Det(A) \in (2, \infty) \\[0.5em] (C) \, Det(A) \in (2, 4) \quad &(D) Det(A) \in [2,4] \end{array} \]

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Choose the correct answer. If a, b, c, are in A.P, then the determinant $\begin{vmatrix} x+2 & x+3 &x+2a \\ x+3 & x+4 &x+2b \\ x+4 & x+5 &x+2c \end{vmatrix}$ is: \[\] $(A)\;0 \hspace{20 mm} (B)\;1 \hspace{20 mm} (C)\; x \hspace{20 mm} (D)\; 2x $

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Using properties of determinants, prove that: $\begin{vmatrix} sin\alpha&cos\alpha&cos(\alpha+\delta)\\ sin\beta&cos\beta&cos(\beta+\delta)\\ sin\gamma&cos\gamma&cos(\gamma+\delta)) \end{vmatrix}= 0.$

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Using properties of determinants, prove that: $\begin{vmatrix} 1&1+p&1+p+q\\ 2&3+2p&4+3p+2q\\ 3&6+3p&10+6p+3q \end{vmatrix}= 1.$

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Using properties of determinants, prove that: $\begin{vmatrix} \alpha & \alpha^2 & \beta+\gamma\\ \beta & \beta^2 & \alpha+\gamma\\ \gamma & \gamma^2 & \alpha+\beta \end{vmatrix} = (\beta-\gamma) (\gamma - \alpha) (\alpha-\beta) (\alpha+\beta+\gamma)$

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Evaluate $\begin{vmatrix} 1 & x & y\\ 1 & x+y & y\\ 1 & x & x+y \end{vmatrix}$

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Evaluate $ \begin{vmatrix} x & y & x+y\\ y & x+y & x\\ x+y & x & y \end{vmatrix}$

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Solve the equation $ \begin{vmatrix} x+a & x & x \\ x & x+a & x\\ x & x & x+a \end{vmatrix}=0, \; a \neq 0. $

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Examine the consistency of the system of equations:\[\] \[\quad 5x -y +4z = 5 \] \[\quad2x + 3y + 5z= 2\] \[\quad 5x - 2y + 6z = -1\]

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Examine the consistency of the system of equations:\[\] \[\quad 3x -y -2z = 2 \] \[\quad 2y -z = -1\] \[\quad 3x -5y = 3\]

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Examine the consistency of the system of equations:\[\] \[\quad x + y + z = 1 \] \[\quad 2x + 3y +2z = 2\] \[\quad ax + ay +2az = 4\]

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Examine the consistency of the system of equations:\[\] \[\quad x + 3y = 5 \] \[\quad 2x + 6y = 8\]

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Examine the consistency of the system of equations:\[\] \[\quad 2x -y = 5 \] \[\quad x + y = 4\]

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Examine the consistency of the system of equations:\[\] \[\quad x + 2y = 2 \] \[\quad 2x + 3y = 3\]

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Solve the following Linear Programming Problems graphically: Maximise $Z = 3x + 4y$ . subject to the constraints : $x + y \leq 4, x \geq 0, y \geq 0.$

asked Nov 29, 2012 by fingeazy

1 answer

Solve the following Linear Programming Problems graphically: Minimise $Z =$ –$3x + 4 y$ subject to $ x + 2y \leq 8, 3x + 2y \leq 12, x \geq 0, y\geq 0.$

asked Nov 29, 2012 by fingeazy

1 answer

Solve the following Linear Programming Problems graphically: Maximise $Z = 5x + 3y$ subject to $3x + 5y \leq 15, 5x + 2y \leq 10, x \geq 0, y \geq 0.$

asked Nov 29, 2012 by fingeazy

1 answer

Solve the following Linear Programming Problems graphically: Minimise $Z = 3x + 5y$. such that $ x + 3y \geq 3, x + y \geq 2, x, y \geq 0.$

asked Nov 29, 2012 by fingeazy

1 answer

If A is an invertible matrix of order 2, then det$(A^{-1})\;$ is equal to: $ (A)\; det\;(A) \quad (B)\; \frac{1}{det\;(A)} \quad (C)\; 1 \quad (D)\; 0 $

