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1.	Three concurrent force of the same magnitude are in equilibrium. What is the angle between the forces? Also name the triangle formed by the forces as sides.A. `60^(@)` equilateral triangleB. `120^(@)` equilibrium triangleC. `120^(@),30^(@),30^(@)` an isosceles triangleD. `120^(@)` an obtuse angled triangle.
Answer» Correct Answer - B

2.	For the equation `x=ACsin (Bt)+D e^((BCt))`, where x and t represent position and time respectively, which of the following is/are CORRECT :-A. Dimension of AC is `LT^(-1)`B. Dimension of B is `T^(-1)`C. Dimension of AC and D are sameD. Dimension of C is `T^(-1)`
Answer» Correct Answer - B::C

3.	Personnel at an air post control tower track a UFO. At 11:02 am it was located at position A and at 11:12 am is was located at position B. Displacement vector of UFO is A. `400hati+2200hatj+400hatk`B. `1200hati+1000hatj+800hatk`C. `2000hati+2200hatj+2000hatk`D. `400hati+1000hatj+400hatk`
Answer» Correct Answer - A

4.	Consider three vectors `A=hati +hatj-2hatk`, `B=hati +hatj+2hatk and 2hati -3hatj +4hatk` A vector X of the from `alphaA +betaB (alpha and beta"are numbers")` is perpendicular to C .The ratio of `alpha and beta` isA. `1:1`B. `2:1`C. `-1:1`D. `3:1`
Answer» Correct Answer - A

5.	Which of the following is perpendicular to `hati-hatj-hatk`?A. `hati+hatj+hatk`B. `-hati+hatj+hatk`C. `hati+hatj-hatk`D. none of these.
Answer» Correct Answer - D

6.	Which of the following statement about the sum of the two vectors `vecA " and " vecB`, is/are correct ?A. `\|vecA+vecB\|leA+B`B. `\|vecA+vecB\|ge A+B`C. `\|vecA+vecB\|ge\|vecA-vecB\|`D. `\|vecA+vecB\|ge\|A-B\|`
Answer» Correct Answer - A::D

7.	A man moves towards 3m north then 4 m towards east and finally 5 m towards `37^(@)` south of west. His displacement from origin is :-A. `5sqrt(2)m`B. 0mC. 1mD. 12m
Answer» Correct Answer - B

8.	Find the resultant of the following two vector `vecA ` and `vecB`. `vec(A):40` units due east and , `vec(B):25` units `37^(@)` north of westA. 25 units `37^(@)` north of westB. 25 units `37^(@)` north of eastC. 40 units `53^(@)` north of westD. 40 units `53^(@)` north of east
Answer» Correct Answer - B

9.	L,M and T are units of length, Mass and Time respectively in a system of units In which of the following system unit of enery is `10^(9)` ergA. (III)(i)(S)B. (IV)(iii)(R)C. (II)(iv)(Q)D. (I)(iii)(P)
Answer» Correct Answer - B::D

10.	A man is standing at point `(x=5m, y=0)` . Then be walks along staight line to `(x=0 , y=5m)` . A second man walks from the same initial position along the x-axis to the arigin and then along the y-axis to `(x=0, y=5m)` . Mark the correct statement(s) :A. Displacement vector of first man and second man are equalB. Distance travelled by second man is greater.C. Magnitude of displacement of second man is same that of first man but direction is differentD. Magnitude of displacement is `sqrt(50)m` for `2^(nd)` man.
Answer» Correct Answer - A::B::D

11.	L,M and T are units of length, Mass and Time respectively in a system of units In which of the following combination unit of force is `10^(6)` dyne.A. (IV)(i)(P)B. (II)(iii)(S)C. (III)(iv)(P)D. (I)(ii)(Q)
Answer» Correct Answer - B::C

12.	A physical quantity is a phyical property of a phenomenon , body, or substance , that can be quantified by measurement. The magnitude of the components of a vector are to be considered dimensionally distinct. For example , rather than an undifferentiated length unit L, we may represent length in the x direction as `L_(x)`, and so forth. This requirement status ultimately from the requirement that each component of a physically meaningful equation (scaler or vector) must be dimensionally consistent . As as example , suppose we wish to calculate the drift S of a swimmer crossing a river flowing with velocity `V_(x)` and of widht D and he is swimming in direction perpendicular to the river flow with velocity `V_(y)` relation to river, assuming no use of directed lengths, the quantities of interest are then `V_(x),V_(y)` both dimensioned as `(L)/(T)` , S the drift and D width of river both having dimension L. with these four quantities, we may conclude tha the equation for the drift S may be written : `S prop V_(x)^(a)V_(y)^(b)D^(c)` Or dimensionally `L=((L)/(T))^(a+b)xx(L)^(c)` from which we may deduce that a+b+c=1 and a+b=0, which leaves one of these exponents undetermined. If, however, we use directed length dimensions, then `V_(x)` will be dimensioned as `(L_(x))/(T), V_(y) as (L_(y))/(T), S as L_(x)" and " D as L_(y)`. The dimensional equation becomes : `L_(x)=((L_(x))/(T))^(a) ((L_(y))/(T))^(b)(L_(y))^(c)` and we may solve completely as a=1,b=-1 and c=1. The increase in deductive power gained by the use of directed length dimensions is apparent. From the concept of directed dimension what is the formula for a range (R) of a cannon ball when it is fired with vertical velocity component `V_(y)` and a horizontal velocity component `V_(x)`, assuming it is fired on a flat surface. [Range also depends upon acceleration due to gravity , g and k is numerical constant]A. `R=(k(V_(x)V_(y)))/(g)`B. `R=(k(V_(x))^(2))/(g)`C. `R=(k(V_(x))^(3))/(V_(y)g)`D. `R=(k(V_(y))^(3))/(V_(x)g)`
Answer» Correct Answer - A

13.	A body lost in a jungle finds a note. In the note was written the following things. Displacements 1. 300 m `53^(@)` South of East . 2. 400 m `37^(@)` North of East 3. 500 m North 4. `500sqrt(2) m ` North- West 5. 500 m South He starts walking at constant speed 2m/s following these displacements in the given order. How far and in which direction is he from the starting ponit after 5 min. and 50 s ?A. 500 m due EastB. 500 m due WestC. 700 m due South- WestD. 700 m due North-East
Answer» Correct Answer - A

14.	The four pairs of force vectors are given, which pairs of force vectors cannot be added to give a resultant vector of magnitude 10N ?A. 2N,13NB. 5N,16NC. 7N,8ND. 100N,105N
Answer» Correct Answer - A::D

15.	If in a system the force of attraction between two point masses of `1kg` each situated `1km` apart is taken as a unit force and is called notwen (newton written in reverse order) If `G = 6.67 xx 10^(-11) N-m^(2)kg^(-2)` in `SI` units, the relation of newton and nowton isA. `1 " notwen " = 6.67xx10^(-11)` newtonB. `1 " newton " = 6.67xx10^(-17)` notwenC. `1 " notwen " = 6.67xx10^(-17)` newtonD. `1 " newton " = 6.67xx10^(-12)` notwen
Answer» Correct Answer - C