ECAT Mathematics Chapter 23 Conic Section With Answers

ECAT Mathematics Chapter 23 Conic Section

Sr. # Questions Answers Choice
1 If u = 2ai + i - k and v = i +ai + 4k are perpendicular then a = 4 1/2 3 4/3
2 The angle between the vectors u =2i - i + k and v = -i + i is: 3π/2 2π/3 5π/6 π/3
3 The angle between the vectors u = [-3 , 5] and v = [6 , -2] is: π/2 -3π/2 π None of these
4 If the angle between two vectors u and v is 0 orπ, then the vectors u and v are: Orthogonal Collinear Perpendicular None of these
5 If the angle between two vectors u and v is 0 orπ, then the vectors u and v are: Orthogonal Collinear Perpendicular None of these
6 If u =2i +pi + 5k and v = 3i + i +pk are perpendicular , then p= 1 2 -1 -3
7 The modulus of a vector i-i+ k is: √3 1 √2 ∞
8 If u =[3,-4],then modulus of uis: 5 5i -5 √5
9 If aand bare two vectors then a+b = b + a b - a ab a^ b
10 If a≠ , b≠ 0 and|a=b|=|a-b|,then vectors a and b are: Parallel to each other Perpendicular to each other Inclined at 60<sup>o</sup> neither parallel nor perpendicular
11 If the sum of two unit vectors is a unit vector the the magnitude of their difference is √2 √3 1 None of these
12 The vector k = [0,0,1] is called unit vector along: x -axis y - axis z- axis None of these
13 Vector i = [1,0] [0,1,0] [0,0,1] None of these
14 The vector i = [1,0] is called unit vector along: x-axis y - axis z- axis Botha a and y-axis
15 O (0,0)is called: Position vector Free vector Unite vector Null vector
16 Vector additon is: Commutative Associative Commutative and Associative None of these
17 The positive real number which is the measure of the length of a vector is called the Unit vector Modulus Inverse None of these
18 If|a| =|b| = |a+b|=1, then|a-b| is equal to: 1 √3 √2 7
19 If|a| =|b|=|a + b|=1, then|a+ b| = 5, then|a-b| = 4 6 5 3
20 If a = 2i +2j, b= 3i -j and c=4i +5j, the 3b -a-2c = -i -15j i-15j i-3j None of these
21 If a = [1,4,3] and B= [2,-1,5] athen the mid point M of AB is: [1,1,1.5] [2,2,1.5] [1.5,1.5,4] None of these
22 If c = 2i+j+k and d= -1 + 4j +2k, then [c-d]= √7 √41 √19 √(2&amp;7)
23 If a=5j + 2j,b=2i -3j, then|a+2b|= √21 √97 √39 None of these
24 I f a =5i + 2j, then|a| = √13 √7 1/√13 √29
25 If m and n be two scalars, then (m+n) g = 0 m+n<img width="9" height="20" src="file:///C:/Users/Softsol/AppData/Local/Temp/msohtmlclip1/01/clip_image002.png" v:shapes="_x0000_i1025"><p class="MsoNormal"><!--[endif]--><o:p></o:p></p> m▁a+n▁a ma - m▁a<p class="MsoNormal"><!--[endif]--><o:p></o:p></p>
26 If G is the centroid of the triangle, then GA +GB+GC= 0 1 -1 3
27 The modulus of 12-5i is: 7 13 √7 119
28 The magnitude of vector a=i-3j+5k is: 3 √35 √17 √35
29 The magnitude of vector a 2i-7j is √23 √43 3 √53
30 a ______quantity is one that possesses both magnitude and direction. Scalar Vector Segment None of these
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