Recent questions in Model Papers

Use product $\begin{bmatrix} 1 & -1 & 2 \\ 0 & 2 & -3 \\ 3 & -2 & 4 \end{bmatrix}$ $\begin{bmatrix} -2 & 0 & 1 \\ 9 & 2 & -3 \\ 6 & 1 & -2 \end{bmatrix}$ to solve the system of equations: $x-y+2z=1, \: 2y-3z=1, \: 3x-2y+4z=2$

asked Feb 2, 2013 by thanvigandhi_1

0 answers

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

asked Feb 2, 2013 by thanvigandhi_1

0 answers

A wire of length 36 cm is cut into two pieces. One of the pieces is turned in the form of a square and the other in the form of an equilateral triangle. Find the length of each piece so that the sum of the areas of the two be minimum.

asked Feb 2, 2013 by thanvigandhi_1

1 answer

Use definite integration, find the area of triangle whose vertices are (-1,6),(1,2) and (5,4).

asked Feb 2, 2013 by thanvigandhi_1

1 answer

Find the area of the smaller region boundary by the ellipse $\large\frac{x^2}{9}+\large\frac{y^2}{4}=1$ and the straight line $\large \frac{x}{3}+\frac{y}{2}=1$ .

asked Feb 2, 2013 by thanvigandhi_1

1 answer

Solve the differential equation : $(x+y)dy + (x-y) dx=0$

asked Feb 2, 2013 by thanvigandhi_1

1 answer

Find the equation of the plane passing through the line intersection of the plane $x-2y+z=1$ and $2x+y+z=8$ and parallel to the line with direction ratios 1,2,1. Also, find the perpendicular distance of the point P(3,1,2) from this plane.

asked Feb 2, 2013 by thanvigandhi_1

0 answers

A retired person has 70000 to invest and two types of bonds are available in the market for investment. First type of bond yields an annual income of 8% on the amount invested and the second type of bond yields 10% per annum. As per norms, he has to invest minimum of 10000 in the first type and not more than 30000 in the second type. How should he plan his investment, so as to get maximum return after one year of investment. Make it an L.P.P. and solve the above problem.

asked Feb 2, 2013 by thanvigandhi_1

1 answer

Probability of solving a mathematical problem by A, B, and C respectively are $\frac{1}{3}, \frac{1}{2} \: and \: \frac{1}{4}$ . If they try to solve the problem indepently. 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.

asked Feb 2, 2013 by thanvigandhi_1

0 answers

A company has two plants to manufacture bicycles. Plant I manufactures 70% of the bicycles and plant II manufactures 30%. At plant I 80% of the bicycles are rated as of standard quality and a plant II 90% of the bicycles are rated as of standard quality. A bicycle is choosen at random and is found to be of standard quality. What is the probability that it has come from plant II?

asked Feb 2, 2013 by thanvigandhi_1

1 answer

If A is square matrix of order 3 such that | adj.A |=81, find | A |.

asked Feb 2, 2013 by thanvigandhi_1

2 answers

If a matrix has 12 elements, what are the possible order it can have?

asked Feb 2, 2013 by thanvigandhi_1

1 answer

Differentiate $\cos^{-1}x^4$ w.r.t. $x.$

asked Feb 2, 2013 by thanvigandhi_1

1 answer

Find the product of matrix $A = \begin{bmatrix} 3 \\ 2 \\ -5 \end{bmatrix}$ and its transpose.

asked Feb 2, 2013 by thanvigandhi_1

1 answer

Find a, for which $f(x) = x^2-2ax+6$ is strictly increasing when x > 0.

asked Feb 2, 2013 by thanvigandhi_1

1 answer

Evaluate : $\int_0^{1.5} [x] \: dx$

asked Feb 2, 2013 by thanvigandhi_1

1 answer

Find the differential equation that will represent the family of straight lines $y=mx+c$ , where m,c are parameters.

asked Feb 2, 2013 by thanvigandhi_1

1 answer

For what values of p, $\overrightarrow a = (2\hat i + 6\hat j + 3\hat k)$ p is a unit vector.

asked Feb 2, 2013 by thanvigandhi_1

1 answer

A coin is tossed twice, where E : Tail appear on one coin and F : one coin shows head. Find P(E/F).

asked Feb 2, 2013 by thanvigandhi_1

0 answers

If A and B are independent events such that $P(A) = 0.2, P(A \cup B)=0.5, \: find \: P(B).$

asked Feb 2, 2013 by thanvigandhi_1

1 answer

Solve : $\tan^{-1}2x+tan^{-1}3x = \large\frac{\pi}{4}.$

asked Feb 2, 2013 by thanvigandhi_1

1 answer

If $A = \begin{bmatrix} 4 & 3 \\ 2 & 5 \end{bmatrix}$ , find $x$ and $y$ such that $A^2-xA+yI=0.$

asked Feb 2, 2013 by thanvigandhi_1

1 answer