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Recent questions tagged modelpaper

(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

0 answers

(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

0 answers

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

0 answers

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

0 answers

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

0 answers

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

asked Jan 13, 2013 by thanvigandhi_1

0 answers

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

0 answers

Find the differential equation \( y=e^x+1\)

asked Jan 11, 2013 by thanvigandhi_1

0 answers

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

0 answers

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

0 answers

If \( y=e^{\large a \: cos^{-1}\: x} ; -1 \: \leq \: x \leq \: 1\), show that $ (1+x^2) \large\frac{d^2y}{dx^2}-x\frac{dy}{dx}-$$a^2y=0.$

asked Jan 11, 2013 by thanvigandhi_1

0 answers

If \( x \sqrt {1+y} + y \sqrt{1+x}=0 \: for \: -1 < x < 1\) Prove that : $\large \frac{dy}{dx}=\frac{1}{(1+x)^2} $

asked Jan 11, 2013 by thanvigandhi_1

0 answers

Find the equation of tangent to the curve \( x=sin \: 3t, \: y=cos\: 2t, \: at \: t=\large\frac{\pi}{4}. \)

asked Jan 11, 2013 by thanvigandhi_1

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At what point will the tangent to the curve \( y=2x^3-15x^2+36x-21\) be parallel to x - axis? Also, find the equations of tangents to the curve at these points ?

asked Jan 11, 2013 by thanvigandhi_1

0 answers

Evaluate : $ \int \sin x \sqrt {1+\cos2x} dx.$

asked Jan 11, 2013 by thanvigandhi_1

0 answers

Evaluate : $ \int \large\frac{x^2+x+1}{(x+2)(x+1)^2}$$dx.$

asked Jan 11, 2013 by thanvigandhi_1

0 answers

Evaluate : $ \int \large\frac{dx}{x[6(log \: x)^2]+7( log \: x)+2}$$dx.$

asked Jan 11, 2013 by thanvigandhi_1

0 answers

Evaluate : $ \int \tan^{-1} \sqrt{ \large\frac{1-sinx}{1+sinx}}dx. $

asked Jan 11, 2013 by thanvigandhi_1

1 answer

Solve the following differential equation $ x(1+y^2)dx-y(1+x^2)dy=0 $ given that $ y=0, \: when \: x=1$

asked Jan 11, 2013 by thanvigandhi_1

0 answers

Solve the following differential equation $\large\frac{dy}{dx}$$+\sec x.y = \tan \: x. $

asked Jan 11, 2013 by thanvigandhi_1

0 answers

Find the magnitude of two vectors $ \overrightarrow a \: and \overrightarrow b $ having the same magnitude and such that the angle between them is $ 60^{\circ} $ and their scalar product is $\large\frac{1}{2}$.

asked Jan 11, 2013 by thanvigandhi_1

0 answers

A man is known to speak the truth 3 out of 5 times. He throws a dice and reports that it is 1. Find the probability that it is actually 1.

asked Jan 11, 2013 by thanvigandhi_1

0 answers

Two bags A and B contain 2 white, 4 red and 3 white, 3 red balls respectively. One of the bags is selected at random and a ball is drawn from it. If the selected ball is of white colour, find the probability that it is drawn from bag A.

asked Jan 11, 2013 by thanvigandhi_1

1 answer

Let A = R-{3} and B = R-{1}. Consider the function\( f:A \rightarrow B\) defined by \( f(x)=\large\frac{x-2}{x-3}\). Is f one-one and onto? Justify your answer.

asked Jan 11, 2013 by thanvigandhi_1

0 answers

Solve, using matrices : $ 2x-y+3z=5;3x+2y-z=7 ; 4x+5y-5z = 9$

asked Jan 11, 2013 by thanvigandhi_1

1 answer

Using matrix solve the following system of linear equations : $ 2x+y+z=3 ; 3x-y+z=0 ;x-2y+3z = -6$

asked Jan 11, 2013 by thanvigandhi_1

0 answers

Find the largest possible area of the right-angled triangle whose hypotenuse is 5 cm.

asked Jan 11, 2013 by thanvigandhi_1

0 answers

Prove that the radius of the right circular cylinder of the greatest curved surface that can be inscribed in a given cone is half of the radius of the cone.

asked Jan 11, 2013 by thanvigandhi_1

0 answers

Find the region included between the parabola \( y^2=x \) & the line \( x+y=2.\)

asked Jan 11, 2013 by thanvigandhi_1

0 answers

Find the shortest distance between the lines : $\overrightarrow r = (1+2\lambda ) \hat i + (2+3\lambda)\hat j + (3+4\lambda)\hat k $ and $ \overrightarrow r = (2+3\mu ) \hat i + 4(1+\mu)\hat j + 5(1+\mu)\hat k $

asked Jan 11, 2013 by thanvigandhi_1

0 answers

Find the angle between the planes \( 4x+8y+z-8=0 \: and \: y+z-4=0. \)

asked Jan 11, 2013 by thanvigandhi_1

0 answers

Relation R is the set N of natural numbers defined as R = (x, y): y=x+5 and x < y}.

asked Jan 10, 2013 by thanvigandhi_1

0 answers

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

Compute the following $ \begin{bmatrix} a & b \\ -b & a \end{bmatrix} + \begin{bmatrix} a & b \\ b & a \end{bmatrix} $

asked Jan 10, 2013 by thanvigandhi_1

1 answer

Show that the matrix $A = \begin{bmatrix} 1 & -1 & 5 \\ -1 & 2 & 1 \\ 5 & 1 & 3 \end{bmatrix} $ is a symmetric matrix.

asked Jan 10, 2013 by thanvigandhi_1

1 answer

If $ \begin{bmatrix} x & 2 \\ 18 & x \end{bmatrix} = \begin{bmatrix} 6 & 2 \\ 18 & 6 \end{bmatrix} $ then what is the value of x.

asked Jan 10, 2013 by thanvigandhi_1

1 answer

The radius of a circle is increasing at 0.7 cm/s. What is the rate of increase of its circumference?

asked Jan 10, 2013 by thanvigandhi_1

0 answers

\( \int (ax^2+bx+c)dx.\)

asked Jan 10, 2013 by thanvigandhi_1

0 answers

If \( \overrightarrow P (1, 5, 4) \: and \overrightarrow Q (4, 1, -2),\) find the dr. of \( \overrightarrow {PQ}.\)

asked Jan 10, 2013 by thanvigandhi_1

0 answers

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