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Solve the following Linear Programming Problems graphically: Maximise $Z = 3x + 2y$ subject to $x + 2y \leq 10, 3x + y \leq 15, x, y \geq 0.$

asked Nov 29, 2012 by fingeazy

1 answer

Let $A$ be a nonsingular square matrix of order $3 \times 3.$ Then $| adj \;A| $ is equal to:

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Find the general solution of the differential equation$\large\frac{dy}{dx}+\sqrt{\frac{1-y^2}{1-x^2}}\;$$=\;0$

asked Nov 29, 2012 by sreemathi.v

1 answer

Find the inverse of the matrix (if it exists): \[ \begin{bmatrix} 1&0&0 \\ 0&cos\alpha&sin\alpha \\ 0&sin\alpha&-cos\alpha \\ \end{bmatrix} \]

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Find the inverse of the matrix (if it exists): $ \begin{bmatrix} -1&5 \\ -3&2 \\ \end{bmatrix} $

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Find the inverse of the matrix (if it exists): $ \begin{bmatrix} 2&-2 \\ 4&3 \\ \end{bmatrix} $

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Find the adjoint of the matrix: $\begin{bmatrix} 1&2 \\ 3&4 \end{bmatrix} $

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Find the equation of the curve passing through the point$\bigg(0,\large\frac{\pi}{4}\bigg)$ whose differential equation is $\sin x\cos y\;dx+\cos x\sin y\;dy\;=\;0$

asked Nov 29, 2012 by sreemathi.v

1 answer

If $\Delta = \begin{vmatrix} a_11&a_12&a_13 \\ a_21&a_22&a_23 \\ a_31&a_32&a_33 \end{vmatrix} $ and $A_y$ is Cofactor of $a_y$, then value of $\Delta$ is:

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Using Cofactors of elements of third column, evaluate $ \Delta = \begin{vmatrix} 1&x&yz \\ 1&y&zx \\ 1&z&xy \end{vmatrix} $

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Using Cofactors of elements of second row, evaluate $ \Delta = \begin{vmatrix} 5&3&8 \\ 2&0&1 \\ 1&2&3 \end{vmatrix} $

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Write Minors and Cofactors of the elements of following determinants: $ (i) \quad \begin{vmatrix} 1&0&0 \\ 0&1&0 \\ 0&0&1 \end{vmatrix} $

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Choose the correct answer $\sin (\tan^{-1}x), |x| <1 $ is equal to

asked Nov 28, 2012 by vaishali.a

1 answer

The general solution of the differential equation $\large\frac{ydx-xdy}{y}$$=0\;is$

asked Nov 28, 2012 by sreemathi.v

1 answer

The general solution of a differential equation of the type $\large\frac{dx}{dy}$$+p_1x=Q_1\;is$

asked Nov 28, 2012 by sreemathi.v

1 answer

The general solution of the differential equation$ e^xdy+(ye^x+2x)dx=0\; is$

asked Nov 28, 2012 by sreemathi.v

1 answer

For each of the differential equations given below,indicate its order and degree(if defined) $(i)\;\large\frac{d^2y}{dx^2}+5x\bigg(\frac{dy}{dx}\bigg)^2-6y=\log x$

asked Nov 28, 2012 by sreemathi.v

1 answer

The order of the differential equation $2x^2\large\frac{d^2y}{dx^2}$$-3\frac{dy}{dx}$$+y=0\;is$

asked Nov 28, 2012 by sreemathi.v

1 answer

Write Minors and Cofactors of the elements of following determinants: $ (i) \quad \begin{vmatrix} 2&-4 \\ 0&3 \end{vmatrix}$

asked Nov 28, 2012 by balaji.thirumalai

1 answer

If area of triangle is $35\; sq\; units$ with vertices $(2, -6), (5, 4)$ and $(k, 4)$. Then $k$ is

asked Nov 28, 2012 by balaji.thirumalai

1 answer

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