Recent questions in Model Papers

There are 20% chances for a worker of an industry to suffer from an occupational disease, 50 workers were selected at random and examined for the ocupational disease. Find the probabilty that (i) None is suffering from the disease. (ii) Only one is suffering from the disease.

asked Jan 24, 2013 by thanvigandhi_1

0 answers

The probability of student E passing an examination is 0.6 and of student F is 0.2. Assuming that the two events 'E passes' and 'F passes' are independent. Find the probability of : (i) both the students passing the examination (ii) Only E passing the examination.

asked Jan 24, 2013 by thanvigandhi_1

0 answers

Find the equation of the plane through point (2, 0, -1) and perpendicular to the line joining the two points (1, 2, 3) and (3, -1, 6)

asked Jan 24, 2013 by thanvigandhi_1

1 answer

Find the projection of $\overrightarrow a = 2\hat i - \hat j + \hat k \: on \: \overrightarrow b = \hat i - 2\hat j + \hat k$

asked Jan 24, 2013 by thanvigandhi_1

0 answers

If $|\overrightarrow a | = 3, |\overrightarrow b | = \large\frac{\sqrt 2}{3}$ $\: and \; \overrightarrow a \times \overrightarrow b$ is a unit vector, then find angle between $\overrightarrow a \: and \overrightarrow b$ .

asked Jan 24, 2013 by thanvigandhi_1

0 answers

Evaluate : $\int \large\frac{1+\cos x}{1-\cos x}$ $dx$

asked Jan 24, 2013 by thanvigandhi_1

0 answers

If the function $f : Q \rightarrow Q$ defined by $f(x) = 3x+5$ for all $x \in Q$ is invertible, find $f^{-1}$ .

asked Jan 24, 2013 by thanvigandhi_1

0 answers

Using principal values, evaluate $tan^{-1} \bigg( tan\frac{7\pi}{6} \bigg).$

asked Jan 24, 2013 by thanvigandhi_1

1 answer

Find a matrix X such that 2A + 2B + X = 0, where $A = \begin{bmatrix} -1 & 3 \\ 2 & 1 \end{bmatrix}$ and $B = \begin{bmatrix} 1 & 5 \\ 3 & 2 \end{bmatrix}$

asked Jan 24, 2013 by thanvigandhi_1

1 answer

If $A = \begin{bmatrix} 4 & 1 \\ 5 & 8 \end{bmatrix},$ show that A + A' is symmetric matrix.

asked Jan 24, 2013 by thanvigandhi_1

1 answer

If |A| = 5, where A is 3 x 3 matrix, find | adj A |.

asked Jan 24, 2013 by thanvigandhi_1

0 answers

Evaluate : $\int \sec^2(5-7x)dx .$

asked Jan 24, 2013 by thanvigandhi_1

0 answers

Find the differential equation of the family of ellipses having foci on y- axis and centre at the origin.

asked Jan 24, 2013 by thanvigandhi_1

1 answer

Solve the differential equation $\bigg( y-x\large\frac{dy}{dx} \bigg)$ $= a \bigg( y^2+\large\frac{dy}{dx} \bigg).$

asked Jan 24, 2013 by thanvigandhi_1

0 answers

Let $\overrightarrow a, \overrightarrow b, \overrightarrow c$ be three vectors of magnitude 3, 4, 2 respectively. If ech one is perpendicular to sum of other two vectors, prove that $| \overrightarrow a + \overrightarrow b + \overrightarrow c | = \sqrt {29} .$

asked Jan 24, 2013 by thanvigandhi_1

0 answers

Find the vector equation of the plane through the intersection of the plane : $\overrightarrow r . (\hat i + \hat j + \hat k ) = 6 \: and \: \overrightarrow r . (2\hat i + 3\hat j + 4\hat k ) = -5$ and the point (1, 1, 1).

asked Jan 24, 2013 by thanvigandhi_1

0 answers

Two cards are drawn one by one without replacement from well shuffled pack of 52 cards. Find the probability distribution of the number of aces.

asked Jan 24, 2013 by thanvigandhi_1

2 answers

Find the probability of number of doublets in three throws of a pair of dice.

asked Jan 24, 2013 by thanvigandhi_1

0 answers

If R is a relation in N x N, show that the relation R defined by : (a, b)R(c, d)if and only if ad = bc is an equivalence relation.

