Recent questions tagged 2012

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

asked Jan 15, 2013 by thanvigandhi_1

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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

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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

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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

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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

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Evaluate : $ \int \sin\: x \cos \: dx $

asked Jan 15, 2013 by thanvigandhi_1

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

asked Jan 15, 2013 by thanvigandhi_1

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

asked Jan 15, 2013 by thanvigandhi_1

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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

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

asked Jan 15, 2013 by thanvigandhi_1

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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

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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

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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

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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

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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

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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

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

asked Jan 15, 2013 by thanvigandhi_1

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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

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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

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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

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(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

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(i) If a young lady drives her scooty at 30 km/hour, she had to spend Rs. 2.00 per km on petrol. If she drives at speed 50 km/h the petrol cost is Rs. 4.00 per km. She has Rs. 150 to spend on petrol and wants to describe the maximum distance she can travel within 2 hours. Express this as L.P.P and solve it graphically. (ii) Which mode of transport you suggest to a student and why?

asked Jan 13, 2013 by thanvigandhi_1

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(i) In the village of 50 people 25 people have their fast on republic day. Two persons are selected at random out of them, write the probability distribution who are on fast. Also find the mean of the distribution. (ii) What do you mean by republic?

asked Jan 13, 2013 by thanvigandhi_1

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An insurance company insured 2000 scooter drivers, 4000 car drivers and 6000 truck drivers. The probability of an accident involving a scooter driver, car driver and a truck driver is 0.01, 0.03 and 0.15 respectively. One of the insured person meet with an accident. What is the probability that he is a scooter driver? What do you know by 'insurance'?

asked Jan 13, 2013 by thanvigandhi_1

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Using integration find the area of the following region $ \{ (x, y):|x-1| \geq y \geq \sqrt{5-x^2} \} .$

asked Jan 13, 2013 by thanvigandhi_1

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Find the maximum area of an isosceles triangle inscribed in the ellipse $ \frac{\large x^2}{\large a^2}+\frac{\large y^2}{\large b^2}=1$ with its vertex at one end of the major axis.

asked Jan 13, 2013 by thanvigandhi_1

0 answers

Show that $ \int_0^{\pi} \frac{\large x\: sin\: x}{\large 1+sin \: x}= \frac{\large \pi}{\large 2}(\pi-2) $

asked Jan 13, 2013 by thanvigandhi_1

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Show that $ \int_0^{\pi} \log(1+tan \: \theta ) d\theta. $

asked Jan 13, 2013 by thanvigandhi_1

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Find the shortest distance between the lines : $\large \frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}$$ \: and \: \large\frac{x-2}{3}=\frac{y-4}{4}=\frac{z-5}{5} $ Also, find equation of the shortest distance.

asked Jan 13, 2013 by thanvigandhi_1

0 answers

Show that the matrix $ A = \begin{bmatrix} 0 & 1 & -1 \\ -1 & 0 & 1 \\ 1 & -1 & 0 \end{bmatrix} $ is a skew - symmetric matrix.

asked Jan 11, 2013 by thanvigandhi_1

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

Let A be a square matrix of order 3 x 3, then what is the value of | KA |.

asked Jan 11, 2013 by thanvigandhi_1

0 answers

If $ y=3e^{2x}+2e^{3x}$, prove that : $\large \frac{d^2y}{dx^2}-$$5\large\frac{dy}{dx}$$+6y=0.$

asked Jan 11, 2013 by thanvigandhi_1

0 answers

At what points of the ellipse $ 16x^2+9y^2=400$, does the coordinate decrease at the same rate at which the abscissa increases.

asked Jan 11, 2013 by thanvigandhi_1

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$ \int x^2 \bigg( 1-\large\frac{1}{x^2} \bigg) $$dx.$

asked Jan 11, 2013 by thanvigandhi_1

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Find the differential equation $ y=e^x+1$

asked Jan 11, 2013 by thanvigandhi_1

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Represent graphically a displacement of 40 km , $ 30^{\circ} $ east of length.

asked Jan 11, 2013 by thanvigandhi_1

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Compute $ P (A/B)$if, $P(B)=0.5, P(A \cap B)=0.32.$

asked Jan 11, 2013 by thanvigandhi_1

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Evaluate : $ P(A \cup B)$ if $2P(A) = P(B)=\large\frac{5}{13}\: and \: $$P(A/B) =\large \frac{2}{5} $.

asked Jan 11, 2013 by thanvigandhi_1

0 answers

Let L be the set of all lines in XY - planes and R be the relation in L defined as R = $ { (L_1, L_2 ) : L_1 \: is \: parallel\: to\: L_2} $. Show the R is an equivalence relation. Find the set of all the lines related to the line $ y=2x+4.$

asked Jan 11, 2013 by thanvigandhi_1

1 answer

Using properties of determinants, prove the following : $ \begin{bmatrix} b+c & a & a \\ b & c+a & b \\ c & c & a+b \end{bmatrix} = 4abc.$

asked Jan 11, 2013 by thanvigandhi_1

0 answers

Using properties of determinants, prove the following : $ \begin{bmatrix} b+c & c+a & a+b \\ q+r & r+p & p+q \\ y+z & z+x & x+y \end{bmatrix} = 2 \begin{bmatrix} a & b & c \\ p & q & r \\ x & y & z \end{bmatrix}. $

asked Jan 11, 2013 by thanvigandhi_1

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