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AP Inter 1st Year Maths 1B Question Paper March 2025
Time : 3 Hours
Max. Marks: 75
Section – A
(10 × 2 = 20)
I. Very Short Answer Type Questions
Answer all questions.
Each question carries two marks.
1. Find the distance between parallel lines 5x – 3y – 4 = 0 and 10x – 6y – 9 = 0.
2. Show that the points A(3, 2, -4), B(5, 4, -6) and C(9, 8, -10) are collinear.
3. Write the equation of plane 4x – 4y + 2z + 5 = 0 in intercepts form.
4. If the increase in the side of the square is 4%, then find the approximate percentage of the increase in the area of the square.
5. Transform the equation 3–√x + y + 10 = 0 into
slope- intercept form
normal form.
6. Find the second-order derivative of y = tan-1(2x1−x2).
7. Find the derivative of e2x.log (3x + 4) (x > −43)
8. Verify Rolle’s theorem for the function f(x) = x2 – 1 on [-1, 1]
9. Compute limx→2+([x] + x) and limx→2 ([x] + x).
Section – B
(5 × 4 = 20)
II. Short Answer Type Questions.
Answer ANY FIVE questions.
Each question carries FOUR marks.
11. If f, given by is a continuous function on R, then find values of k.
12. Find the derivative of ‘sec 3x’ from the first principle.
13. 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 12 cm ?
14. Find the lengths of normal and sub-normal at a point on the curve
y = a2(ex/a+e−x/a).
15. Find the equation of locus of ‘P’, if the ratio of distances from P to A(5, -4) and B(7, 6) is 2 : 3.
16. When the axes are rotated through an angle, find the transformed equation of 3x2 + 10xy + 3y2 = 0.
17. Find the point on the straight line 3x + y + 4 = 0 which is equidistant from the points (-5, 6) and (3, 2).
Section – C
(5 × 7 = 35)
III. Long Answer Type Questions.
Answer ANY FIVE questions.
Each question carries SEVEN marks.
18. Find the orthocentre of triangle formed by the lines x + 2y = 0, 4x + 3y – 5 = 0 and 3x + y = 0.
19. Find the angle between the lines joining the origin to the points of intersection of the curve x2 + 2xy + y2 + 2x + 2y – 5 = 0 and the line 3x – y + 1 = 0.
20. Show that the area of the triangle formed by the lines ax2 + 2hxy + by2 = 0 and lx + my + n = 0 is ∣∣n2h2−ab√am2−2hlm+bl2∣∣
21. Find the angle between the lines whose direction cosines are given by the equations 3l + m + 5n = 0 and 6mn – 2nl + 5lm = 0.
22. If xy + yx = ab, then show that dydx = –(y⋅xy−1+yx⋅logyxylogx+x⋅yx−1).
23. If the tangent at any point on the curve x2/3 + y2/3 = a2/3 intersects the coordinate axes in A and B, then show that the length AB is a constant.
24. The profit function P(x) of a company selling x items per day is given by P(x) = (150 – x) x – 1000. Find the number of items that the company should manufacture to get maximum profit. Also, find the maximum profit.
is a continuous function on R, then find values of k.
