Recent questions in Model Papers

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

(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