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DPP 39-M

This document contains a practice test for the JEE Advanced exam. It includes 10 multiple choice questions testing concepts in vectors, differential equations, integration, geometry, and matrices. The questions cover both conceptual and numerical problems. An answer key is provided at the end listing the correct response for each question.

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shalini singh
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126 views2 pages

DPP 39-M

This document contains a practice test for the JEE Advanced exam. It includes 10 multiple choice questions testing concepts in vectors, differential equations, integration, geometry, and matrices. The questions cover both conceptual and numerical problems. An answer key is provided at the end listing the correct response for each question.

Uploaded by

shalini singh
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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DPP No.

39
TARGET : JEE-2021
Maximum Time : 40 Min.

DPP No. : 39 (JEE–ADVANCED)


SCQ (Single Correct Type) :
 
1. P, Q have position vectors a & b relative to the origin 'O' & X, Y divide
 
PQ internally and externally respectively in the ratio 2 : 1 . Vector XY =

3   4   5   4  
(A) (b  a) (B) (a  b) l (C) (b  a) (D) (b  a)
2 3 6 3

2. The solution of differential equation (ex + 1) y dy = (y + 1) ex dx is


(A) (ex + 1) (y + 1) = cey (B) (ex + 1) (y + 1) = ce–y

(C) (ex + 1) (y + 1) = ce2y (D) none of the above

2
5 2/3 9 x  2 
 
e 
(x 5)2
3. dx  3 e  3 dx is equal to
4 1/3

(A) 1 (B) – 1 (C) 0 (D) – 2

4. The area bounded by the curves x  y  1 and x + y = 1 is

1 1 1
(A) (B) (C) (D) None of these
3 6 2

     
5. If | a | 3,| b | 4, then a value  for which a   b is perpendicular to a   b , is :-

9 3 3 4
(A) (B) (C) (D)
16 4 2 3

        
6. If | a | 3,| b | 5,| c | 7 and a  b c  O .The angle between a and b is

 3 
(A) (B) (C) (D) 0
3 4 6

x  y 1
7. If gradient of a curve at any point P(x, y) is 2y  2x  1 and it passes through origin, then curve is

3x  3y  2 3x  3y  2
(A) 2(x  3 y)   n (B) x  3 y   n
2 2

3x  3y  2
(C) 3y + x = n (3x + 2y + 1) (D) 6y  3 y   n
2

PAGE # 1
Numerical based Questions :

(  /4)1/ 3
x2
8. Evaluate :  1/ 3
7
(1  sin2 x3 )(1  e x )
dx
(  /4)

9. Evaluate the following

 1  sin2x 
e
2x
(i)  1  cos 2x  dx
 

x sin1 x
(ii)  (1  x 2 3/2
)
dx

Matrix Match Type :

10. Match the following. Normals are drawn at point P, Q and R lying on the parabola y2 = 4x which
intersect at (3, 0). Then

Column - I Column - II

(A) Area of PQR (p) 2

(B) Radius of circumcircle of PQR (q) 5/2

(C) Centroid of PQR (r) (5/2, 0)

(D) Circumcentre of PQR (s) (2/3, 0)

Answer Key of DPP No. 38

1. (A) 2. (B) 3. (ACD) 4. (BD) 5. (ACD)


32
6. (AB) 7. 8. (5/2) 9. (0) 10. (215)
9

PAGE # 2

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