#### My Profile

1. Inform you about time table of exam.

2. Inform you about new question papers.

3. New video tutorials information.

If p ˄ q = F, p → q = F, then the truth value of p and q is :

(A) T, T

(B) T, F

(C) F, T

(D) F, F

If `A^-1=1/3[[1,4,-2],[-2,-5,4],[1,-2,1]]` and | A | = 3, then (adj. A) = _______

(A)`1/9[[1,4,-2],[-2,-5,4],[1,-2,1]]`

(B)`[[1,-2,1],[4,-5,-2],[-2,4,1]]`

(C)`[[1,4,-2],[-2,-5,4],[1,-2,1]]`

(D)`[[-1,-4,2],[2,5,-4],[1,-2,1]]`

The slopes of the lines given by 12x^{2} + bxy + y^{2} = 0 differ by 7. Then the value of b is :

(A) 2

(B) ± 2

(C) ± 1

(D) 1

Find ‘k’, if the equation kxy + 10x + 6y + 4 = 0 represents a pair of straight lines.

If A, B, C, D are four non-collinear points in the plane such that `bar(AD)+bar( BD)+bar( CD)=bar O` then prove that point D is the centroid of the ΔABC.

Find the direction cosines of the line

`(x=2)/2=(2y-5)/3; z=-1`

Show that the points (1, 1, 1) and (-3, 0, 1) are equidistant from the plane `bar r (3bari+4barj-12bark)+13=0`

how that every homogeneous equation of degree two in x and y, i.e., ax^{2} + 2hxy + by^{2} = 0 represents a pair of lines passing through origin if h^{2}−ab≥0.

Prove that the volume of a parallelopiped with coterminal edges as ` bara ,bar b , barc `

Hence find the volume of the parallelopiped with coterminal edges `bar i+barj, barj+bark `

Find the inverse of the matrix, `A=[[1,3,3],[1,4,3],[1,3,4]]`

by using column transformations.

Show that the lines ` (x+1)/-3=(y-3)/2=(z+2)/1; ` are coplanar. Find the equation of the plane containing them.

Express `-bari-3barj+4bark ` as a linear combination of vectors `2bari+barj-4bark,2bari-barj+3bark `

Find the length of the perpendicular from the point (3, 2, 1) to the line ``

Show that the angle between any two diagonals of a cube is `cos^-1(1/3)`

Minimize : Z = 6x + 4y

Subject to the conditions:

3x + 2y ≥ 12,

x + y ≥ 5,

0 ≤ x ≤ 4,

0 ≤ y ≤ 4

The solution of the differential equation dy/dx = sec x – y tan x is:

(A) y sec x = tan x + c

(B) y sec x + tan x = c

(C) sec x = y tan x + c

(D) sec x + y tan x = c

Find the area bounded by the curve y^{2} = 4ax, x-axis and the lines x = 0 and x = a.

Find k, such that the function P(x)=k(4/x) ;x=0,1,2,3,4 k>0

=0 ,otherwise

Discuss the continuity of the function

`f(x)=(1-sinx)/(pi/2-x)^2, `

** = 3, for x=π/2**

If `f'(x)=k(cosx-sinx), f'(0)=3 " and " f(pi/2)=15`, find f'(x).

Each of the total five questions in a multiple choice examination has four choices, only one of which is correct. A student is attempting to guess the answer. The random variable x is the number of questions answered correctly. What is the probability that the student will give atleast one correct answer?

If f (x) = x 2 + a, for x ≥ 0 ` =2sqrt(x^2+1)+b, ` is continuous at x = 0, find a and b.

Find the approximate value of cos (89°, 30'). [Given is: 1° = 0.0175°C]

Solve the differential equation: `x+ydy/dx=sec(x^2+y^2)` Also find the particular solution if x = y = 0.

Find the expected value, variance and standard deviation of random variable X whose probability mass function (p.m.f.) is given below:

X=x | 1 | 2 | 3 |

P(X=x) | 1/5 | 2/5 | 2/5 |