Recent questions tagged q2

The function $ f(x)=2 log (x-2) - x^2+4x+1 $increases in the interval.\[(a)\;(1,2)\qquad(b)\;(2,3)\qquad(c)\;(5/2,3)\qquad(d)\;(2,4)\]

asked Jan 28, 2013 by meena.p

1 answer

Prove that $ \cos^{-1}(4x^3-3x)=3\cos^{-1}x.$

asked Jan 28, 2013 by thanvigandhi_1

1 answer

If $ sin \bigg( \sin^{-1} \frac{1}{5} + \cos^{-1} x \bigg) = 1,$ find x.

asked Jan 27, 2013 by thanvigandhi_1

0 answers

If $ \tan^{-1}2-\tan^{-1}1=\tan^{-1}x,$ then find x.

asked Jan 25, 2013 by thanvigandhi_1

1 answer

Show that $ sin^{-1} \bigg( 2x \sqrt{1-x^2} \bigg) = 2 sin^{-1}x.$

asked Jan 25, 2013 by thanvigandhi_1

1 answer

Let f be a non zero continuous function satisfying f(x+y) = f(x).f(y) for all x, y $ \epsilon$ R. If f(2) = 9 then find the value of f(3).

asked Jan 24, 2013 by meena.p

1 answer

Find the projection of $ \overrightarrow a = 2\hat i - \hat j + \hat k \: on \: \overrightarrow b = \hat i - 2\hat j + \hat k $

asked Jan 24, 2013 by thanvigandhi_1

0 answers

If $ \begin{bmatrix} p & q \\ r & -p \end{bmatrix}$ is such that $A^2=1$ then find the value of $1-p^2+qr$

asked Jan 24, 2013 by meena.p

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Find the value of $\tan^{-1}1+\tan^{-1}2+\tan^{-1}3.$

asked Jan 23, 2013 by meena.p

1 answer

Find the principal value of $ \cos^{-1} \bigg( -\frac{1}{2} \bigg). $

asked Jan 23, 2013 by thanvigandhi_1

1 answer

If $f(x)=\sin^2x+\sin^2\big(x+\frac{\pi}{3}\big)+\cos x.cos\big(x+\frac{\pi}{3}\big)\;and\;g\big(\frac{5}{4}\big)=1$, then find the value of gof(x)=x.

asked Jan 22, 2013 by meena.p

0 answers

Evaluate : $ \sin \bigg[ \large\frac{\pi}{3} - $$\sin^{-1} \bigg( -\large\frac{1}{2} \bigg) \bigg] $

asked Jan 22, 2013 by thanvigandhi_1

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Find the differential equation of all non vertical lines in a plane.

asked Jan 17, 2013 by sreemathi.v

1 answer

Solve $ 2tan^{-1}(cos \: x)=tan^{-1}(2 cosec \: x)$

asked Jan 17, 2013 by thanvigandhi_1

1 answer

If $\overrightarrow{a}=\hat i-\hat j+2\hat k\;and\;\overrightarrow{b}=2\hat i-\hat j-2\hat k,$then find the unit vector in the direction of $ 6 \overrightarrow{b} $

asked Jan 17, 2013 by sreemathi.v

1 answer

Find the value of $ \cos^{-1} \bigg( \frac{1}{2} \bigg) + 2 \sin^{-1} \bigg(\large \frac{1}{2} \bigg) $

asked Jan 16, 2013 by thanvigandhi_1

1 answer

Find the area of the region bounded by the parabola $y^2=2px,x^2=2py.$

asked Jan 16, 2013 by sreemathi.v

1 answer

Let f be the greatest integer function and g be the modulus function. Find the value of g o f $ \bigg(\large \frac{5}{3} \bigg)$ - f o g $ \bigg( \large\frac{5}{3} \bigg)$

asked Jan 15, 2013 by thanvigandhi_1

0 answers

Verify the following $ \large\int\frac{2x+3}{x^2+3x}dx=log \mid x^2+3x\mid+C$

asked Jan 14, 2013 by sreemathi.v

1 answer

If A, B are symmetric matrices of the same order then AB-BA is a : \[ \begin{array} ((A)\: skew\: symmetric \: matrix \\ (B) \: symmetric\: matrix \\ (C)\: Zero \: matrix \\ (D)\: Identity \: matrix \end{array} \]

asked Jan 11, 2013 by thanvigandhi_1

1 answer

If the area of a circle increases at a uniform rate,then prove that perimeter varies inversely as the radius.

asked Jan 10, 2013 by sreemathi.v

1 answer

Find the value of $ \cos^{-1} \bigg( \large\frac{1}{2} \bigg)=$$2\sin^{-1} \bigg(\large \frac{1}{2} \bigg) $

asked Jan 10, 2013 by thanvigandhi_1

0 answers

Find the value of the following: $ \tan^{-1}(1)+\cos^{-1} \bigg(\large -\frac{1}{2} \bigg)+$$\sin^{-1} \bigg(\large-\frac{1}{2} \bigg) $

asked Jan 10, 2013 by thanvigandhi_1

1 answer

Find the principal value of the following : $ \sin^{-1} \bigg( -\frac{\large 1}{\large 2} \bigg). $

asked Jan 9, 2013 by thanvigandhi_1

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For a loaded die,the probabilities of outcomes are given as under P(1)=P(2)=0.2,P(3)=P(5)=P(6)=0.1 and P(4)=0.3.The die is thrown two times.Let A and B be the events,'same number each time',and 'a total score is 10 or more',respectively.If the die were fair,determine whether or not the events A and B are independent.