asked Jan 24, 2013 by thanvigandhi_1

0 answers

Three forces acting on a particle are in equilibrium. If the angle between the first force and the second force be 120 0 and that between the second force and the third force be 135 0 , find the ratio of their magnitudes.

asked Jan 24, 2013 by fingeazy

0 answers

Find the Cartesian as well as the vector equation of the plants passing through the intersection of the plants $\overset \rightharpoonup {r}. (2 \hat{i} + 6 \hat{j}) + 12 = 0$ and $\overset \rightharpoonup {r}. (3 \hat{i} - \hat{j} + 4 \hat{k}) = 0$ . Which are at unit distance from the origin?

asked Jan 24, 2013 by fingeazy

0 answers

Solve for x : $\tan^{-1} \bigg(\large \frac{x-1}{x+1} \bigg) + \tan^{-1} \bigg( \frac{2x-1}{2x+1} \bigg) = \tan^{-1} \bigg( \frac{23}{36} \bigg).$

asked Jan 24, 2013 by thanvigandhi_1

1 answer

Prove that $\tan^{-1} \large\frac{1}{7}$ $+ 2\tan^{-1} \large\frac{1}{3} = \frac{\pi}{4}$

asked Jan 24, 2013 by thanvigandhi_1

1 answer

(i) Assume that on a diwali day Neeraj Gautam went to market with Vanya and Paurush to buy fireworks. Each of them selected fireworks of their choice. Neeraj gave Rs.60 for 3 rockets, 4 fountains and 2 bombs, while Vanya gave Rs. 76 for 6 fountains, 2 rockets and 3 bombs and Paurush gave Rs.80 for the cost of 2 fountains, 4 rockets and 6 bombs. If the cost of same item of firework is same. Find the cost of each item per unit by matrix method.

asked Jan 24, 2013 by thanvigandhi_1

0 answers

If the function $f(x) = \left\{ \begin{array}{l l} 3ax+b, & \quad if { x > 3}\\ 11, & \quad if { x=1} \\ 5ax-2b, & \quad if {x < 1} \end{array} \right.$ is continuous at x = 1 , find the values a and b.

asked Jan 24, 2013 by thanvigandhi_1

0 answers

Solve the following linear programming problem graphically: Maximize z = 60 + 15y Subject to constraints $x + y \le 50$ $3x + y \le 90$ $x , y \ge 0$

asked Jan 24, 2013 by fingeazy

0 answers

Two tailors A and B earn Rs.150 and Rs.200 per day respectively. A can stitch 6 shirts and 4 plants per day while B can stitch 10 shirts and 4 pants per day. Form a linear programming problem to minimize the labour cost to produce at lest 60 shirts and 32 pants.

asked Jan 24, 2013 by fingeazy

0 answers

A company has two plants to manufacture motor cycled. 70% motor cycles are manufactured at the first plant, while 30% are manufactured at the second plant. At the first plant, 80% motor cycles are rated of the standard quality while at the second plant, 90% are rated of standard quality. A motor cycle, randomly picked up, is found to be of standard quality. Find the probability that it has come out from the second plant.

asked Jan 24, 2013 by fingeazy

1 answer

The probability that student entering a university will graduate is 0.4. Find the probability that out of 3 students of the university: • None will graduate, • Only one will graduate, • All will graduate.

asked Jan 24, 2013 by fingeazy

1 answer

In a book of 200 pages, 200 misprints are randomly distributed. Using Poisson's distribution calculate the probability that a randomly observed page of the book will be found to have atlest 3 errors. [Use: e -1 =0.3679]

asked Jan 24, 2013 by fingeazy

0 answers

A, B and C are engaged in a printing business. A being the working partner, receives 10% of the net profit as salary. The remaining profit is divided among themselves in the ratio 4:5:9. If A gets in total Rs. 3,00,000, find the total profit in the business and the shares of B and C in it.

asked Jan 24, 2013 by fingeazy

1 answer

A and B are partners in a business sharing profits and losses equality. They admit a new partner C and it is agreed that now the profit and losses will be shared amongst A, B and C in the ratio 9 : 8 : 7 respectively. If C paid Rs. 2.10 lakh as premium for the good will, find the shares of A and B in the premium.

