If we measure the side of a cube to be 4 cm with an error of 0.1cm,then the error in our calculation of the volume is
2 cu.cm
0.45 cu.cm
4.8 cu.cm
0.4 cu c.m
Required
3. lf g(x)=x²+sin x then dg =
2x+sin x
2x+ cos x
(2x+cos x) dx
(x²+ cos x)dx
Required
4. The maximum value of the function x ² e⁻²ˣ, x>0 is
1/e²
1/2e
4/e⁴
1/e
Required
5. limₓ→₀ [sin mx/x] =
m
0
π/2
1
Required
6. The angle between the curve y=sin x and the positive X axis is
π/3
0
π/4
π/2
Required
7. If f ( x )=x/ x+1 then its differentials is given by
-1/(x+1)
1/(x+1)² dx
-1/(x+1)² dx
1/(x+1) dx
Required
8. The radius of the circle passing through the point (6,2) two of whose diameters are x+y=6 and x+2y=4 is
10
4
6
2√5
Required
9. log₁₀ᵉ=0.4343 then the approximate value of log₁₀1003=
3.3
3.00013029
3.0013029
3.000014.
Required
10. The slope of the line normal to the curve f(x )=2cos 4x at x=π/12 is
-4
-4√3
4√3
√3/12
Required
11. If a and b are unit vectors such that [a b axb] =1/4 then the angle between vector a and vector b is
π/6
π/2
π/3
π/4
Required
12. The approximate value of √9.2 (by linear approximation method)
3.03333
3.3
3.0003
3.2
Required
13. If x+y=k is normal to the parabola y²=12x then the value of k is
-1
9
3
1
Required
14. The diagonals of a parallellogram are equal then it is a
square
rhombus
rectangle
parallellogram
Required
15. The radius of the circle 3x²+by²+4bx-6by+b²=0 is
3
1
√10
√11
Required
16. Distance between the parallel planes x +2y- 2z+1=0 and 2x+4y-4z+5=0 is
2
1
-1/2
1/2
Required
17. The vertex of the parabola y²=16x is....
(4,0)
(0,0)
16
(0,4)
Required
18. Distance from the origin to the plane 3x-6y+2z +7=0 is
0
2
1
3
Required
19. If the coordinates at one end of a diameter of the circle x²+y² -8x -4y+c=0 are(11,2)the coordinates of the other end are
(-3,2)
(5,3)
(11,-8)
(3,5)
Required
20. If a.b=b.c=c.a=0 then the value of [ a b c] is
-1
1
1/3|a | |b | |c |
|a| | b||c |
Required
21. The circle x²+y²=4x+8y+5 intersects the line 3x-4y=m at two distincts points if
35
-85
-35
15
Required
22. The function sin⁴ x+cos⁴ x is increasing in the interval
[π/2,5π/8[
[0,π/4]
[π/4,π/2]
[5π/8,3π/4]
Required
23. Three vectors a,b&c are coplanar then [a b c]=
2
0
π
1
Required
24. If a and b are parallel vectors then[a b c] is equal to
0
2
-1
1
Required
25. The position of a particle moving along a horizontal line of any time t is given by s (t)=3t²-2t-8.The time at which the particle is at rest is t=
1
1/3
0
3
Required
26. The local extrema for the functions f(x)=x⁴ +32x is
(-2,48)
(-2,-48)
(2,-48)
(2,48)
Required
27. The product of two positive numbers is 20 and their sum is minimum then they are
2√5,2√5
4,5
2, 19
5√2 ,√2
Required
28. The condition for the line y=mx+c to be a tangent to the parabola y²=4ax then c=
4a
am
a/m
(a/m,2a/m)
Required
29. The eccentricity of the ellipse (x-3)²+(y-4 )²= y²/9 is
1/3
1/√2
1/√3
√3/2
Required
30. The percentage error of fifth root of 31is approximately how many times the perpentage error in 31?
1/31
5
31
1/5
Answers
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