BIHAR UNIVERSITY (Muzaffarpur) Exam Important Questions
Graduation TDC Part 1 (2019-2022) Math/Physics/Chemistry/Zoology
Exam Important Questions
Graduation TDC Part 1 (2019-2022) Bihar University
PG 1st semester (2019-21) – Physics/Math – Important questions
Are you searching for BSc 1st year and PG 1st semester important questions in Math/Physics/Chemistry/Zoology ?
Well, you are in the right place. In this post, we are go to share some of the most important questions of Math/Physics/Chemistry (SCIENCE) for TDC Part 1 and PG 1st semester students. (B.R.A BIHAR UNIVERSITY)
TDC PART 1 MATHEMATICS (Hons.)
TDC Part 1 (2019-22)
MATHEMATICS (Hons.) Paper- II
(Answer any six questions, selecting at least one from each group.)
1. (a) In the curve r(1-cos 0) = 2a, prove p2 = a.r.
(b) State and prove Euler’s theorem on homogeneous functions of two Variables of degree n.
2 (a) State and prove Leibnitz’s theorem to find the nth derivative of a product of two functions of X.
(b) If Y y + Y-ym = 2x prove that
(x2 – 1) yn+2 + (2n + 1) xy,+1+ (n?M²) y, 0.
3. (a) Find the radius of curvature of a curve in Cartesian form. (b) Find the chord of curvature through the pole of the curve = a” cos Q.
1 (a) Find the area of the loop of the curve ay2 = x? (a – x)2 (b) Find the whole length of the loop of the curve 3 ay2 = x (x – 2)2
2(a) Find the volume of the right circulars cones of height h and base of Radius a.
(b) Find the area of the loop of the curve 32 = x (x – 1)2
1. (a) Find the equation of ellipse in standard form. (b) Find the equation of director circle to the conic =1+e cos 0
2. (a) Find the equation of the circle passing through the origin and cutting The circles x2 + y2 -4x + 6y + 10 = 0 and x2 + y2 + 12y + 6 = 0 Orthogonally.
(b) Find the equation of Radical acis of two circles.
3. (a) Find the equation of the tangent to the parabola y2 = 4ax at a point on it.
(b) Show that the radical axis of two circles is perpendicular to the line Joining their centres.
4. Find the condition for the circle X2 + y2 +28,*+2fy + = 0 And x2 + y2 +282x + 2/2y + 2 = 0 may cut each other orthogonally.
1. (a) Find the equation of the place in terms of the intercepts which it makes
On the axes.
(b) The length of two opposite edges of a tetrahedron are a, b; their shortest distance equal to d and the angle between them is 0. Prove That the volume is abd sin e.
2. (a) If I, m, n are the direction cosines of a line, then show that R+ m2 + 12 = 1.
(b) A line makes angles a, B, y with four diagonals of a cube. Prove that
Cosa + cos2B + cos?y + cos28 = 4/3.
3. (a) Find the volume of the tetrahedron whose co-ordinates of vertices are Given.
(b) Prove that every first degree equation in x, y, z represents a plane