1. No category

www.plusacademy.in
|
www.facebook.com/plusacademy
Guess paper proof
III
18 – 03 – 2015
Part – III
MATHEMATICS, Paper – I (B)
(English version)
Time: 3 hours
Max. Marks: 75
Section – A
Very short answer types questions.
i)
Answer all questions
ii)
Each questions carries two marks
1. Find the area of the triangle formed by the straight line 3x – 4y + 12 = 0 with co –
ordinate axes.
Method , Q.NO: 17
2. Find the equation of the straight line passing through (-2, 4) and making non – zero
intercepts whose sum is zero. plus academy – guess problem -direct
3. If (3, 2, -1), (4, 1, 1) and (6, 2, 5) are three vertices and (4, 2, 2) is the centroid of a
tetrahedron, find the fourth vertex. plus academy – guess problem -direct
4. Find the angle between the planes x + 2y + 2z - 5 = 0 and 3x + 3y + 2z – 8 = 0 plus
academy – guess problem -direct
5. Compute
. plus academy – guess problem -direct
6. Show that
(
7. If y =
| |
, find
8. If y =
)
plus academy – guess problem -direct
. plus academy – guess problem -direct
then prove that
plus academy – guess problem -
direct
9. If y = x2+x; x=10,
plus academy – guess problem –
direct
10. Find the value of ‘c’ in Rolle’s theorem for the function f(x) = log (x2 + 2) – log 3 on
[-1, 1] plus academy – guess problem –direct
Junior Intermediate
|
1B IPE 2015 Question paper
|
[email protected]
www.plusacademy.in
|
www.facebook.com/plusacademy
Section – B
Short answer types questions.
(i) Attempt any five questions
(ii) Each questions carries four marks
11. Find the equation of locus of p, if A= (2, 3), B= (2, -3) & PA + PB=8. plus academy –
guess problem -direct
12. When the axes are rotated through an angle , find the transformed equation of
x2+2√ xy-y2=2a2 plus academy – guess problem -direct
13. Find the points on the 3x – 4y – 1 = 0 which are at a distance of 5 units from the point (3,
2). plus academy – guess problem -direct
14. Check the continuity of f given by
plus academy – guess problem -direct
{
15. Find the derivative of x sinx from the first principle. plus academy – guess problem direct
16. The volume of a cube is increasing at the rate of 8 cm3/sec. how fast is the surface
area increasing when the length of an edge is 12cm?
plus academy – guess
problem -direct
17. A particle is moving in a straight line so that after t seconds its distance is “s” (in
cms) from a fixed point on the line is given by s = f(t) = 8t + t3. Find (i) the velocity at
time t = 2 sec (ii) the initial velocity (iii) acceleration at t = 2 sec. plus academy –
guess problem -direct
Section – C
Long answer types questions.
a. Attempt any five questions
b. Each questions carries seven marks
18. Find the orthocentre of the triangle whose vertices are (-2, -1) (6, -1) (2, 5) plus
academy – guess problem -direct
Junior Intermediate
|
1B IPE 2015 Question paper
|
[email protected]
www.plusacademy.in
|
www.facebook.com/plusacademy
19. If the equation S = ax2 + 2hxy + by2 + 2gx + 2fy + c = 0 represents a pair of parallel
straight lines, then (i) h2 = ab (ii) af2 = bg2 and (iii) the distance between the parallel
lines = √
plus academy – guess problem -direct
20. Show that line joining the origin to the points of intersection of the curve x2 – xy +
y2 + 3x + 3y – 2 = 0 and the straight line x – y - √ =0 are mutually perpendicular.
plus academy – guess problem -direct
21. Find the angle between two diagonals of a cube. plus academy – guess problem direct
22. If
√
√
, then find
.
23. Find two positive integers x and y such that x + y = 60 andxy3 is maximum. plus
academy – guess problem -direct
24. Show that the curves 6x2 – 5x + 2y = 0, 4x2 + 8y2 = 3 touch each other at (
Direct problems total scoring
Method problems total scoring
)
: 18 + 28 + 35
:2
Plus academy guess paper
Total Scoring (with choice):
Total Scoring (without choice):
81 + 2 = 83/97
75/75 Marks
www.plusacademy.in
[email protected]
Junior Intermediate
|
1B IPE 2015 Question paper
|
[email protected]