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Intermediate Math Series Test

This document contains a test with multiple choice and short answer questions about vectors, circles, and linear inequalities. Some of the questions ask about properties of vectors like the dot product and unit vectors. Other questions involve graphing and finding properties of circles like their centers, radii, and points of intersection with other curves. Additional questions address topics like feasible regions defined by systems of linear inequalities, proving geometric properties of lines and circles, and minimizing objective functions subject to constraints. The test covers fundamental concepts in algebra, geometry, and linear programming.

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60 views1 page

Intermediate Math Series Test

This document contains a test with multiple choice and short answer questions about vectors, circles, and linear inequalities. Some of the questions ask about properties of vectors like the dot product and unit vectors. Other questions involve graphing and finding properties of circles like their centers, radii, and points of intersection with other curves. Additional questions address topics like feasible regions defined by systems of linear inequalities, proving geometric properties of lines and circles, and minimizing objective functions subject to constraints. The test covers fundamental concepts in algebra, geometry, and linear programming.

Uploaded by

punjabcollegekwl5800
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© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Intermediate Part-2 Series Test Ch#5,6,7

Q.#1. Choose the correct option and encircle it.


1. A unit vector having magnitude
(a) 4 (b) 3 (c) 2 (d) 1
2. If v=[ 1 ,−3 ] , w=[ 2 ,5 ] then 4v+2w=
(a)[ 2 ,5 ] (b)[ 8 ,−2 ] (c) 25 (d) 33
3. If v=[ 2 ,1 , 3 ] w=[ −1 , 4 , 0 ] then |v−2 w| =
(a)√ 74 (b) √
3
20 (c) 21 (d) √−20
4. Commutative property is
(a) a+b=b+a (b) ab=ba (c) a=a (d) a-b=b-a
5. By the definition of dot product i.j=
(a) k (b) 0 (c) 1 (d) -k
6. By the definition of dot product u.v=0 then u and v are
(a)parallel (b)equal (c)orthogonal (d) none
7. Altitudes of a triangle are
(a) parallel (b)equal (c) null (d) concurrent
8. |u||v|COSθ=¿
(a) u+v (b) u-v (c) u×v (d) u.v
9. (c u).v=
(a) u2 (b) u.v (c) cv (d) c (u.v)
10. (-g,-f) is ……… of circle.
(a) radius (b) centre (c) both a and b (d) none
11. X2+y2=
(a) m (b) 0 (c) 1 (d) r2
12. Corner points are also called
(a) vertex (b) origin (c) point (d) equation
13. While tackling a certain problem from everyday life each linear inequality concerning the problem is
named as _________
(a) problem constraints (b) problem (c) main problem (d) none
14. A function which is maximized or minimized is called _________ function.
(a) objective (b) subjective (c) optimal (d) none
Section-II
Q.#2. Attempt any (10) parts.
1. Graph the following system of inequalities. 2x+1≥0
2. Graph the feasible region and find the corner point of x + y ≤ 5 ,−2 x + y ≥ 0 , x ≥0
3. Define feasible region of the graph.
4. What is corner points.
5. Find the centre and radius of 4 x 2+4y2-8x+12y-25=0
6. Check the position of the point (5,6) with respect to the circle x2+y2=81.
7. Find the length of the tangent from the point P(-5,10) to the circle 5X2+5y2+14x+12y-10=0
8. Prove that normal lines of a circle pass through the centre of the circle.
9. Find a unit vector in the direction of the vector ⃗v =[ −2 , 4 ]
10. If O is the origin and ⃗ OP =⃗ AB , find the point P when A and B are (−3 , 7 ) and (1,0) respectively.
11. Is the following given triple can be the direction angles of a single vector , 30 ° , 45° ,60° .
12. Prove that i⃗ . i⃗ = ⃗j. ⃗j =⃗k . ⃗k =1

Section-II
NOTE:- Attempt any three questions. 03*10=30
1. Show that the circles x 2+ y 2+2x-2y-7=0 and x 2+ y 2-6x+4y+9=0 touch externally.
2. Find the coordinates of the points of intersection of the line x+2y=6 with the circle x 2+ y 2-2x-2y-39=0
3. Minimize z=2x+y : subject to the constraints: x+y≥3; 7x+5y≤35; x≥0; y≥0.
4. Show that the line segment joining the mid points of two sides of a triangle is parallel to third side and half as long.
5. Prove that cos(α + β ¿ =cosα cos β – sinα sin β

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