Application of Derivatives

Solved Examples of Application of Derivatives

 

PRACTICAL GEOMETRY & VISUALISING SOLID SHAPES

Put a tick mark(√) on the correct answer :

Q1.What the point of intersection of the medians of a triangle  called ?

(i)  circum center             (ii) In center          (iii) centroid                 (iv) ortho center

Q2.What the point of intersection of the altitudes of a triangle  called ?

(i)  circum center             (ii) In center          (iii) centroid                 (iv) ortho center

Q3.What the point of intersection of the side bisectors of a triangle  called ?

(i)  circum center             (ii) In center          (iii) centroid                 (iv) ortho center

Q4.What the point of intersection of the angle bisectors of a triangle  called ?

(i)  circum center             (ii) In center          (iii) centroid                 (iv) ortho center

Q5.Which of the following is a three dimensional figure ?

(i)  Square                  (ii) Trapezium (iii) Cube                (iv) Parallelogram

Q6.Find the number of edges of  a  polyhedron having 20 faces & 12 vertices ?

(i)  10                             (ii) 20                         (iii) 25                      (iv) 30

Q7.Find the number of faces of  a  polyhedron having 6 vertices & 12 edges ?

(i)  8                               (ii) 10                         (iii) 12                     (iv) 14

Q8.Find the number of vertices of  a  polyhedron having 5 faces & 9  edges ?

(i)  18                               (ii) 12                         (iii) 6                    (iv) 4

Q9.What the name of the polyhedron is whose base & top are congruent polygons & whose lateral faces are  parallelograms in shape ?

(i)  Tetrahedron            (ii) Trapezium           (iii) Prism               (iv) Parallelogram

Q10.How many faces a tetrahedron has ?

(i)  14                               (ii) 12                         (iii) 6                     (iv) 4

Practice Questions of Differentiation for JEE Mains

Cube and Cube roots

 Practice Questions
1- 10³ का तात्पर्य हैं -
    (A) 10 का घन    (B) 10 का घनमूल  (C) 10 का वर्ग    (D) 10 का वर्गमूल

2- संख्या 243 का घनमूल करने पर प्राप्त संख्या का इकाई का अंक होगा -
    (A)    3    (B)    7   (C)    5    (D)    9

3-  किसी संख्या का घनमूल ज्ञात करने के लिए अभाज्य गुणनखंड लेते है -
     (A)  त्रिक समूह में   (B)  युग्म रूप में  (C)  a व  b दोनों  (D)  कोई नहीं

4-  220 तक कितनी संख्याएं पूर्ण घन है -
     (A)  5    (B)  6    (C)  15    (D) 100

5-  पूर्ण घन कौन सा है -
    (A)    392    (B)    2744  (C)    106480    (D)    53240

6-  कौन सी संख्या पूर्ण घन है -
    (A)    64    (B)    26  (C)    126    (D)    344

7-  कौन सी संख्या पूर्ण घन नहीं है -
    (A)    8    (B)    27  (C)    64    (D)    26

8. 1259712 का घनमूल क्या होगा यदि 1259712 = 5832 × 216 हो
    (A)    108    (B)    98    (C)    88    (D)    118

9. 571787 के घनमूल के इकाई का अंक होगा -
    (A)    7    (B)    3  (C)    1    (D)    9

10.  57066625=166375 × 343 का घनमूल है -
     (A) 55 × 7      (B)    15 × 16   (C)    125 × 7    (D)    55 × 9

Practice Questions on Quadratic Equations

Sets, Relations and Functions

Practice Questions
1.  Which of the following is set
    (a)    Collection of beautiful girls of Delhi
    (b)    Numbers divisible by 3 between 1 and 20
    (c)    Collection of handsome boys in a class
    (d)    Collection of most precious gems of India

2. Set A = {4, 10, 12, 16, 20}, set builder form is
    (a)    {x : x is even number less than 2}
    (b)    {x : x is natural number multiple of 4 and less than 2}
    (c)    {x : x is odd natural number greater than 3}
    (d)    {x : x is odd natural number less than 3}

3. A set which contains number of elements which can not be counted is
    (a)    Empty set    (b)    finite set    (c)    Singlton set    (d)    Infinite set

4. If A and B are such that n (A) = n (B) then
    (a)    A and B are equal sets
    (b)    A and B are conjugate of each other   
    (c)    A and B are singleton sets
    (d)    A and B are equivalent sets

5. If A = {1, 2, 3, 4} , B = {4, 5, 6, 7} then
    (a)    A = B    (b) A and B are equivalent  (c) A and B are singleton  (d)  A and B are null sets

6.    The set of odd prime numbers is
    (a)    Null set    (b)    singleton set    (c)    Infinite set    (d)    Finite set

Word Problems for Quantitative Aptitude Section of BANK PO/SSC/Other Exams

1.    The difference between a two digit number.and the number obtained by interchanging the two digits of the number is 9. What is the difference between the two digits of the number?
    (1)    3  
    (2)    2
    (3)    1
    (4)    Cannot be determined
    (5)    None of these
Ans. (3)
2.    In a class there are 32 boys and 28 girls. The average age of the boys in the class is 14 years and the average age of the girls in the class is 13 years. What is the average age of the whole class ? (Rounded off to two digits after decimal)
    (1)    13.50  
    (2)    13.53
    (3)    12.51 
    (4)    13.42
    (5)    None of these
Ans. (3)   
3.     In a test consisting of 80 questions carrying one mark each, Arpita answers 65% of the first 40 questions correctly. What percent of the other 40 questions does she need to answer correctly to score 75% on the entire test?
    (1)    60  
    (2)    80
    (3)    75  
    (4)    40
    (5)    None of these
Ans. (5)   
4.    Manisha invests an amount of Rs. 39,300/- for 4 years at the rate of 4 p. c. p. a. What amount of approximate compound interest will she obtain at the end of 4 years ?
    (1)    Rs. 6,675/-
    (2)    Rs. 6,650/-
    (3)    Rs. 6,288/-
    (4)    Rs. 6,356/-
    (5)    Rs, 6,450/-
Ans. (1)   
5.    The average marks of 65 students in a class was calculated as 150. It was later realised that the marks of one of  the students was calculated as 142, whereas his actual marks were 152. What is the actual average marks of the group of 65 students? (Rounded off to two digits after decImal)
    (1)    151.25  
    (2)    150.15
    (3)    151.10  
    (4)    150.19
    (5)    None of these
Ans. (2)