Key points in Adam Smith’s definition:
(a) Non-intervention of the Government.
(b) Capital & Wealth accumulation.
(c) Study of an ordinary man.
(d) Economics is a science of wealth.
Options:
(1) a, b and c
(2) a and b
(3) a, b and d
(4) b, c, and d
1 Answers
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Show that the points `A(-1,4,-3), B(-3,2,1),C(3,2,-5)` and `D(-3,8,-5)` are coplanar. Also find the equation of the plane passing through these points
Correct Answer - `x+y+z=0`
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The coordinates of the centre of the circle having the points (9, 3) and (1, -1) as the end points of the diameter is ………………..
Correct option is B) (5, 1)
2 Answers 1 views
Let `l_(1) and l_(2)` be the two skew lines. If P, Q are two distinct points on `l_(1)` and R, S are two distinct points on `l_(2)`, then prove that P
Let equation of the line `l_(1)` be `vecr=veca+lamdavecb` and equation of the line `l_(2)` be `vecr=vecc+muvecd`, where `veca-vecc, vecb and vecd` are non-coplanar. Let the position vectors of points P...
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If each of the points `(x-1,4),(-2,y_1)` lies on the line joining the points `(2,-1)a n d(5,-3)` , then the point `P(x_1,y_1)` lies on the line. `6(x+
Correct Answer - B The equation of the line joining the points (2,-1) and (5,-3) is given by `y+1 = (-1+3)/(2-5)(x-2)` ` "or " 2x+3y-1 = 0 " " (1)` Since...
2 Answers 1 views
Prove that product of parameters of four concyclic points on the hyperbola `xy=c^(2)` is 1. Also, prove that the mean of these four concyclic points b
Given equation of hyperbola is `xy=c^(2)` Let four conyclic point on the hyperbola be `(x_(i),y_(i)),i=1,2,3,4`. Let the equation of the circle through point A, B, C and D be `x^(2)+y^(2)+2gx+2fy+d=0"...
2 Answers 1 views
Two straight lines pass through the fixed points `(+-a, 0)` and have slopes whose products is `pgt0` Show that the locus of the points of intersection
Let the equation of the lines be `y=m_(1)(x-a)` `and y=m_(2)(x+a)` `therefore" "m_(1)m_(2)=p` `therefore" "y^(2)=m_(1)m_(2)(x^(2)-a^(2))=p(x^(2)-a^(2))` Hence, the locus of the points of intersection is `y^(2)=p(x^(2)-a^(2))` `" "px^(2)-y^(2)=pa^(2)` which is a hyperbola.
2 Answers 2 views
Four points are such that the line joining any two points is perpendicular to the line joining other two points. If three point out of these lie on a
Correct Answer - A The point are such that one of the points is the orthocenter of the triangle formed by other three points. When the vertices of a triangle lie...
2 Answers 3 views
Statement 1: If in a triangle, orthocentre, circumcentre and centroid are rational points, then its vertices must also be rational points. Statement :
Correct Answer - D Statement 2 is obvisouly correct. For statement 1. let the circumcentre be at (0,0) and the vertices of the triangle be `(x_1,y_1),(x_1,y_1),(x_2,y_2)` and `(x_3,y_3)`. Then centroid is...
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Points A, B, C lie on the parabola `y^2=4ax` The tangents to the parabola at A, B and C, taken in pair, intersect at points P, Q and R. Determine the
Correct Answer - 2 2 Let the three points on the parabola `y^(2)=4ax` be `A(t_(1)),B(t_(2)) and C(t_(3))`. Area of triangle ABC, `Delta_(1)=(1)/(2)||{:(1,at_(1)^(2),2at_(1)),(1,at_(2)^(2),2at_(2)),(1,at_(3)^(2),2at_(3)):}||` `=a^(2)||{:(1,t_(1),t_(1)^(2)),(1,t_(2),t_(2)^(2)),(1,t_(3),t_(3)^(2)):}||` `=|a^(2)(t_(1)-t_(2))(t_(2)-t_(3))(t_(3)-t_(1))|` Point of intersection of tangents at A,B...
2 Answers 2 views
Match the following: Primary Key, Structured Query Language, Data Definition Language
Column ‘A Column ‘B’ (1) Primary Key (B) Uniquely identify each row (2) Structured Query Language (C) Storing, manipulating, and retrieving data (3) Database designer (D) Define and modify the database (4) Data (A) Managing data within tables
2 Answers 1 views