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Recent questions tagged modelpaper

Prove that : $ \cos^{-1}\large \frac{4}{5}+\tan^{-1}\large\frac{3}{5}$$=\tan^{-1}\large\frac{27}{11} $

asked Jan 16, 2013 by thanvigandhi_1

1 answer

(i) There are 2 men, 3 women and 3 children in family Y. The daily requirement of calories and protiens for men, women and children are 2000, 1800 and 1200 ; 50 g , 40 g and 35 g respectively. Represent the above information by matrices. Using matrix multiplication , calculate the total requirement of calories and protiens for each of the two families. (ii) Explain the importance of balance diet.

asked Jan 16, 2013 by thanvigandhi_1

0 answers

If \( y = tan^{-1}x,\) prove that $ (1+x^2)\large\frac{d^2y}{dx^2}$$+2x\large\frac{dy}{dx}$$=0.$

asked Jan 16, 2013 by thanvigandhi_1

0 answers

If \( x^{\large p}.y^{\large q} = (x+y)^{\large p+q}, \) prove that \( \large\frac{dy}{dx}=\large\frac{y}{x}.\)

asked Jan 16, 2013 by thanvigandhi_1

0 answers

Examine for continuity the function f' defined by $ f(x) = \left\{ \begin{array}{l l} \large\frac{e^{\large \frac{1}{x}} - 1}{e^{\large\frac{1}{x}} + 1}, & \quad { x \neq 0}\\ 0, & \quad \text{ $x$ = 0} \end{array}. \right. \: at\: x = 0.$

asked Jan 16, 2013 by thanvigandhi_1

0 answers

Compute the area of the bounded by the line $x+2y=2,y-x=1$ and $2x+y=7.$

asked Jan 16, 2013 by sreemathi.v

1 answer

Discuss the applicability of Roll's theorem for the function \( f(x) = x^{\large\frac{1}{3}} \) on [-1, 1].

asked Jan 16, 2013 by thanvigandhi_1

0 answers

Using differentials, find the approximate value of \( \sqrt {0.037}\).

asked Jan 16, 2013 by thanvigandhi_1

0 answers

Evaluate : $ \int_0^{\large\frac{\pi}{2}} \large\frac{x \sin x}{1+\sin x}$$dx $

asked Jan 16, 2013 by thanvigandhi_1

0 answers

Evaluate : $ \int_0^{\Large\frac{\pi}{4}} \log(1+tan \: x) dx.$

asked Jan 16, 2013 by thanvigandhi_1

0 answers

Solve the differential equation $ (x^2-1)\large\frac{dy}{dx}$$+2(x+2) y = 2(x+1). $

asked Jan 16, 2013 by thanvigandhi_1

0 answers

Solve the differential equation : $ 2x^2 \large\frac{dy}{dx}$$-2xy+y^2 = 0, \: y(e) = e.$

asked Jan 16, 2013 by thanvigandhi_1

0 answers

If \( \overrightarrow a = 4\hat i + 2\hat j - \hat k \: and \: \overrightarrow b = 5\hat i + 2\hat j - 3\hat k\), find the angle between \( \overrightarrow a + \overrightarrow b \: and \: \overrightarrow a - \overrightarrow b\).

asked Jan 16, 2013 by thanvigandhi_1

0 answers

Show that the line : $ \large\frac{x-5}{4}=\large\frac{y-7}{4}=\frac{z+3}{-5}$$ \: and \: \large\frac{x+8}{7}=\frac{y-4}{1}=\frac{z-5}{3} $ intersect each other.

asked Jan 16, 2013 by thanvigandhi_1

0 answers

A box contains 2 gold and 3 silver coins. A box is choosen at random and a coin is drawn from it. If the selected coin is a gold coin, find the probability that it was drawn from the second box. A student should not carry ornaments and other precious things to school. why?

asked Jan 16, 2013 by thanvigandhi_1

0 answers

Using properties of determinants, prove the following : \( \begin{bmatrix} (b+c)^2 & ab & ca \\ ab & (a+c)^2 & bc \\ ac & bc & (a+b)^2 \end{bmatrix} = 2abc (a+b+c)^3.\)

asked Jan 16, 2013 by thanvigandhi_1

0 answers

A square piece of tin of side 24 cm is to be made into a box without top by cutting a square from each corner and folding up the flaps to form a box. What should be the side of the square to be cut off so that volume of the box is maximum?

asked Jan 15, 2013 by thanvigandhi_1

1 answer

An open box with a square base is to be made out of given quantity of sheet of area \( a^2\). Show that maximum volume of the box is \( \large\frac{a^3}{6\sqrt 3}. \)

asked Jan 15, 2013 by thanvigandhi_1

0 answers

Evaluate : $ \int \large\frac{x^4}{x^4-1}$$ dx $

asked Jan 15, 2013 by thanvigandhi_1

0 answers

Evaluate : $ \int \: \sqrt {\large\frac{1-\sqrt x}{1+\sqrt x}}dx. $

asked Jan 15, 2013 by thanvigandhi_1

0 answers

Find the area enclosed by the parabolas \( y^2=9x \: and \: x^2=9y\)

asked Jan 15, 2013 by thanvigandhi_1

0 answers

Find the image of (1, 3, 4) in the plane x-y+z=5.

asked Jan 15, 2013 by thanvigandhi_1

0 answers

A factory owner wants to purchase two types of machines. A and B for his factory. The machine A requires an area of 1000 \( m^2\) and 12 skilled men for running it and its daily output is 50 units, whereas the machine B requires 1200 \( m^2\) area and 8 skilled men and its daily output is 40 units. If an area of 7600 \( m^2\) and 72 skilled men be available to operate the machine, how many machines of each type should be bought to maximise the daily output.? Keeping unemployment in mind justify the values to be promoted for selection of the manually operated machine.

asked Jan 15, 2013 by thanvigandhi_1

0 answers

A compay has two plants to manufacture bicycles. Plant I manufacture 70% of the bicycles and plant II manufacture 30%. At plant I, 80% of the bicycles are rated as of standard quality and a plant II , 90% of the bicycles are rated as of standard quality. A bicycle is choosen at random and is found to be of standard quality. What is the probability that it has come from plant II. Which mode of conveyance preferred by you at the most? why?

asked Jan 15, 2013 by thanvigandhi_1

0 answers

Find x if \( tan^{-1} 4 + cot^{-1}x =\large \frac{\pi}{2} \)

asked Jan 15, 2013 by thanvigandhi_1

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

If \( \begin{bmatrix} 3a-b & -2b \\ 3 & 7 \end{bmatrix} = \begin{bmatrix} 5 & 3 \\ 3 & 7 \end{bmatrix}\) then find a.

asked Jan 15, 2013 by thanvigandhi_1

1 answer

If $A = \begin{bmatrix} 2 & 4 \\ 3 & 2 \end{bmatrix}$ and $ B = \begin{bmatrix} 1 & 3 \\ -2 & 5 \end{bmatrix}$, then find BA.

asked Jan 15, 2013 by thanvigandhi_1

1 answer

Write the cofactor of elements of third column of the determinant. $ \begin{bmatrix} 4 & -5 & -11 \\ 1 & -3 & 1 \\ 2 & 3 & -7 \end{bmatrix} $

asked Jan 15, 2013 by thanvigandhi_1

0 answers

Evaluate : \( \int \sin\: x \cos \: dx \)

asked Jan 15, 2013 by thanvigandhi_1

0 answers

\( \int_0^1 \large\frac{dx}{\sqrt{1-x^2}} \)

asked Jan 15, 2013 by thanvigandhi_1

0 answers

Evaluate the product of \( (3\overrightarrow a - 5\overrightarrow b ).(2\overrightarrow a + \overrightarrow b)\)

asked Jan 15, 2013 by thanvigandhi_1

0 answers

Show that the points A (1, 2, 7), B (2, 6, 3) and C(3, 10, -1) are collinear.

asked Jan 15, 2013 by thanvigandhi_1

0 answers

Find the distance of (3, -2, 1) from the plane \( 2x-y+2z+3=0\).

asked Jan 15, 2013 by thanvigandhi_1

0 answers

Let * be the binary operation on N given by p * q = LCM of p and q. Find (i) 12 * 56 (ii) whether * is commutative? (iii) whether * is associative (iv) identity of * in N.

asked Jan 15, 2013 by thanvigandhi_1

0 answers

Prove that $ \cot^{-1} \bigg( \large\frac{\sqrt{1+\sin x}+\sqrt{1-\sin x}}{\sqrt{1+\sin x}-\sqrt{1-\sin x}} \bigg) = \large\frac{x}{2}$$, x \in \bigg( 0, \large\frac{\pi}{4} \bigg).$

asked Jan 15, 2013 by thanvigandhi_1

0 answers

Find the value of $ \tan\large\frac{1}{2}$$ \bigg[ \sin^{-1}\large \frac{2x}{1+x^2}$$+\cos^{-1}\large\frac{1-y^2}{1+y^2} \bigg].$$ \: where \: |x| < 1, y > 0 \: and \: xy < 1.$

asked Jan 15, 2013 by thanvigandhi_1

1 answer

Naimish, a food supplier from Amritsar supplies three food products x, y and z to Shimla and Guwahati. His annual sale is given below: (a) If unit sale prices of x, y and z are Rs. 3.00, Rs. 2.50 and 1.00. Find the total revenue obtained from supply to Shimla and Guwahati. Which market generate more revenue? (b) If the unit costs of the above three food products are Rs. 2.00, Rs. 1.00 and Rs. 0.50 respectively, find the gross profit. Which supply has more profit? (C) In which direction from Delhi, Shimla and Guwahati lies. Which economic mode of transport do you suggest to your friend travelling to Shimla and Guwahati?

asked Jan 15, 2013 by thanvigandhi_1

0 answers

If $ y =\large \frac{2}{\sqrt {a^2-b^2}}$$\tan^{-1} \bigg( \sqrt {\large\frac{a+b}{a-b}}\tan\frac{x}{2} \bigg)$. Prove that $\large \frac{dy}{dx}=\frac{1}{a-b\cos x} .$

asked Jan 15, 2013 by thanvigandhi_1

0 answers

Verify mean value theorem, if \( f(x)=x^3-5x^2-3x\) in the interval [a, b], where a = 1, b = 3. Find all \( c \in (1, 3)\) for which f' (c) = 0.

asked Jan 15, 2013 by thanvigandhi_1

0 answers

Prove that every real valued function which is derivable at a point of its domain is also continuous at that point. Is the converse true?

asked Jan 15, 2013 by thanvigandhi_1

1 answer

A window is in the form of a rectangle surmounted by a semicircular opening. The total perimeter of the window is 10m . Find the dimensions of the window to admit maximum light through the whole opening.

asked Jan 15, 2013 by thanvigandhi_1

0 answers

$ \int \large\frac{2+\sin x}{1+\cos x}e^{\Large\frac{x}{2}}$$dx. $

asked Jan 15, 2013 by thanvigandhi_1

0 answers

Solve the following differential equation : $ \cos^2\: x\large\frac{dy}{dx}$$+y=\tan x$

asked Jan 15, 2013 by thanvigandhi_1

1 answer

Show that the differential equation : $ x\: cos \bigg(\large \frac{y}{x} \bigg)\large \frac{dy}{dx}=$$y\cos \bigg(\large \frac{y}{x} \bigg)$$ + x $ is homogeneous and solve it.

asked Jan 15, 2013 by thanvigandhi_1

0 answers

Solve the following differential equation : $ \large\frac{ dy}{ dx}=\frac{\large y(2y-x)}{\large x(2y+x)},$$ \: if \: y=1 \: when \: x=1.$

asked Jan 15, 2013 by thanvigandhi_1

0 answers

Find the position vector of a point R which divides the line joining two points P and Q whose position vectors are \( \hat i +2\hat j - \hat k \: and \: -\hat i + \hat j + \hat k\) respectively in the ratio 2 : 1 (i) internally (ii) externally

asked Jan 14, 2013 by thanvigandhi_1

0 answers

Show that the plane passing through (1, 1, 1),(1, 01, 1) and (-7, -3, -5) is perpendicular to ZX-plane.

asked Jan 14, 2013 by thanvigandhi_1

0 answers

A variable plane is at a constant distance '3p' from the origin and meets the axes in A, B, C respectively, then show that locus of the centroid of \( \Delta \)ABC is $ \frac{1}{x^2}+\frac{1}{y^2}+\frac{1}{z^2}=\frac{1}{p^2} $

asked Jan 14, 2013 by thanvigandhi_1

0 answers

(i) In a group of student, selection of four students for cultural activity from 3 boys and 3 girls has to be done. Find the probability that either 3 boys and 1 girl or 3 girls and one boy are selected. (ii) Write the importance of co-curricular activities in inculcating human values.

asked Jan 14, 2013 by thanvigandhi_1

0 answers

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