3D Geometry QA 5
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JEE Mathematics/ Lakshmikanta Satapathy/ 3D Geometry QA Part 5/ Question on line and plane taken from Previous JEE paper solved with complete understanding
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This document provides a summary of 3 key points:
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2) It contains solved GATE papers for Electronics & Communication Engineering Mathematics from 2013-2008.
3) Contact information is provided for Nodia & Company, the publisher located in Jaipur, India.
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Level # 1 51
Level # 2 30
Level # 3 24
Level # 4 12
Total no. of questions 117
LEVEL-1
Equation and properties of the ellipse
Q.1 The equation to the ellipse (referred to its axes as the axes of x and y respectively) whose foci are(± 2,0) and eccentricity1/2,is-
Q.9 The equation of the ellipse (referred to its axes as the axes of x and y respectively) which passes through the point (– 3, 1) and has eccentricity
2
5 , is-
(A) 3x2 + 6y2 = 33 (B) 5x2 + 3y2 = 48
x 2 y2
x 2 y2
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(A) 12 16 = 1 (B) 16
x 2 y2
12 = 1
Q.10 Latus rectum of ellipse
4x2 + 9 y2 – 8x – 36 y + 4 = 0 is-
(C) 16 8 = 1 (D) None of these 5
Q.2 The eccentricity of the ellipse
(A) 8/3 (B) 4/3 (C) 3
(D) 16/3
9x2 + 5y2 – 30 y = 0 is-
(A) 1/3 (B) 2/3
(C) 3/4 (D) None of these
Q.3 If the latus rectum of an ellipse be equal to half of its minor axis, then its eccentricity is-
(A) 3/2 (B) 3 /2
(C) 2/3 (D) 2 /3
Q.4 If distance between the directrices be thrice the distance between the foci, then eccentricity of ellipse is-
(A) 1/2 (B) 2/3
Q.11 The latus rectum of an ellipse is 10 and the minor axis is equal to the distance between the foci. The equation of the ellipse is-
(A) x2 + 2y2 = 100 (B) x2 + 2 y2 =10
(C) x2 – 2y2 = 100 (D) None of these
Q.12 If the distance between the foci of an ellipse be equal to its minor axis, then its eccentricity is-
(A) 1/2 (B) 1/ (C) 1/3 (D) 1/
Q.13 The equation 2x2 + 3y2 = 30 represents-
(A) A circle (B) An ellipse
(C) 1/
(D) 4/5
(C) A hyperbola (D) A parabola
Q.5 The equation ax2 + 2hxy + by2 + 2gx + 2fy + c = 0 represents an ellipse if-
(A) = 0, h2 < ab (B) 0, h2 < ab
(C) 0, h2 > ab (D) 0, h2 = ab
Q.14 The equation of the ellipse whose centre is (2,– 3), one of the foci is (3,– 3) and the corresponding vertex is (4,– 3) is-
Q.6 Equation of the ellipse whose focus is (6,7) directrix is x + y + 2 = 0 and e = 1/ 3 is-
(A) 5x2 + 2xy + 5y2 – 76x – 88y + 506 = 0 (B) 5x2 – 2xy + 5y2 – 76x – 88y + 506 = 0 (C) 5x2 – 2xy + 5y2 + 76x + 88y – 506 = 0
(x 2)2
(A) 3
(x 2)2
(B)
4
(y 3)2
+ = 1
4
(y 3) 2
+ 3 = 1
(D) None of these
Q.7 The eccentricity of an ellipse
x2
a 2 +
y2
b2 = 1 whose
x 2
(C) 3
+ y = 1
4
latus rectum is half of its major axis is-
1
(D) None of these
Q.15 Eccentricity of the ellipse
(A) 2
(B)
4x2 +y2 – 8x + 2y+ 1= 0 is-
(C)
3 (D) None of these
2
(A) 1/ 3 (B) 3/2
(C) 1/2 (D) None of these
Q.8 The equation of the ellipse whose centre is at origin and which passes through the points (– 3,1) and (2,–2) is-
(A) 5x2 + 3y2 = 32 (B)3x2 + 5y2 = 32
(C) 5x2 – 3y2 = 32 (D) 3x2 + 5y2 + 32= 0
Q.16 The equation of ellipse whose distance between the foci is equal to 8 and distance between the directrix is 18, is-
(A) 5x2 – 9y2 = 180 (B) 9x2 + 5y2 = 180
(C) x2 + 9y2 =180 (D) 5x2 + 9y2 = 180
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JEE Physics/ Lakshmikanta Satapathy/ Wave Motion Theory/ Formation of a wave/ Wave function/ Condition for wave function/ Particle velocity and slope/ Sinusoidal wave function/ Illustrative example
Definite Integrals 8/ Integration by Parts
JEE Mathematics/ Lakshmikanta Satapathy/ Definite integrals part 8/ JEE question on definite integral involving integration by parts solved with complete explanation
Vectors QA 2/ Resultant Displacement
JEE Physics/ Lakshmikanta Satapathy/ Question on the magnitude and direction of the resultant of two displacement vectors asked by a student solved in the slides
Quadratic Equation 2
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Probability QA 12
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JEE Mathematics/ Lakshmikanta Satapathy/ Inverse trigonometry QA part 6/ Questions on Inverse trigonometric functions involving tan inverse function solved with the related concepts
Inverse Trigonometry QA 5
This document contains two problems from inverse trigonometry. The first problem involves finding the values of x and y given trigonometric expressions involving tan(x) and tan(y). The second problem proves the identity x = -x + pi for x in the range (-pi, pi). Both problems are solved step-by-step using trigonometric identities and properties. The document also provides contact information for the physics help website.
Transient Current QA 1/ LR Circuit
This document discusses the transient current in an LR circuit with two inductors (L1 and L2) and a resistor connected to a 5V battery. It provides the equations for calculating the transient current in an LR circuit. It then calculates that for L1, the ratio of maximum to minimum current (Imax/Imin) is 8. Similarly, for L2 the ratio is 5. The total maximum current drawn from the battery is 40A and the minimum is 5A, giving a ratio of 8.
Rotational Motion QA 8
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Electromagnetism QA 7/ Ammeter
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- 1. Physics Helpline L K Satapathy 3D Geometry QA 5
- 2. Physics Helpline L K Satapathy 3 D Geometry QA 5 Question: The distance of the point ( 1 , 0 , 2 ) from the point of intersection of the line and the plane x – y + z =16 , is ( ) 2 14 ( ) 8 ( ) 3 21 ( ) 13a b c d Answer : 12 2 . . . (1) 3 4 12 yx z 12 2 3 4 12 yx z A(1,0,2) d B L The situation is shown in the figure The given line is L , whose equation is The given plane is , whose equation is 16 . . . (2)x y z Let the given point be A whose coordinates are ( 1 , 0 , 2 ) 12 2 3 4 12 yx zLet Coordinates of any point on the line is (3 2 , 4 1, 12 2)
- 3. Physics Helpline L K Satapathy 3 D Geometry QA 5 Correct option = (d) Since B lies on the plane x – y + z =16 , we have (3 2) (4 1) (12 2) 16 (3 2 , 4 1,12 2) (5 , 3 ,14) 2 2 2 (5 1) (3 0) (14 2)d The required distance between the points ( 1 , 0 , 2 ) and ( 5 , 3 , 14 ) is For some value of , coordinates of B =(3 2 , 4 1, 12 2) Let the point of intersection of the line and the plane be B Coordinates of B 16 9 144 169 13 11 11 1
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