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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
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
Show that the points (1, 1, 1) and (-3, 0, 1) are equidistant from the plane `bar r (3bari+4barj-12bark)+13=0`
Using truth table prove that p ↔ q = (p ∧ q) ∨ (~p ∧ ~q).
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.
In ΔABC, prove that : `tan((a-b)/2)=(a-b)/(a+b)cotC/2`
Show that the lines ` (x+1)/-3=(y-3)/2=(z+2)/1; ` are coplanar. Find the equation of the plane containing them.
Construct the simplified circuit for the following circuit:
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
If `tan^-1((x-1)/(x-2))+cot^-1((x+2)/(x+1))=pi/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 y2 = 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
Solve the differential equation `y-xdy/dx=0`
Discuss the continuity of the function
= 3, for x=π/2
If `f'(x)=k(cosx-sinx), f'(0)=3 " and " f(pi/2)=15`, find f'(x).
Differentiate `cos^-1((3cosx-2sinx)/sqrt13)` w. r. t. 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: