AP Inter 1st Year Mathematics 1B Guess Paper 2025

1

Transform the equation x + y + 1 = 0 into normal form.

2

Find the circum centre of the triangle whose vertices are (-2, 3), (2, -1) and (4, 0).

3

Find two positive integers x and y such that x + y = 60 and xy ³ is maximum.

4

Show that the points (5, 4, 2), (6, 2, -1) and (8, -2, -7) are collinear.

5

Define Rolle’s theorem.

6

Find the derivatives of tan 2x from the first principle.

7

It the distance from P to the points (2, 3) and (2, -3) are in the ratio 2:3, then find the equation of the locus of P.

8

Find the lengths of sub tangent, sub normal at a point t on the curve x = a (cost + tsint), y = a (sint - tcost).

9

Find the equation of the plane whose intercepts on x, y, z - axes are 1, 2, 4 respectively.

10

Find the value of k, if the straight lines 6x - 10y + 3 = 0 and kx - 5y + 8 = 0 are parallel.

11

Find the approximate value of sin (62°).

12

Find the derivative of cosax from the first principle.

13

Find the equation of locus of a point P, if the distance of P from A(3, 0) is twice, the distance of P from B(-3, 0).

14

Find the equation of the straight line passing through (-2, 4) and making non-zero intercepts whose sum is zero.

15

A window is in the shape of a rectangle surmounted by a semicircle. If the perimeter of the window is 20 ft., find the maximum area.

16

Show that the points (2, 3, 5), (-1, 5, -1) and (4, -3, 2) from a right angled isosceles triangle.

17

Find the derivative of sin ^-1 (cosx).

18

If the increase in the side of a square is 2% then find the approximate percentage of increase in its area.

19

Find the derivative of tan 2x from the first principle.

20

Find the points on the line 3x - 4y - 1 = 0, which are at a distance of 5 units from the point (3, 2).