Class 12 Mathematics (Maths) Previous Year Paper - 3 | Mathematics (Maths) Class 12 - JEE PDF Download

 Page 1


 
 
Std. 12  Time : 3 hrs. 
   Half Yearly Examination in   MATHEMATICS   (Set - 2)       M. Marks :100 
 
  GENERAL INSTRUCTIONS: 
  i) Attempt all the questions. 
  ii) Section - A consists of 4 questions of 1 mark each. 
  iii) Section-B consists of 8 questions of 2 marks each. 
  iv) Section- C consists of 11 questions of 4 marks each. 
  v) Section- D consists of 6 questions of 6 mark each. 
SECTION - A 
1.  If A =  is a 2 matrix such that  =   write A. 
2. Evaluate:  +  +  . 
3. If = 5, where A is a 3x3 matrix find . 
4.  If A =  find A
4
. 
SECTION - B 
5. If y= , show that . 
6.  Evaluate . 
7. The bookshop of a particular school has 10 dozen Chemistry books, 8 dozen English,  
 10 dozen economics books. Their selling prices are Rs. 80, Rs. 60 and Rs. 40 each  
 respectively. Find the total amount the book shop will receive from selling all the books  
 using matrix multiplication method. 
8. If   +    = 1, Prove that  at ( , is -1. 
9.  If A = and A
2
 – 4A + I = 0, then find A
-1
 using the given equation. 
10. Prove that the diagonal elements of a skew symmetric matrix are all zeroes. 
11. Evaluate:  dx. 
12.  Write   in the simplest form where -  x . 
 
Page 2


 
 
Std. 12  Time : 3 hrs. 
   Half Yearly Examination in   MATHEMATICS   (Set - 2)       M. Marks :100 
 
  GENERAL INSTRUCTIONS: 
  i) Attempt all the questions. 
  ii) Section - A consists of 4 questions of 1 mark each. 
  iii) Section-B consists of 8 questions of 2 marks each. 
  iv) Section- C consists of 11 questions of 4 marks each. 
  v) Section- D consists of 6 questions of 6 mark each. 
SECTION - A 
1.  If A =  is a 2 matrix such that  =   write A. 
2. Evaluate:  +  +  . 
3. If = 5, where A is a 3x3 matrix find . 
4.  If A =  find A
4
. 
SECTION - B 
5. If y= , show that . 
6.  Evaluate . 
7. The bookshop of a particular school has 10 dozen Chemistry books, 8 dozen English,  
 10 dozen economics books. Their selling prices are Rs. 80, Rs. 60 and Rs. 40 each  
 respectively. Find the total amount the book shop will receive from selling all the books  
 using matrix multiplication method. 
8. If   +    = 1, Prove that  at ( , is -1. 
9.  If A = and A
2
 – 4A + I = 0, then find A
-1
 using the given equation. 
10. Prove that the diagonal elements of a skew symmetric matrix are all zeroes. 
11. Evaluate:  dx. 
12.  Write   in the simplest form where -  x . 
 
 
 
 
SECTION - C 
13. If  y =  +  , find dy/dx. 
14. Solve for x:    +    =  . 
15. If A =  Show that  A
/
A
-1
 =  . 
16. Evaluate: dx. 
17. Prove that   -  =  . 
    (OR) 
    Prove that: ) + ) = . 
Std. 12       - 2 -   MATHEMATICS (Set - 2) 
18. Evaluate:          (OR)         
19. Find the points on the curve y = x
3
 at which the slope of the tangent is equal to the  
 y-coordinate of the point. 
      (OR) 
 Prove that the curves x = y
2
 and xy = k cut at right angles if 8k
2
 = 1. 
20. Evaluate:    . 
21. A water tank has the shape of an inverted right circular cone with its axis vertical and  
 vertex lowermost.  Its semi vertical angle is . Water is poured into it at a constant  
 rate of 5 cubic metres per hour. Find the rate at which the level of the water is rising at the  
 instant when the depth of water in the tank is 4m. What is the importance of conservation  
 of water? 
22. Find the inverse of matrix A using row elementary operations, where A = . 
23. Evaluate:   . 
 
 
Page 3


 
 
Std. 12  Time : 3 hrs. 
   Half Yearly Examination in   MATHEMATICS   (Set - 2)       M. Marks :100 
 
  GENERAL INSTRUCTIONS: 
  i) Attempt all the questions. 
  ii) Section - A consists of 4 questions of 1 mark each. 
  iii) Section-B consists of 8 questions of 2 marks each. 
  iv) Section- C consists of 11 questions of 4 marks each. 
  v) Section- D consists of 6 questions of 6 mark each. 
SECTION - A 
1.  If A =  is a 2 matrix such that  =   write A. 
2. Evaluate:  +  +  . 
3. If = 5, where A is a 3x3 matrix find . 
4.  If A =  find A
4
. 
SECTION - B 
5. If y= , show that . 
6.  Evaluate . 
7. The bookshop of a particular school has 10 dozen Chemistry books, 8 dozen English,  
 10 dozen economics books. Their selling prices are Rs. 80, Rs. 60 and Rs. 40 each  
 respectively. Find the total amount the book shop will receive from selling all the books  
 using matrix multiplication method. 
8. If   +    = 1, Prove that  at ( , is -1. 
9.  If A = and A
2
 – 4A + I = 0, then find A
-1
 using the given equation. 
10. Prove that the diagonal elements of a skew symmetric matrix are all zeroes. 
11. Evaluate:  dx. 
12.  Write   in the simplest form where -  x . 
 
 
 
 
SECTION - C 
13. If  y =  +  , find dy/dx. 
14. Solve for x:    +    =  . 
15. If A =  Show that  A
/
A
-1
 =  . 
16. Evaluate: dx. 
17. Prove that   -  =  . 
    (OR) 
    Prove that: ) + ) = . 
Std. 12       - 2 -   MATHEMATICS (Set - 2) 
18. Evaluate:          (OR)         
19. Find the points on the curve y = x
3
 at which the slope of the tangent is equal to the  
 y-coordinate of the point. 
      (OR) 
 Prove that the curves x = y
2
 and xy = k cut at right angles if 8k
2
 = 1. 
20. Evaluate:    . 
21. A water tank has the shape of an inverted right circular cone with its axis vertical and  
 vertex lowermost.  Its semi vertical angle is . Water is poured into it at a constant  
 rate of 5 cubic metres per hour. Find the rate at which the level of the water is rising at the  
 instant when the depth of water in the tank is 4m. What is the importance of conservation  
 of water? 
22. Find the inverse of matrix A using row elementary operations, where A = . 
23. Evaluate:   . 
 
 
 
 
 
 
SECTION - D 
24.  Using properties of determinants prove that: 
                   = . 
                                                           (OR) 
  If p ,  q  and  = 0 then using the properties of 
determinants,  prove that atleast one of the following  statements is true: (i) p, q, r are in 
G.P   (ii)  is the root  
 of equation px
2
+2qx+r=0. 
25. Show that the height of the cylinder of greatest volume that can be inscribed in a right 
circular 
 cone of height h and semi vertical angle  is one third that of the cone and greatest volume 
of  
 the cylinder is . 
26. Find the sub intervals for which y =  –  is increasing or decreasing function of  
in . 
27. If   = c
2
  for some c > 0 . Prove that   is independent of a and 
b. 
      (OR) 
 If x = asin2t (1+cos2t) and y = bcos2t (1-cos2t), show that is . 
28. Evaluate: dx using limit as a sum. 
29. Evaluate:   (OR)        Evaluate:  .