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Functions Home Assignment - 5

This document is a mathematics home assignment from Vidyamandir Classes focused on functions, intended for IIT JEE preparation. It includes a series of questions related to properties of functions, solutions to equations, and domain definitions. The assignment is structured with multiple-choice questions, each presenting different mathematical scenarios and concepts.

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73 views2 pages

Functions Home Assignment - 5

This document is a mathematics home assignment from Vidyamandir Classes focused on functions, intended for IIT JEE preparation. It includes a series of questions related to properties of functions, solutions to equations, and domain definitions. The assignment is structured with multiple-choice questions, each presenting different mathematical scenarios and concepts.

Uploaded by

forstudyonly161.3
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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Vidyamandir Classes

IIT JEE - 2021


Home Assignment - 5 Mathematics
M.M. : 40
Functions Date : 10.04.2020

5
Sgnx 9
1.   
f x  sin x 7 e x  is:

(A) an even function (B) an odd function


(C) neither even nor odd (D) None of these

2. Which of the following functions is an odd function:


(A) f (x) = constant (B)  
f x  sin x  cos x

  
(C) f x  sin  log  x  x 2  1  
  (D) f x  1  x  2x 3
 
  

    5
3. If f  x   sin 2 x  sin 2  x    cos x cos  x   and g    1 then (gof ) (x) is equal to:
 
3  
3 4
   
(A) 1 (B) 0 (C) sin x (D) None of these

1
4.  
If f x 
1x
              
, g x  f  f x  and h x  f  f f x  ,  x  R  0, 1 then the value of

     
f x  g x  h x is:

(A) 1 (B) 1 (C) 0 (D) None of these

Paragraph for Questions 5 – 7

Let a function f (x) be such that f  x   x2  3  2 .

5.  
Equation f x   has 2 solutions if :

(A) 2 (B) 2 (C) 1  2 (D) 2

6.  
Equation f x   has 4 solutions if :

(A)   2, 0 (B) 2 (C) 1  2 (D) 1  2

7.  
Equations f x   has 8 solutions if :

(A)  1 (B) 2 (C) 1  2 (D) 0   1

8. For the equation log x  log 3 x x  0 , which of the following do not hold good?
3 x

(A) No real solution (B) One prime solution


(C) One integral solution (D) None of these

VMC | Mathematics 1 Home Assignment – 5 | Functions


Vidyamandir Classes

sin x cos x
9. If x  0, 2 , then y1  , y2  are identical functions for x  :
sin x cos x

     3   3 
I.  0,  II.  ,  III.  ,  IV.  , 2 
 2 2   2   2 
      
(A) I, II (B) I, III (C) II, III (D) I, IV

  1  
10. The domain of definition of f  x   log 2   log1/2 1    1 is :
 

  x 1/4 


(A) (0, 1) (B) (0, 1] (C) [1,  ) (D) (1,  )

VMC | Mathematics 2 Home Assignment – 5 | Functions

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