Recent questions in Model Papers

Using matrix method solve the following system of linear equations : $x+2y+z=7; x+3z=11 ; 2x-3y = 1$

asked Jan 9, 2013 by thanvigandhi_1

0 answers

Find the equation of the line through the point P(3, 4) which cuts from the first quadrant a triangle of the minimum area. Also find the area of the triangle.

asked Jan 9, 2013 by thanvigandhi_1

0 answers

Find the area of the region bounbed by $ y^2=4x, \: x=1, \: x=4$ and $ x$ - axis in the first quadrant.

asked Jan 9, 2013 by thanvigandhi_1

0 answers

Evaluate : $ \int_0^2 (x^2+x+1)dx$ as limit of a sum.

asked Jan 9, 2013 by thanvigandhi_1

0 answers

Evaluate : $ \int_0^{\pi} \large\frac{dx}{5+4cos\: x}. $

asked Jan 9, 2013 by thanvigandhi_1

0 answers

Show that the line joining the origin to the point (2, 1, 1) is perpendicular the line determined by the point (3, 5, -1),(4, 3, -1).

asked Jan 8, 2013 by thanvigandhi_1

0 answers

There are two types of fertilisers $ F_1 and F_2. F_1$ contain 10% nitrogen and 6% phosphoric acid and $ F_2$ consists of 5% of nitrogen and 10% phosphoric acid. After testing the soil conditions, a farmer finds that she needs atleast 14kg of phosphoric acid for the crop. If $ F_1 $ costs Rs.6/kg and $ F_2 $ costs Rs. 5/kg, determine how much of each type of fertilizer should be used so that nutrient requirements are met at a minimum cost. What is the minimum cost?

asked Jan 8, 2013 by thanvigandhi_1

0 answers

An electronic assembly consists of two subsystems say A and B. From the previous testing procedures, the following probabilities are assumed to be known : P(A fails)=0.2, P(B fails alone)=0.15. Evaluate the following probabilities : (i) P(A fails / B has failed) (ii) P(A fails alone).

asked Jan 8, 2013 by thanvigandhi_1

0 answers

Let * be a operation on N given by ab=H.C.F, (a, b), a,b $ \in $ N. Write the value of 224.

asked Jan 8, 2013 by thanvigandhi_1

0 answers

Using principal value, calculate the following : $ \sin^{-1} \bigg( \sin \large\frac{3\pi}{5} \bigg). $

asked Jan 8, 2013 by thanvigandhi_1

1 answer

Find the value of x if $ \begin{bmatrix} 3x+y & -y \\ 2y-x & 3 \end{bmatrix} = \begin{bmatrix} 1 & 2 \\ -5 & 3 \end{bmatrix} $

asked Jan 8, 2013 by thanvigandhi_1

1 answer

If A is an invertible matrix of order 3 and |A|=5 then find [adj.A].

asked Jan 8, 2013 by thanvigandhi_1

1 answer

Evaluate : $ \int \large\frac{\sec^2x}{3+tan\: x}$$dx$

asked Jan 8, 2013 by thanvigandhi_1

0 answers

Evaluate : $ \int \large\frac{\sin\: \sqrt x}{\sqrt x}$$dx.$

asked Jan 8, 2013 by thanvigandhi_1

0 answers

Find the value of $ p$ if $ (2\hat i + 6\hat j + 27\hat k) \times (\hat i + 3\hat j + p\hat k) =0.$

asked Jan 8, 2013 by thanvigandhi_1

0 answers

If $ p$ is a unit vector and $ (\overrightarrow x - \overrightarrow p)(\overrightarrow x+\overrightarrow p)=80$ then find |x|.

asked Jan 8, 2013 by thanvigandhi_1

0 answers

Write the value of $\overrightarrow P $ for which $ \overrightarrow a = 3\hat i + 2\hat j + 9\hat k \: and \: \overrightarrow b = \hat i + p\hat j + 3\hat k$ are parallel vectors.

asked Jan 8, 2013 by thanvigandhi_1

0 answers

Show that the relation R in the set A of points, given by R: {P, Q): distance of the point P from the origin is the same as the distance of Q from the origin }, is an equivalence relation. Further, show that the set of all points related to P = (0, 0) is the circle passing through P with origin as the centre.

asked Jan 8, 2013 by thanvigandhi_1

0 answers

Prove that : $ \cot^{-1} \bigg(\large \frac{ \sqrt{1+\sin x}+\sqrt{1-\sin\: x}}{\sqrt{1+\sin\: x}-\sqrt{1-\sin x}} \bigg)=\frac{x}{2}.$

asked Jan 8, 2013 by thanvigandhi_1

0 answers