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) = _______
The slopes of the lines given by 12x2 + bxy + y2 = 0 differ by 7. Then the value of b is :
(B) ± 2
(C) ± 1
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.
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., ax2 + 2hxy + by2 = 0 represents a pair of lines passing through origin if h2−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 `(x-7)/2=(y-7)/2=(z-6)/3=lambda (say)`
Minimize : Z = 6x + 4y
Subject to the conditions:
3x + 2y ≥ 12,
x + y ≥ 5,
0 ≤ x ≤ 4,
0 ≤ y ≤ 4
If `int_(-pi/2)^(pi/2)sin^4x/(sin^4x+cos^4x)dx`, then the value of I is:
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
Prove that : `int_-a^af(x)dx=2int_0^af(x)dx` , if f (x) is an even function.
= 0, if f (x) is an odd function.
If y = f (u) is a differential function of u and u = g(x) is a differential function of x, then prove that y = f [g(x)] is a differential function of x and `dy/dx=dy/(du) xx (du)/dx`
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?
Solve the differential equation: `x+ydy/dx=sec(x^2+y^2)` Also find the particular solution if x = y = 0.