Recent questions in Model Papers

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

asked Jan 30, 2013 by thanvigandhi_1

0 answers

Evaluate : $\int \large\frac{dx}{sin\: x (3+2\cos x) }$

asked Jan 30, 2013 by thanvigandhi_1

0 answers

The surface area of a spherical bubble of water increasing at the rate of $2 \: cm^2/sec.$ Find the rate at which the volume of the water bubble is increasing at that instant when its radius is 6 cm.

asked Jan 30, 2013 by thanvigandhi_1

0 answers

Evaluate : $\int_1^4 \large\frac{\sqrt x \: dx}{\sqrt{5-x}+\sqrt x}$

asked Jan 30, 2013 by thanvigandhi_1

0 answers

Evaluate : $\int_0^{\Large\frac{\pi}{2}} \log \sin\: x\: dx$

asked Jan 30, 2013 by thanvigandhi_1

0 answers

Find the equation of the line which is perpendicular from the point (3,-1,1) to the line $\large\frac{x}{2}=\frac{y-2}{3}=\frac{z-3}{4}$ Also find the foot of perpendicular and the length of the perpendicular.

asked Jan 30, 2013 by thanvigandhi_1

0 answers

The items produced by a company contain 100% defective items. Show that probability of getting 2 defective items in a sample space is $\large\frac{28 \times 9^6}{10^8}$ .

asked Jan 30, 2013 by thanvigandhi_1

0 answers

A problem in mathematics is given to three students A, B and C whose probabilities of solving are $\frac{1}{3},\frac{2}{7}$ and $\frac{3}{8}$ respectively. If all the three try to solve the problem simultaneously, find the probability that exactly one of them, solve the problem.

asked Jan 30, 2013 by thanvigandhi_1

0 answers

Find the matrix P satisfying the matrix equation $\begin{bmatrix} 1 & 2 \\ 2 & 3 \\ \end{bmatrix} P \begin{bmatrix} 4 & 7 \\ 3 & 5 \\ \end{bmatrix} = \begin{bmatrix} 1 & 0 \\ 0 & 1 \\ \end{bmatrix}.$

asked Jan 30, 2013 by thanvigandhi_1

0 answers

Find point on the curve $y^2=4x$ which is nearest to point (2, -8).

asked Jan 30, 2013 by thanvigandhi_1

0 answers

The surface area of a spherical bubble is increasing at the rate of 2 $cm^2$ /sec. Find the rate at which the volume of the bubble is increasing at the instant its radius is 6 cm.

asked Jan 30, 2013 by fingeazy

0 answers

Show that the semi-vertical angle of the right circular cone of given slant height and maximum volume is $tan^{-1}\sqrt 2$

asked Jan 30, 2013 by thanvigandhi_1

0 answers

Sketch the graph $y= |x+1|.$ Evaluate $\int_{-3}^1 |x+1|dx.$ What does the value represent on graph?

asked Jan 30, 2013 by thanvigandhi_1

0 answers

Evaluate: $\int \large\frac{2x -1}{(x-1))(x+2)(x-3)}$ $dx$

asked Jan 30, 2013 by fingeazy

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

asked Jan 30, 2013 by thanvigandhi_1

0 answers

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

asked Jan 30, 2013 by thanvigandhi_1

0 answers

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

asked Jan 30, 2013 by thanvigandhi_1

0 answers

Kellogg is a new cereal fromed of a mixture of bran and rice that contains at least 88 g of protein and at least 36 milligram of iron. Knowing that bran contains 80 g of protein and 40 milligram of iron per kilogram, and that rice contains 100 g of protein and 30 milligrams of iron per kilogram, find the minimum cost of producing this new cereal if bran costs Rs.5 per kilogram and rice costs Rs. 4 per kilogram.

asked Jan 30, 2013 by thanvigandhi_1

0 answers

Let X denote the number of hours you study during a randomly selected school day. The probability that X can take the values X has the following form, where k is some unknown constant. $p(X=x) = \left\{ \begin{array}{l l}0.1, & \quad if{ x = 0}\\ kx, & \quad if{ x = 1 \: or\: 2} \\ k(5-x), & \quad if{ x = 3 \: or\: 5} \\ 0, & \quad \: otherwise \end{array}. \right.$ (i) Find the value of K (ii) What is the probability that you study atleast two hours? Exactly two hours? Atmost two hours?

asked Jan 30, 2013 by thanvigandhi_1

1 answer

Evaluate: $\int\limits_0^{\large \pi}\large\frac{dx}{5 + 4\cos x}$

asked Jan 29, 2013 by fingeazy

0 answers

Using matrices, solve the following system of linear equations: $x + y + z = 4$ $2x - y + z = -1$ $2x + y - 3z = -9$

asked Jan 29, 2013 by fingeazy

1 answer

If $A= \begin{bmatrix} 3 & 1 \\[0.3em] 7 & 5 \end{bmatrix}$ find x and y such that $A2 + xl = yA$ . Hence find A - 1.

asked Jan 29, 2013 by fingeazy

0 answers