Recent questions tagged modelpaper

A fruit grower can use two types of fertilzer in his garden, brand P and brand Q. The amounts ( in kg ) of nitrogen , phosphoric, potash and chlorine in a bag of each brand are given in the table. Tests indicate that the garden needs atleast 240 kg of phosphoric acid, at least 270 kg of potash and at most 310 kg of chlorine. If the grower wants to minimise the amount of nitrogen added to the garden, how many bags of each brand should he use? What is the minimum amount of nitrogen added in the garden? What steps do you advice to a farmer to avoid overuse of fertilizers.

asked Jan 21, 2013 by thanvigandhi_1

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In a class having 70% boys, 20% of the boys, and 10% of the girls are players. A student is selected at random from the class and found to be a player. Find the probability that the selected is a girl. Explain the contribution of sports in inculcating human values.

asked Jan 21, 2013 by thanvigandhi_1

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A student is given a test with 8 questions of true-false type. If he gets 6 or more questions correct, he is declared pass, given that he guesses the answer to each question, compute the probability that student will pass in the exam. Evaluation is necessary in student learning, Explain.

asked Jan 21, 2013 by thanvigandhi_1

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Give an example of relation which is reflexive but neither symmetric nor transitive.

asked Jan 21, 2013 by thanvigandhi_1

1 answer

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

asked Jan 17, 2013 by thanvigandhi_1

1 answer

If $ \begin{bmatrix} x & 2 \\ 18 & x \end{bmatrix} = \begin{bmatrix} 6 & 2 \\ 18 & 6 \end{bmatrix} $, then find x?

asked Jan 17, 2013 by thanvigandhi_1

1 answer

For what value of k, the matrix $ \begin{bmatrix} k & 2 \\ 3 & 4 \end{bmatrix} $ has no inverse?

asked Jan 17, 2013 by thanvigandhi_1

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Using properties of determinant, prove that $ \begin{bmatrix} 1 & x & y+z \\ 1 & y & z+x \\ 1 & z & x+y \end{bmatrix} = 0 $

asked Jan 17, 2013 by thanvigandhi_1

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

asked Jan 17, 2013 by thanvigandhi_1

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Evaluate : $ \int\large \frac{1}{\sin^2x\cos^2x}$$dx.$

asked Jan 17, 2013 by thanvigandhi_1

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Find a vector in the direction of vector $ 5\hat i - \hat j + 2\hat k $ which has magnitude 8 units.

asked Jan 17, 2013 by thanvigandhi_1

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If |$ \overrightarrow a $ | =1 , | $ \overrightarrow b $ | = 2 and $ \overrightarrow a . \overrightarrow b$ = 1, find the angle between $ \overrightarrow a \: and \overrightarrow b.$

asked Jan 17, 2013 by thanvigandhi_1

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Find the direction cosine of the line joining the points (-2, 4, -5) and (1,2,3).

asked Jan 17, 2013 by thanvigandhi_1

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Show that the relation R : N $ \rightarrow $ N defined by (a,b)R(c,d) $ \iff $ a+d = b+c for all (a,b), (c,d) $ \in $ N x N is an equivalence relation.

asked Jan 17, 2013 by thanvigandhi_1

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If $ cos^{-1}x+cos^{-1}y+cos^{-1}z=\pi$ prove that $ x^2+y^2+z^2+2xyz=1$

asked Jan 17, 2013 by thanvigandhi_1

1 answer

Solve: $ \tan^{-1}(x+1)+\tan^{-1}(x-1)=\tan^{-1}\large\frac{8}{31}$$;x > 0.$

asked Jan 17, 2013 by thanvigandhi_1

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(i) The cost of 5 kg of sugar, 5kg of wheat and 2kg of rice is Rs. 340. The cost of 4 kg of rice, 2kg of sugar and 5kg of wheat is Rs. 270. Rs. 264 is the cost of 3kg of wheat, 2kg of rice and 4 kg of sugar. Represent the above problem by a system of linear equations and find the cost of each item per kg by matix method. (ii) How increase in the prices of essential commodities affect economic weaker section of society?

asked Jan 17, 2013 by thanvigandhi_1

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If the function $ f(x) = \left\{ \begin{array}{l l} x^2+3x+a, & \quad { x \leq 1}\\ bx+2, & \quad { x > 1} \end{array}. \right. $ is differentiable for all x. Find a and b.

asked Jan 17, 2013 by thanvigandhi_1

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Differentiate : $\large \frac{x}{a} $$\sqrt {x^2-a^2}+\large\frac{a^2}{2}$$\sin^{-1}\large\frac{x}{a}$

asked Jan 17, 2013 by thanvigandhi_1

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If $ y=x^{x^{x....^{\infty}}} $, then prove that $ \large\frac{dy}{dx}=\frac{y^2}{x(1-ylog\: x )}$

asked Jan 17, 2013 by thanvigandhi_1

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Show that $ y = \log (1+x)-\large\frac{2x}{2+x}$ is an increasing function of x for all value of x > -1.

asked Jan 17, 2013 by thanvigandhi_1

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Show that the line $ \large\frac{x}{a}+\frac{y}{b}$$=1$ touches the curve $y=be^{\large\frac{-x}{a}}$ at the point where it crosses the y - axis.

