Mth103 tma1.
  1. 50N
  2. 10i+8j
  3. 5
  4. Cosines
  5. Scalar
  6. -3i - 9j
  7. Vec(AF)
  8. Mass
  9. 2
 10. A

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1).Obtain the \\(lim_{x\\rightarrow 2}\\frac{x^2-x-2}{x^2-2x}\\)
(A)\\(0\\)
(B)1
(C)\\(\\frac{3}{2}\\)
(D)Undefined
Ans: \\(\\frac{3}{2}\\)

2).If the value of the function \\(y(x)\\) get arbitrary close to \\(b\\) as \\(x\\) approaches the point \\(a\\) , the statement can be mathematically written as
(A)\\(lim_{x\\rightarrow b}y(x)=a\\)
(B)\\(lim y(x)=b-a\\)
(C)\\(lim_{x\\rightarrow a}y(x)=b\\)
(D)\\(lim y(x)=a-b\\)
Ans: \\(lim_{x\\rightarrow a}y(x)=b\\)

3).Determine the diffenetiation of 120
(A)\\(0\\)
(B)120
(C)\\(x\\)
(D)\\(120x\\)
Ans: \\(0\\)

4).What is the inverse of thee function \\(y=x^2\\)
(A)\\(x=y^{1/2}\\)
(B)\\(x=y^2\\)
(C)\\(x=2y\\)
(D)\\(x=\\frac{1}{2}y^2\\)
Ans: \\(x=y^{1/2}\\)

5).If \\(x^x\\), find \\(\\frac{dy}{dx}\\)
(A)\\(lnx\\)
(B)\\(1+lnx\\)
(C)\\(x(1+lnx)\\)
(D)\\(x^x(1+lnx)\\)
Ans: \\(x^x(1+lnx)\\)

6).Obtain the range of \\(f(x)=\\sqrt{9-x^2}\\) for which \\(f(x)\\) is a reaal function
(A)\\(0\\leq x\\leq 3\\)
(B)\\(x\\geq 3\\)
(C)\\(-3(D)\\(-3\\leq x \\leq 3\\)
Ans: \\(0\\leq x\\leq 3\\)

7).Differentiate with respect to \\(t\\) the function \\(f(t)=3c0s2t\\)
(A)\\(-3sin2t\\)
(B)\\(6cos2t\\)
(C)\\(2sin3t\\)
(D)\\(-6sin2t\\)
Ans: \\(-6sin2t\\)

8).If \\(p\\) is a polynomial function and \\(c\\) is any real number, then
(A)\\(lim_{x\\rightarrow c}p(c)=p(x)\\)
(B)\\(lim_{x\\rightarrow c}p(c)=0\\)
(C)\\(lim_{x\\rightarrow c}p(c)=\\infty\\)
(D)\\(lim_{x\\rightarrow c}p(c)=p(x)\\)
Ans: \\(lim_{x\\rightarrow c}p(c)=p(x)\\)

9).Evaluate the derivative of \\(y(x)=x^2\\) at the point \\(x\\)
(A)\\(2x^2\\)
(B)\\(2x\\)
(C)\\(x^2\\)
(D)2
Ans: \\(2x\\)

10).Determine the equation that defines \\(y\\) as a function of \\(x\\).
(A)\\(y^2-2y=-1\\)
(B)\\(x-y=2\\)
(C)\\(2y^2+x=1\\)
(D)\\(y^2+2x^2=3\\)
Ans: \\(x-y=2\\)


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1).Find the points of intersection of the circle \\((x-3)^2+(y-4)^2=25\\) and the locus \\(x+y-12=0\\).

(A)(3, 9) and (8,4)
(B)(9, 3) and (4, 8)
(C)(3, 8) and (9, 4)
(D)(8, 4) and (9, 3)

Ans: (3, 9) and (8,4)

2).Determine \\(a-b-c\\), if \\(a=5i-2j\\), \\(b=3i+3j\\) and \\(c=4i-j\\)

(A)\\(-2i+4j\\)
(B)\\(2i-4j\\)
(C)\\(-2i-4j\\)
(D)\\(2i+4j\\)

Ans: \\(-2i-4j\\)

3).Evaluate the sum of the vectors \\(\\bar{AK}+\\bar{KL}+\\bar{LP}+\\bar{PQ}\\)

(A)\\(\\bar{KP}\\)
(B)\\(\\bar{AQ}\\)
(C)\\(\\bar{LK}\\)
(D)\\(\\bar{AP}\\)

Ans: \\(\\bar{AQ}\\)

4).Determine the value of x so that \\(A=2i+xj+k\\) and \\(B=4i-2j-2k\\) are perpendicular.

(A)-1
(B)3
(C)4
(D)-2

Ans: 3

5).Given \\(r= -i+2j+2k\\), find the magnitude of \\(r\\)

(A)2
(B)1
(C)5
(D)3

Ans: 3

6).The distance between the centre of a circle and its circumference is called?

(A)Diameter
(B)Radius
(C)Equator
(D)Centre line

Ans: Radius

7).Determine the x and y intercepts of the ellipse equation \\(4y^2+9x^2=36

(A)(3,6)
(B)(6,2)
(C)(2,3)
(D)(3,2)

Ans: (2,3)

8).Obtain the equation of the line with slope and passing through the point (-3, 4).

(A)\\(4y-3x+1=0\\)
(B)\\(3y+4x+7=0\\)
(C)\\(4y-2x+12=0\\)
(D)\\(3y+2x-6=0\\)

Ans: \\(3y+2x-6=0\\)

9).Which of the following defined a unit vector a in the direction of a

(A)\\(\\hat{a}=\\frac{a}{|a|}\\)
(B)\\(\\hat{a}=a+|a|\\)
(C)\\(\\hat{a}=a|a|\\)
(D)\\(\\hat{a}=\\frac{|a|}{a}\\)

Ans: \\(\\hat{a}=\\frac{a}{|a|}\\)

10).The direction of a quantity is indicated by?

(A)Line
(B)Point
(C)Arrow head
(D)Angle

Ans: Arrow head


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1.        Which of the following quantities has magnitude but no direction?
ANS. Speed

2.        A vector having unit magnitude is called?
ANS. Unit vector

3.        Determine the radius of the circle \\(4x^2+4y^2-12x=-5\\)
ANS. 1

4.        Find the point of intersection of the two loci \\(3x-y-5=0\\) and \\(12x+y-25=0\\).
ANS. (2,1,)

5.        Find the unit vector parallel to the resultant \\(a+b\\) if \\(a=2i+4j-5k\\) and \\(b=i+2j+3k\\)
ANS. \\(\\frac{3i+6j-2k}{7}\\)

6.        Find the sum \\(\\bar{BC}-\\bar{DC}+\\bar{DE}+\\bar{FE}\\)
ANS. \\(\\bar{BF}\\)

7.        If \\(p=2i+4j+3k\\) and \\(q=i+5j-2k\\), obtain \\(p\\times q\\)
ANS. \\(-23i+7j+6k\\)

8.        A line is said to be straight when it has a constant?
ANS. Gradient

9.        Which of the following is not a type of vectors?
ANS. Magnitude of vector

10.     Find the anglebetween \\(A=2i+2j-k\\) and \\(B=6i-3j+k\\)
ANS. \\(\\theta=79^0\\.