asked Jan 8, 2013 by sreemathi.v

1 answer

Using principal value, calculate the following : $ \sin^{-1} \bigg( \sin \large\frac{3\pi}{5} \bigg). $

asked Jan 8, 2013 by thanvigandhi_1

1 answer

Maximise $Z=3x+4y$,subject to the constraints: $x+y\leq 1,x\geq 0,y\geq 0$.

asked Jan 7, 2013 by sreemathi.v

1 answer

Write the principal value of : $ \cos^{-1}\bigg( \cos\large\frac{7\pi}{6} \bigg). $

asked Jan 6, 2013 by thanvigandhi_1

1 answer

Compute the following : $ \begin{bmatrix} cos^2x & sin^2x \\ sin^2x & cos^2x \end{bmatrix} + \begin{bmatrix} sin^2x & cos^2x \\ cos^2x & sin^2x \end{bmatrix} $

asked Jan 4, 2013 by thanvigandhi_1

1 answer

If $ A' = \begin{bmatrix} -2 & 3 \\ 1 & 2 \end{bmatrix} $ and $ B = \begin{bmatrix} -1 & 0 \\ 1 & 2 \end{bmatrix} $ then find $( A + 2B)'.$

asked Jan 3, 2013 by thanvigandhi_1

1 answer

Find the vector equation of the line which is parallel to the vector $3\hat i+2\hat j+6\hat k$ and which passes through the point $(1,-2,3).$

asked Jan 3, 2013 by sreemathi.v

1 answer

Find the value of $ cosec^{-1} (2) $

asked Jan 2, 2013 by thanvigandhi_1

1 answer

Using principle value, evaluate the following : $ \cos^{-1} \bigg( \cos\large\frac{2\pi}{3} \bigg)$$ + \sin^{-1} \bigg( \sin\large\frac{2\pi}{3} \bigg) .$

asked Jan 2, 2013 by thanvigandhi_1

1 answer

Examine the continuity of f(x) at the indicated point $f(x)=\left \{\begin{array}{1 1}3x+5 & if\;x\geq 2\\x^2 & if\;x<2\end{array}\right.$ at $x=2.$

asked Dec 31, 2012 by sreemathi.v

1 answer

Find $ x \: if \;\tan^{-1} 4 + \cot^{-1} x =\large \frac{\pi}{2} $

asked Dec 29, 2012 by thanvigandhi_1

0 answers

Write the principal value of $ cos^{-1} \bigg( cos \frac{5\pi}{3} \bigg) $

asked Dec 26, 2012 by thanvigandhi_1

0 answers

Write the principal value of $ \cos^{-1} \bigg( \cos\large\frac{7\pi}{6} \bigg) $.

asked Dec 25, 2012 by thanvigandhi_1

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Using the properties of determinants, evaluate $\begin{vmatrix} a+x & y & z \\ x & a+y & z \\ x & y & a+z \end{vmatrix}$

asked Dec 24, 2012 by sreemathi.v

1 answer

If $ sin^{–1} x = y$ , then \[ \begin{array} ((A)\: 0 ≤ y ≤ π \quad & (B) \: \frac{-\pi}{2} ≤ y ≤ \frac{\pi}{2} \\ (C)\: 0 < y < π \quad & (D) \: \frac{-\pi}{2} < y < \frac{\pi}{2} \end{array} \]

asked Dec 24, 2012 by thanvigandhi_1

0 answers

What is the order of the matrix $A=\begin{bmatrix} a & 1 & x \\ 2 & \sqrt 3 & x^2 y \\ 0 & 5 & \frac{2}{5} \end{bmatrix}$

asked Dec 21, 2012 by sreemathi.v

1 answer

Let * be a binary operation on N given by a * b = HCF (a, b) , a, b $ \in $ N. Write the value of 22 * 4.

asked Dec 21, 2012 by thanvigandhi_1

0 answers

Evaluate : $ \sin \bigg[ \large\frac{\pi}{3}$$ - \sin^{-1} \bigg(-\large\frac{1}{2} \bigg) \bigg] $

asked Dec 20, 2012 by thanvigandhi_1

0 answers

Let $D$ be the domain of the real valued function $f$ defined by $f(x)=\sqrt{25-x^2}.$Then, write $D$

asked Dec 18, 2012 by sreemathi.v

1 answer

Find the vector equation of a plane which is at a distance of 7 units from the origin and normal to the vector $3\hat i + 5\hat j - 6 \hat k.$

asked Dec 15, 2012 by thanvigandhi_1

1 answer

Find the value of the following:<br> $ tan^{-1} \bigg(tan \frac{7\pi}{6}\bigg)$

asked Dec 10, 2012 by thanvigandhi_1

1 answer

If a matrix has 24 elements,what are the possible orders it can have? What, if it has 13 elements?

asked Dec 7, 2012 by sreemathi.v

1 answer

Classify the following measures as scalars and vectors. $(i)\;10\: kg$

asked Dec 7, 2012 by thanvigandhi_1

1 answer

Prove the following \[3\cos^{-1}x=\cos^{-1}(4x^3-3x), \;x\;\in\bigg[\frac{1}{2},1\bigg]\]

asked Dec 6, 2012 by sreemathi.v

1 answer

Write two different vectors having same magnitude.

asked Dec 6, 2012 by thanvigandhi_1

1 answer

Find the angle between the vectors $\hat i - 2\hat j + 3\hat k$ and $ 3\hat i - 2\hat j + \hat k$

asked Dec 6, 2012 by thanvigandhi_1

1 answer

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