asked Jan 24, 2013 by fingeazy

0 answers

Find the present worth of an ordinary annuity of Rs. 1,200 per annum for 10 years at 12% per annum, compounded annually. [Use (1.12) -10 =0.3221]

asked Jan 24, 2013 by fingeazy

1 answer

A calculator manufacturing company finds that the daily cost of producing calculators is given by C(x) = 200x + 7500. • If each calculator is sold for Rs. 350, find the minimum number of calculators that must be produced daily and sold to ensure no loss. • If the selling price is increased by Rs. 150, what would be the break-even point?

asked Jan 24, 2013 by fingeazy

1 answer

A bill was drawn on April 4, 2004 at 8 months after date and was discounted on July 14, 2004 at 5% per annum. If the Banker's gain is Rs.200, find the face value of the bill.

asked Jan 24, 2013 by fingeazy

0 answers

If $(cos\: x)^{\Large y }= (cos\: y)^{\Large x}$ find $\large\frac{dy}{dx}$

asked Jan 23, 2013 by thanvigandhi_1

0 answers

If $\sqrt{1-x^2}+\sqrt{1-y^2}=a(x-y),$ prove that $\large\frac{dy}{dx}=\frac{\sqrt{1-y^2}}{\sqrt{1-x^2}}$ .

asked Jan 23, 2013 by thanvigandhi_1

0 answers

Find the intervals in which the functions $f(x) = sin^4x+cos^4x, 0 \leq x \leq \large\frac{\pi}{2}$ is strictly increasing or decreasing.

asked Jan 23, 2013 by thanvigandhi_1

0 answers

Evaluate : $\large\frac{1-\cos x}{\cos x (1+\cos x)}$ $dx$

asked Jan 23, 2013 by thanvigandhi_1

0 answers

Evaluate : $\int e^{2x}\sec 2x(1+\tan2x)dx$

asked Jan 23, 2013 by thanvigandhi_1

0 answers

A man is known to speak the truth 3 out of 4 times. He throws a die and reports that it is a number 6. Find the probability that it is actually a number 6.

asked Jan 23, 2013 by thanvigandhi_1

0 answers

A toy company manufactures two types of dolls, A and B. Each doll of type B takes twice as long as to produce as one of type A. If the company produces only type A. It can make a maximum of 2000 dolls per day. The supply of plastic is sufficient to produce 1500 dolls per day. Type B requires a fancy dress which cannot be available for more than 600 per day. If the company makes profit of Rs.3 and Rs.5 per doll respectively on doll A and doll B, how many of each should be produced per day in order to maximise the profit?

asked Jan 23, 2013 by thanvigandhi_1

1 answer

Compute the area bounded by the lines $x+2y=2, y-x+ 1 \: and \: 2x+y=7.$

asked Jan 23, 2013 by thanvigandhi_1

0 answers

Using integration, find the area of the triangle ABC. Coordinates of whose vertices are A(2, 0), B(4, 5) and C(6 ; 3).

asked Jan 23, 2013 by thanvigandhi_1

0 answers

Evaluate : $\int_0^{\pi} \large\frac{x\: \sin x}{1+\cos^2x}$ $dx$

asked Jan 23, 2013 by thanvigandhi_1

0 answers

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

asked Jan 23, 2013 by thanvigandhi_1

0 answers

A variable plane, which remains at a constant distance '3p' from the origin cuts the coordinate axes at A, B and C. Show that locus of the centroid of the triangle is $\large \frac{1}{x^2} + \frac{1}{y^2} + \frac{1}{z^2} = \frac{1}{p^2} .$

asked Jan 23, 2013 by thanvigandhi_1

0 answers

(i) A stone is dropped into a quite lake and waves move in circles at the speed of 5 cm/s. At the instant when the radius of circular wave is 8cm, how fast is the enclosed area increasing?

asked Jan 23, 2013 by thanvigandhi_1

0 answers

If $A = \begin{bmatrix} 1 & -1 & 1 \\ 2 & 1 & -3 \\ 1 & 1 & 1 \end{bmatrix}$ , find $A^{-1}$ and hence solve the equation : $x+2y+z=4, -x+y+z=0 ,x-3y+z = 2$

asked Jan 23, 2013 by thanvigandhi_1

1 answer

Find the principal value of $\cos^{-1} \bigg( -\frac{1}{2} \bigg).$

asked Jan 23, 2013 by thanvigandhi_1

1 answer

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