CSVTU Question Bank

Will you please give here sample question paper of BE (1st Semester) examination of Chhattisgarh Swami Vivekanand Technical University (CSVTU) ?

As you want I am here giving you sample question paper of BE (1st Semester) examination of Chhattisgarh Swami Vivekanand Technical University (CSVTU).

Sample paper :

1. (a) State De Moire’s theorem.
(b) cos a + cos ? + cos ? = sin a + sin ? + sin ? = 0 Prove that
(i) cos2 a + cos2 ? + cos2 ? = sin2 a + sin2 ? + sin2 ?
(ii)cos2a + cos2 ? + cos 2 ? = sin2a + sin2 ? + sin 2 ? = 0
(c) If tan (? + i?) = eia, Show that:
? – (n +1) ? and log tan(? + a)
2 2 4 2
(d) Sum the series: ? – 1
2
sin2 ? 1 sin 2? sin2? + 1 sin3? – 1 sin 4?sin4 ?+……….. ?
2
3 4
UNIT- II
2. (a) Solve d2y – 3dy – 4y =0
dx2 dx
(b) Solve d2y – 5dy + 6y =sin3x
dx2 dx
(c) Solve by method of variation of parameters d2y + 4y=tan2x
dx2
(d) Solve the simultaneous equations: dx + 2x +5y=tt
dt
dx + 4x +3y=t
dt

UNIT- III
3. (a)Define Bet function .
a b a
(b) Evaluate: ? ? ?(x2 + y2 + z2)dzdydx
a b a
(c) Evaluate: 01?xm(log)ndx = (-1)n n!
(m+1)n+1
Where n is a positive integer and m>-1.
(d) Find the area included between the parabola y= 4x – x2 and the line y = x.

UNIT- IV
4. (a) Define Gradient.
(b) Find the constants a and b so that the surface ax2 – byz= (a+2)x is orthogonal to the surface
ax2y + z3 = 4 at the point (1, -1, 2)
(c) If F = (x2 + y2)i + 2xyj + (y2-xy)k, then find div F and Curl F.
(d) Verify stake’s theorem for :
F = (x2 + y2)I + 2xyj Taken round the rectangle bounded by x= ±a, y = y = b


UNIT- V
5. (a)Find the number of roots of the equation x3 – x24x + 4 = 0
(b) Find the condition that the equation x3 + px24x + 4 = 0 had roots a, ? which satisfy a? + 1 = 0
(c) If a, ?, ? are roots of the equation .x3 + qx + r = 0 find the equation whose roots are
(a – ?)2, (? - ? )2, (? – a)2
(d) Solve the equation x2 -15x – 126 = 0 Cardoon’s method



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