#### My Profile

1. Inform you about time table of exam.

2. Inform you about new question papers.

3. New video tutorials information.

If`[bar a barb barc]!=0 ` then `bar a . barp +bar b . bar q+bar c. bar r ` is equal to

(a) 0

(b) 1

(c) 2

(d) 3

The inverse of the matrix `[[2,0,0],[0,1,0],[0,0,-1]]`is --------

(a) `[[1/2,0,0],[0,1,0],[0,0,-1]]`

(b) `[[-1/2,0,0],[0,-1,0],[0,0,1]]`

(c) `[[-1,0,0],[0,-1/2,0],[0,0,1/2]]`

(d) `1/2[[-1/2,0,0],[0,-1,0],[0,0,-1]]`

Direction cosines of the line passing through the points A (- 4, 2, 3) and B (1, 3, -2) are.........

(a) `+-1/sqrt51,+-5/sqrt51,+-1/sqrt51`

(b) `+-5/sqrt51,+-5/sqrt51,+-5/sqrt51`

(c) `+-sqrt5,+-1,+-5`

(d) `+-sqrt51,+-sqrt51+-sqrt51`

Write truth values of the following statements :`sqrt5` is an irrational number but 3 +`sqrt 5` is a complex number.

Write truth values of the following statements : ∃ n ∈ N such that n + 5 > 10.

Find the vector equation of the plane which is at a distance of 5 units from the origin and which is normal to the vector `2hati + hatj + 2hatk.`

The Cartesian equations of line are 3x+1=6y-2=1-z find its equation in vector form.

Find the direction ratios of a vector perpendicular to the two lines whose direction ratios are -2, 1, -1, and -3, -4, 1.

Using truth table, prove the following logical equivalence :

(p ∧ q)→r = p → (q→r)

Find the joint equation of the pair of lines through the origin each of which is making an angle of 30° with the line 3x + 2y - 11 = 0

Solve the following equations by the method of reduction :

2x-y + z=1, x + 2y +3z = 8, 3x + y-4z=1.

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 `

Solve the following LPP by using graphical method.

Maximize : Z = 6x + 4y

Subject to x ≤ 2, x + y ≤ 3, -2x + y ≤ 1, x ≥ 0, y ≥ 0.

Also find maximum value of Z.

In ΔABC with usual notations, prove that 2a `{sin^2(C/2)+csin^2 (A/2)}` = (a + c - b)

If p : It is a day time, q : It is warm, write the compound statements in verbal form

denoted by -

(a) p ∧ ~ q (b) ~ p → q (c) q ↔ p

If the lines `(x-1)/2=(y+1)/3=(z-1)/4 ` and `(x-3)/1=(y-k)/2=z/1` intersect each other then find value of k

Parametric form of the equation of the plane is `bar r=(2hati+hatk)+lambdahati+mu(hat i+2hatj+hatk)` λ and μ are parameters. Find normal to the plane and hence equation of the plane in normal form. Write its Cartesian form.

If the angle between the lines represented by ax^{2} + 2hxy + by^{2} = 0 is equal to the angle between the lines 2x^{2} - 5xy + 3y^{2} =0,

then show that 100(h^{2} - ab) = (a + b)^{2}

If X is a random variable with probability mass function

P(x) = kx , x=1,2,3

= 0 , otherwise

then , k=..............

(a) 1/5

(b) 1/4

(c) 1/6

(d) 2/3

The probability that a certain kind of component will survive a check test is 0.5. Find the probability that exactly two of the next four components tested will survive.

Find the area of the region bounded by the curve y = sinx, the lines x=-π/2 , x=π/2 and X-axis

Examine the continuity of the following function at given point:

`f(x)=(logx-log8)/(x-8) , `

` =8, `

Solve : 3e^{x} tanydx + (1 +e^{x}) sec^{2} ydy = 0

Also, find the particular solution when x = 0 and y = π.

Show that the function defined by f(x) =|cosx| is continuous function.

Given X ~ B(n, p). If n = 20, E(X) = 10, find p_{,} Var. (X) and S.D. (X).

Verify Lagrange’s mean value theorem for the function f(x)=x+1/x, x ∈ [1, 3]