Limits & Derivatives Practice Questions - DPP for JEE

 Page 1


PART-I (Single Correct MCQs)
1. =
(a) e
–1
(b) e
–4
(c) (1 + e
–2
)
(d) e
–2
2. If 
 then  is equal to
(a) 0
(b) 1
(c)
(d) None of these
3. Let a  and ß be the roots of ax
2
 + bx + c = 0,
Page 2


PART-I (Single Correct MCQs)
1. =
(a) e
–1
(b) e
–4
(c) (1 + e
–2
)
(d) e
–2
2. If 
 then  is equal to
(a) 0
(b) 1
(c)
(d) None of these
3. Let a  and ß be the roots of ax
2
 + bx + c = 0,
Then  is equal to :
(a) 0
(b)
(c)
(d) None of these
4.
The value of  
a
i
 > 0, i = 1,  2, ...... n, is
(a)
(b)
(c)
(d)
5. If {x} denotes the fractional part of x, then , where
[a] denotes the integral part of a, is equal to
(a) 0
(b)
(c) e – 2
(d) None of these
6. is equal to –
(a) 1; if l = 1
(b) abc; if l = 1
(c) abc ; if l = 1/3
Page 3


PART-I (Single Correct MCQs)
1. =
(a) e
–1
(b) e
–4
(c) (1 + e
–2
)
(d) e
–2
2. If 
 then  is equal to
(a) 0
(b) 1
(c)
(d) None of these
3. Let a  and ß be the roots of ax
2
 + bx + c = 0,
Then  is equal to :
(a) 0
(b)
(c)
(d) None of these
4.
The value of  
a
i
 > 0, i = 1,  2, ...... n, is
(a)
(b)
(c)
(d)
5. If {x} denotes the fractional part of x, then , where
[a] denotes the integral part of a, is equal to
(a) 0
(b)
(c) e – 2
(d) None of these
6. is equal to –
(a) 1; if l = 1
(b) abc; if l = 1
(c) abc ; if l = 1/3
(d) (abc)
2/3
 ; if l = 2
7. A triangle has two of its vertices at  and the third
vertex  is moving along the straight line  If A be the area
of the triangle, then  is equal to
(a)
(b)
(c)
(d)
8. is equal to
(a) 4
(b) 5
(c) 5e
(d)
9. is equal to
(a)
(b) 1
(c) e
(d) e
2
10. , where [ . ] denotes greatest integer function is
(a) 0
Page 4


PART-I (Single Correct MCQs)
1. =
(a) e
–1
(b) e
–4
(c) (1 + e
–2
)
(d) e
–2
2. If 
 then  is equal to
(a) 0
(b) 1
(c)
(d) None of these
3. Let a  and ß be the roots of ax
2
 + bx + c = 0,
Then  is equal to :
(a) 0
(b)
(c)
(d) None of these
4.
The value of  
a
i
 > 0, i = 1,  2, ...... n, is
(a)
(b)
(c)
(d)
5. If {x} denotes the fractional part of x, then , where
[a] denotes the integral part of a, is equal to
(a) 0
(b)
(c) e – 2
(d) None of these
6. is equal to –
(a) 1; if l = 1
(b) abc; if l = 1
(c) abc ; if l = 1/3
(d) (abc)
2/3
 ; if l = 2
7. A triangle has two of its vertices at  and the third
vertex  is moving along the straight line  If A be the area
of the triangle, then  is equal to
(a)
(b)
(c)
(d)
8. is equal to
(a) 4
(b) 5
(c) 5e
(d)
9. is equal to
(a)
(b) 1
(c) e
(d) e
2
10. , where [ . ] denotes greatest integer function is
(a) 0
(b) 1
(c) does not exist
(d) sin 1
11. If a
1
 = 1 and  and if then the value of
a is
(a)
(b)
(c) 2
(d) None of these
12. is equal to
(a) 0
(b) – 1/6
(c) 1/6
(d) does not exist
13. Let . Then
(a)
(b)
(c) does’t exist
(d) None of these
14. If   then  is equal to
(a) 1
(b) 0
(c)
(d) does not exist
Page 5


PART-I (Single Correct MCQs)
1. =
(a) e
–1
(b) e
–4
(c) (1 + e
–2
)
(d) e
–2
2. If 
 then  is equal to
(a) 0
(b) 1
(c)
(d) None of these
3. Let a  and ß be the roots of ax
2
 + bx + c = 0,
Then  is equal to :
(a) 0
(b)
(c)
(d) None of these
4.
The value of  
a
i
 > 0, i = 1,  2, ...... n, is
(a)
(b)
(c)
(d)
5. If {x} denotes the fractional part of x, then , where
[a] denotes the integral part of a, is equal to
(a) 0
(b)
(c) e – 2
(d) None of these
6. is equal to –
(a) 1; if l = 1
(b) abc; if l = 1
(c) abc ; if l = 1/3
(d) (abc)
2/3
 ; if l = 2
7. A triangle has two of its vertices at  and the third
vertex  is moving along the straight line  If A be the area
of the triangle, then  is equal to
(a)
(b)
(c)
(d)
8. is equal to
(a) 4
(b) 5
(c) 5e
(d)
9. is equal to
(a)
(b) 1
(c) e
(d) e
2
10. , where [ . ] denotes greatest integer function is
(a) 0
(b) 1
(c) does not exist
(d) sin 1
11. If a
1
 = 1 and  and if then the value of
a is
(a)
(b)
(c) 2
(d) None of these
12. is equal to
(a) 0
(b) – 1/6
(c) 1/6
(d) does not exist
13. Let . Then
(a)
(b)
(c) does’t exist
(d) None of these
14. If   then  is equal to
(a) 1
(b) 0
(c)
(d) does not exist
15. The value of is equal to :
(a) e 
–1/3
(b) e 
–2/3
(c) e 
–1
(d) e 
–2
16. Value of is
(a) 2
(b) –2
(c) 1/2
(d) –1/2
17. The value of 
(a)
(b)
(c)
(d)
18. is equal to :
(a) 0
(b) 1
(c)
(d) None of these