Access to a variety of TS Inter 1st Year Maths 1B Model Papers and TS Inter 1st Year Maths 1B Question Paper May 2023 allows students to familiarize themselves with different question patterns.
TS Inter 1st Year Maths 1B Question Paper March 2023
Time : 3 Hours
Max. Marks : 75
Note : This question paper consists of THREE sections A, B and C.
Section – A
(10 × 2 = 20 Marks)
I. Very short answer type questions :
- Attempt all the questions.
- Each question carries two marks.
1. Find the slope of the straight line passing through the points (3, 4), (7, -6).
2. Transform the following straight line equation into normal form 3x + 4y = 5.
3. Find the centroid of the tetrahedron whose vertices are (2,3, -4), (-3, 3, -2),
(-1, 4, 2), (3, 5, 1)
4. Write the equation of the plane 4x – 4y + 2z + 5 = 0 in the intercept form.
5. Compute \(\lim _{x \rightarrow 2}\left(\frac{1}{x-2}-\frac{4}{x^2-4}\right)\)
6. Compute \(\lim _{x \rightarrow 0} \frac{\mathrm{e}^{7 x}-1}{x}\) = 7.
7. If y = log (sin (log x)), find \(\frac{d y}{d x}\).
8. Find the derivative of sin-1(3x – 4x3).
9. Find the slope of the tangent to the curve y = 5x2 at (-1, 5).
10. Find dy and ∆y of y = f(x) = x2 + x at x = 10 when ∆x = 0.1.
Section – B (5 × 4 = 20)
II. Short answer type questions.
- Attempt ANY FIVE questions.
- Each question carries FOUR marks.
11. The ends of the hypotenuse of a right angled triangle are (0, 6) and (6, 0). Find the equation of the locus of its third vertex.
12. When the axes are rotated through an angle \(\frac{\pi}{6}\), find the transformed equation of x2 + 2\(\sqrt{3}\) xy – y2 = 2a2.
13. If Q(h, k) is the foot of the perpendicular from (P(x1, y1) on the straight line ax + by + c = 0 then prove that
\(\frac{\mathrm{h}-x_1}{\mathrm{a}}\) = \(\frac{k-y_1}{b}\) = –\(\frac{\left(a x_1+b y_1+c\right)}{a^2+b^2}\)
14. Compute \(\lim _{x \rightarrow 0} \frac{1-\cos 2 m x}{\sin ^2 n x}\) (m, n ∈ Z).
15. Find the derivative of the function tan 2x from the first principle.
16. If the increase in the side of a square is 2%, then find the approximate percentage of increase in its area.
17. Find the lengths of subtangent, subnormal at a point ‘t’ on the curve
x = a (cos t + t sin t), y = a (sin t – t cos t).
Section – C (5 × 7 = 35)
III. Long answer type questions.
- Answer ANY FIVE questions.
- Each question carries SEVEN marks.
18. Find the orthocentre of the triangle with the following vertices (-2, -1), (6, -1) and (2, 5).
19. If the equation ax2 + 2hxy + by2 = 0 represent a pair of straight lines and ‘0’ is the angle between the lines then prove that cosθ = \(\frac{|a+b|}{\sqrt{(a-b)^2+4 h^2}}\)
20. Find the values of k, if the lines joining the origin to the points of intersection of the curve 2x2 – 2xy + 3y2 + 2x – y – 1 = 0 and the line x + 2y = k are mutually perpendicular.
21. Find the angle between two diagonals of a cube.
22. If \(\sqrt{1-x^2}+\sqrt{1-y^2}\) = a(x – y) then show that \(\frac{d y}{d x}\) = \(\sqrt{\frac{1-y^2}{1-x^2}}\)
23. Show that the curves y2 = 4 (x + 1) and y2 = 36 (9 – x) intersect orthogonally.
24. The volume of a cube is increasing at a rate of 9 cubic centimeters per second. How fast is the surface area increasing when the length of the edge is 10 centimetres ?