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^{if `A=[[2,0,0],[0,2,0],[0,0,2]]`} then A^{6}=^{ ......................}

(a) 6A

(b) 12A

(c) 16A

(d) 32A

The principal solution of cos^{-1}(1/2) is :

(a) π/3

(b) π/6

(c) 2π/3

(d) 3π/2

If an equation hxy + gx + fy + c = 0 represents a pair of lines, then.........................

(a) fg = ch (b) gh = cf

(c) Jh = cg (d) hf= - eg

Write the converse and contrapositive of the statement — “If two triangles are congruent, then their areas are equal.”

Find the angle between the planes `bar r.(2bar i+barj-bark)=3 `

The Cartesian equations of line are 3x -1 = 6y + 2 = 1 - z. Find the vector equation of line.

If A, B, C, D are (1, 1, 1), (2, I, 3), (3, 2, 2), (3, 3, 4) respectively, then find the volume of parallelopiped with AB, AC and AD as the concurrent edges.

Discuss the statement pattern, using truth table : ~(~p ∧ ~q) v q

Find the direction cosines of the line perpendicular to the lines whose direction ratios are -2, 1,-1 and -3, - 4, 1

The sum of three numbers is 6. When second number is subtracted from thrice the sum of first and third number, we get number 10. Four times the sum of third number is subtracted from five times the sum of first and second number, the result is 3. Using above information, find these three numbers by matrix method.

If θ is the acute angle between the lines represented by equation ax^{2} + 2hxy + by^{2} = 0 then prove that `tantheta=|(2sqrt(h^2-ab))/(a+b)|, a+b!=0`

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

Construct the switching circuit for the following statement : [p v (~ p ∧ q)] v [(- q ∧ r) v ~ p]

A random variable X has the following probability distribution:

then E(X)=....................

(a) 0.8

(b) 0.9

(c) 0.7

(d) 1.1

If `int_0^alpha3x2dx=8` then the value of α is :

(a) 0

(b) -2

(c) 2

(d) ±2

The differential equation of y=c/x+c^{2} is :

(a)`x^4(dy/dx)^2-xdy/dx=y`

(b)`(d^2y)/dx^2+xdy/dx+y=0`

(c)`x^3(dy/dx)^2+xdy/dx=y`

(d)`(d^2y)/dx^2+dy/dx-y=0`

If `y=sqrt(sinx+sqrt(sinx+sqrt(sinx+..... oo))),` then show that `dy/dx=cosx/(2y-1)`

A fair coin is tossed five times. Find the probability that it shows exactly three times head.

If `f(x)=[tan(pi/4+x)]^(1/x), `

= k ,for x=0

is continuous at x=0 , find k.

Let the p. m. f. (probability mass function) of random variable x be

`p(x)=(4/x)(5/9)^x(4/9)^(4-x), x=0, 1, 2, 3, 4`

=0 otherwise

find E(x) and var (x)

Examine the maxima and minima of the function f(x) = 2x^{3} - 21x^{2} + 36x - 20 . Also, find the maximum and minimum values of f(x).

Given the p. d. f. (probability density function) of a continuous random variable x as :

`f(x)=x^2/3, -1`

= 0 , otherwise

Determine the c. d. f. (cumulative distribution function) of x and hence find P(x < 1), P(x ≤ -2), P(x > 0), P(1 < x < 2)