GOVERNMENT PRE UNIVERSITY COLLEGE FOR GIRLS , HOSAKOTE

( COLLEGE CODE : BB0136 )

FIRST P U C SECOND TEST DECEMBER 2023
SUB: MATHEMATICS ( 35 )
TIME : 1 Hours 30 minutes [ Total questions : 25 ] Max. Marks : 40
Instructions : 1. The question paper has FOUR parts namely A , B , C and D .
Answer all the parts .
2. Part A has 5 multiple choice questions , 5 fill in the blank questions.
PART - A
I Answer ALL multiple choice questions 5X1= 5
1. The slope of the line 3 x – 2 y + 15 = 0
3 3 2
(A) 4
(B) 2
(C) 3
(D) 3
2. The derivative of f(x) = x 4 with respect to x is
(A) x (B) x 4 (C) 4 x 3 (D) 3 x 4
3. The equation of the parabola with focus ( 0 , 6 ) and directrix is y = - 6 is
(A) y 2 = 24 x (B) x2 = 24 y (C) x2 = 6 y (D) y 2 = 6 x
4. The octant in which the point ( 2 , -4, -7) lie .
(A) 6 (B) 7 (C) 8 (D) 5
5. The mean of the data 4 , 7 , 8 , 9 , 10 , 12 , 13 , 17 .
(A) 8 (B) 9 (C) 7 (D) 10
II . Fill in the blanks by appropriate answer from those given
in the bracket. 5X1=5
3 3
[ 5
, 3 √ 14 , 6 , 4, 8 , 2
]
6. The distance of the point ( 3 , - 5 ) from the line 3 x – 4 y - 26 = 0 is ___
x 15−1
7. = lim 10
____
x→1 x −1
8. The radius of the circle x2 + y2 = 36 is ___
9. The distance between the points P( -2 ,3 , 5 ) and Q( 7 , 0 , -1 ) .
10. Coordinate planes divide the space into ------- octants .
 PART - B
III Answer any THREE questions 3 X2=6
11. Find the equation of the line parallel to the line 3 x – 4 y + 2 = 0 passing through
the point ( - 2 , 3 ) .
sin ax +bx
12. Evaluate lim a,b,a+b≠0
x→0 ax +sin bx
2 2
x y
13. Find the coordinates of the foci and eccentricity of the hyperbola − =1
16 9
14. Show that the points P( -2 , 3 , 5 ) , Q ( 1 , 2 , 3 ) and R ( 7 , 0 , -1 ) are collinear .
15. Find the mean of first n natural numbers .
PART-C
IV Answer any THREE questions 3X 3 = 9
16. Derive two – point form of equation of a line .
17. Compute the derivative of log x from first principle method .
18. Find the ends of latus rectum , equation of directrix and length of latus rectum
of the parabola y 2 = 20 x .
19. Find the centre and radius of the circle ( x -2 ) 2 + ( y – 3 ) 2 = 9 .
20. Are the points A ( 3 , 6 , 9 ) , B ( 10 , 20 , 30 ) and C ( 25 , -41 , 5 ) are the vertices of a
right angled triangle ?
PART-D
V Answer any THREE of the following 3 X 5 = 15
21. Derive the distance of a point P( x1 , y1 ) from a line Ax + By + C = 0 .

22. Prove that lim sin x =1 where x is in radian measure .

x→0 x
2 2
23. Define ellipse and derive its equation in the standard form x 2 + y2 =1 , a > b .
a b

24. Find the mean deviation about the median for the following data .
xi 5 7 9 10 12 15
fi 8 6 2 2 2 6

25. Find the mean deviation about the mean for the following data .
xi 10 30 50 70 90
fi 4 24 28 16 8
 GOVERNMENT PRE UNIVERSITY COLLEGE FOR GIRLS , HOSAKOTE
( COLLEGE CODE : BB0136 )
FIRST P U C SECOND TEST DECEMBER 2023
SUB: MATHEMATICS ( 35 )
TIME : 1 Hours 30 minutes [ Total questions : 25 ] Max. Marks : 40
Instructions : 1. The question paper has FOUR parts namely A , B , C and D .
Answer all the parts .
2. Part A has 5 multiple choice questions , 5 fill in the blank questions.
PART - A
I Answer ALL multiple choice questions 5X1= 5
1. The equation of a line with slope 2 and y intercept is -3 is
(A) y = 2 x –3 (B) y = 3 x – 2 (C) x = 2 y – 3 (D) y = 2 x
2. The derivative of f(x) = log x with respect to x is
1 2
(A) x (B) log x (C) (D) -
x x
3. The equation of the parabola with focus ( 3 , 0 ) and directrix is x = - 3 is
(A) y 2 = 12 x (B) x2 = 12 y (C) x2 = 3 y (D) y 2 = 3 x
4. The octant in which the point ( -2 , 4, -7) lie .
(A) 6 (B) 7 (C) 8 (D) 5
5. The mean of the data 4 , 7 , 8 , 9 , 10 , 12 , 13 , 9 .
(A) 8 (B) 9 (C) 7 (D) 10
II . Fill in the blanks by appropriate answer from those given
in the bracket. 5X1=5
2 3
[ , 2 , 12 , 6, 8 , ]
101 5
6. The distance of the point ( 3 , - 5 ) from the line 3 x – 4 y - 26 = 0 is ___
7. lim x (x +1) = ____
x→3

8. The radius of the circle x2 + y2 = 4 is ___

9. The distance between the points P( -1 , 2 , 1 ) and Q( 1 , -2 , 5 ) .
10. Coordinate planes divide the space into ------- octants .
 PART - B
III Answer any THREE questions 3 X2=6
11. Find the equation of the line parallel to the line 3 x – 4 y + 2 = 0 passing through
the point ( - 2 , 3 ) .
3 2
x −4 x + 4 x
12. Evaluate : lim 2
x→2 x −4
x2 y 2
13. Find the coordinates of the foci and eccentricity of an ellipse + =1 .
25 9
14. Show that the points P( -2 , 3 , 5 ) , Q ( 1 , 2 , 3 ) and R ( 7 , 0 , -1 ) are collinear .
15. Find the mean of first n natural numbers .
PART-C
IV Answer any THREE questions 3X 3 = 9
16. Derive slope - intercept form of equation of a line .
17. Compute the derivative of cos x from first principle method .
18. Find the coordinates of the focus , axis, the equation of the directrix and latus rectum
of the parabola y 2 = 12 x .
19. Find the centre and radius of the circle x2 + y2 – 4 x + 4 y – 1= 0 .
20. Are the points A ( 0 , 7 , -10) , B ( 1 , 6 , -6 ) and C ( 4 , 9 , -6 ) are the vertices of an
isosceles triangle ?
PART-D
V Answer any THREE of the following 3 X 5 = 15
21. Derive the distance of a point P( x1 , y1 ) from a line Ax + By + C = 0 .

22. Prove that lim tan x =1 where x is in radian measure .

x→0 x
2 2
23. Define hyperbola and derive its equation in the standard form x 2 − y2 =1 , a > b .
a b

24.Find the mean deviation about the mean for the following data .
Height in cms 95-105 105-115 115-125 125-135 135-145 145-155
No. of boys 9 13 26 30 12 10
25. Find the mean deviation about the median for the following data .
xi 15 21 27 30 35
fi 3 5 6 7 8