asked Jan 17, 2013 by thanvigandhi_1

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Evaluate : $ \int \large\frac{2x+1}{\sqrt {x^2+4x+3}}$$dx$

asked Jan 17, 2013 by thanvigandhi_1

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

asked Jan 17, 2013 by thanvigandhi_1

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Solve the differential equation $ 2xy+y^2-2x^2\large\frac{dy}{dx}$$=0 : y(1)=2.$

asked Jan 17, 2013 by thanvigandhi_1

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

asked Jan 17, 2013 by thanvigandhi_1

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Let $ \overrightarrow a = 2\hat i + \hat k, \overrightarrow b = \hat i + \hat j + \hat k$ and $ \overrightarrow c = 4\hat i - 3\hat j + 7\hat k$ be three vectors. Find a vector $ \overrightarrow r $ which satisfies $ \overrightarrow r$ x $ \overrightarrow b = \overrightarrow c $ x $ \overrightarrow b$ and $ \overrightarrow r. \overrightarrow a =0.$

asked Jan 17, 2013 by thanvigandhi_1

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Find the shortest distance between the lines $\large\frac{x-3}{1} = \frac{y-5}{-2} = \frac{z-7}{1}$$ \: and \: \large\frac{x+1}{7} = \frac{y+1}{-6} = \frac{z+1}{1}. $

asked Jan 17, 2013 by thanvigandhi_1

0 answers

Assume that each child born is equally likely to be a boy or girl. If a family has two children, what is the conditional probability that both are girls given that (a) the eldest is a girl (b) at least one is a girl (c) pre-natal * determination is a crime. What will you do if you come to know that some of your known is indulging in pre-natal * determination?

asked Jan 17, 2013 by thanvigandhi_1

0 answers

Using matrices, solve the following : $2x+y-3z=13; x+y-z=6 ;2x-y+4z = -12$

asked Jan 16, 2013 by thanvigandhi_1

1 answer

Using elementary transformation, find the inverse of the following matrix $ \begin{bmatrix} 1 & -1 & 2 \\ 0 & 2 & -3 \\ 3 & -2 & 4 \end{bmatrix} $

asked Jan 16, 2013 by thanvigandhi_1

1 answer

Show that the semi-vertical angle of rightcircular of given surface area and maximum volume is $ \sin^{-1} \bigg( \large\frac{1}{3} \bigg).$

asked Jan 16, 2013 by thanvigandhi_1

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Find the area of circle $ x^2+y^2=16$ which is exterior of the parabola $ y^2=6x$.

asked Jan 16, 2013 by thanvigandhi_1

1 answer

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

asked Jan 16, 2013 by thanvigandhi_1

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Evaluate : $ \int_0^3 (x^2+2x)dx $ as limit of a sum.

asked Jan 16, 2013 by thanvigandhi_1

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Find the distance of a point (1, -2, 3) from the plane x-y+z=5, measured parallel to the line $\large\frac{x}{2}=\frac{y}{3}=\frac{z}{-6} $

asked Jan 16, 2013 by thanvigandhi_1

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A housewife wishes to mix up two kind of foods X and Y in such a way that mixture contains at least 10 units of vitamin A, 12 units of vitamin B and 8 units of vitamin C. The vitamin contents of 1 kg of food X and 1 kg of food Y are as given in the table : If 1 kg of food X costs Rs. 6 and 1 kg of food Y costs Rs. 10, find the least cost of the mixture which will produce the desired diet.

asked Jan 16, 2013 by thanvigandhi_1

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Probability of solving a mathematical problem by A, B and C respectively are $\large\frac{1}{3}, \frac{1}{2}$$ \: and \: \frac{1}{4} $. If they try to solve the problem independently, find the probability that : (i) the problem is solved (ii) exactly one of them solve the problem (iii) exactly two of them solve the problem (iv) what do you think that problem solving attitude from books helpful in real life also?

asked Jan 16, 2013 by thanvigandhi_1

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If $ f(x)=x^2-1, g(x)=2x+5$, then find (fog)(x).

asked Jan 16, 2013 by thanvigandhi_1

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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

Evaluate [ 1 2 1 ] $ \begin{bmatrix} 2 \\ 4 \\ 2 \end{bmatrix}$

asked Jan 16, 2013 by thanvigandhi_1

1 answer

Show that elements on the main diagonal of a skew-symmetric matrix are all zero.

asked Jan 16, 2013 by thanvigandhi_1

1 answer

Let $ \begin{bmatrix} 3 & y \\ x & 1 \end{bmatrix} = \begin{bmatrix} 3 & 2 \\ 4 & 1 \end{bmatrix} $. Find the possible values of x and y, if x, y $ \in $ N.

asked Jan 16, 2013 by thanvigandhi_1

1 answer

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

asked Jan 16, 2013 by thanvigandhi_1

0 answers

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

asked Jan 16, 2013 by thanvigandhi_1

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If $ \overrightarrow a. \hat i = \overrightarrow a. (\hat i + \hat j ) = \overrightarrow a.(\hat i + \hat j + \hat k )=1.$then find $ \overrightarrow a$.

asked Jan 16, 2013 by thanvigandhi_1

0 answers

If $ | \overrightarrow a$ x $ \overrightarrow b | = 4, | \overrightarrow a. \overrightarrow b |=2$ then find $| \overrightarrow a |^2 | \overrightarrow b |^2$.

asked Jan 16, 2013 by thanvigandhi_1

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Find the cartesian equation of the line through (5, 2, -4) and which is parallel to the vector $ 3\hat i + 2\hat j - 8\hat k$

asked Jan 16, 2013 by thanvigandhi_1

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'' is a binary operation defined on Q. Find which of the following binary oprations are associative and which are commutative : $(i) ab=a-b\: for \: a,b \in Q (ii) a*b = \large\frac{ab}{4}$$\: for \: a,b \in Q.$

asked Jan 16, 2013 by thanvigandhi_1

0 answers

Show that the relation in the set $ A = { x : x \in W, o \leq x \leq 12} $ given by R = {(a, b) : a-b is a multiple of 4} is an equivalence relation.

asked Jan 16, 2013 by thanvigandhi_1

0 answers

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