TS Inter Maths 1B Exam 2025 Most Expected Questions: The TS Inter Maths 1B exam for 2025 will take place on March 13, 2025. The examination contains a total of 75 marked questions organized across three different sections. Section A of the exam includes various two-mark questions based on very short answer types. Questions in the exam require students to determine distances between parallel lines as well as find equations of lines and establish conditions for lines to be collinear. Section B presents four-mark short answer questions that may explore derivative calculations of cos(ax) and tan(2x). The section C will contain seven-mark long response questions potentially addressing pair of straight lines and applications of differentiation. The marking system awards points according to the question type leading to 75 total theoretical marks. Students need to practice previous year's exam papers and study important chapters including Straight Lines, Pair of Straight Lines, and Differentiation for their preparation.

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TS Inter Maths 1B Exam 2025 Most Expected Questions

Here are the TS Inter Maths 1B Exam 2025 Most Expected Questions, solving them will increase your chances of scoring excellent marks in the upcoming exam:

Long Answer Type Questions

1.  If φ(h,k) is the image of the point P(x1, y1) w.r.t the straight line ax+by+c=0. Then (h-x ₁ ): a = (k ₁ -y ₁ ): b = -2 (ax ₁ +by ₁ +c): a²+b²  OR h-x1/a = K-y1/b = -2 (ax ₁ +by ₁ +c)/ a²+b²

2. Find the orthocentre of the triangle with the vertices (-2,-1), (6, -1) and (2,5).

3. Find the values of k, if the lines joining the points of intersection of the Origin Curves 2x²-2xy + 3y²+2x-y-1=0 and the line x + 2y = k are mutually perpendicular.

4. Show that the lines joining the origin to the Points of intersection of the curve x²-xy + y²+ 3x + 3y-2=0 and the straight line x-y-√2 are mutually Perpendicular.

5. Show that the area of triangles formed by the lines ax²+ ahxy + by² = 0 and Lx+my+n=0 is n²√h²-ab/ |am²-2hlm+bl²|.

6. Show that the product of the perpendicular distances from a point (2, 3) to the pair of straight Lines ax²+ 2hxy + by²=0 is |aα²+2hαβ+bβ²|/ √(a-b)² + 4h²

7. Find the angle between the lines whose direction cosines are given by the equation's 3l+m+5n=0 and 6mn-2nl+5lm = 0.

8. Find the angle between the lines whose direction cosines satisfy the equations l+m+n=0, l²+m²-n²= 0.

9. If y = x √a²+x² + a² log (x+√a²+x²) then prove that dy/dx = 2√a²+x²

10. If y= Tan-1[√1+x² + √1-x²/√1+x² - √1-x²] for 0 < |x| < 1 ;  find dy/dx

11.  If the length at any point on the curve x ^2/3 +y ^2/3 =a ^2/3 intersects the coordinate axes in A and B, then show that the length AB is constant.

12.  Find the angle between the curves y²=4x and  x²+ y²= 5

13. If the curved surface of the right circular Cylinder inscribed in a sphere of radius'r' is maximum, Show the height of the cylinder is √2r.

14. From a rectangular sheet of dimensions 30cm x 80cm, four equal Squares of side x cm are removed at the corners, and the sides are then turned up so as to form an open rectangular box. Find the value of x.

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Short Answer Type Questions

1. A (1,2), B (2,-3), and C (-2,3) are three points. A point P moves such that PA²+ PB² = 2PC². Show that the equation to the locus of P is 7x-7y+4=0

2. A (5,3) and B (3,-2) are two fixed points. Find the equation of locus of P so that the area of triangle PAB is 9 sq. units.

3. When the the origin is shifted to (-1,2) by translation of axes, find the transformed equation of x²+y²+2x-4y+1=0

4. When the origin shifted to the point (2,3) the transformed equation of a is curve x²+3xy-2y²+171-7y-11=0. Find the original equation of the curve

5. A straight line through φ(√3,2) makes an angle π/6 with the positive direction of the x- axis. If the straight line intersects the line √3х-4y+8=0 at P, find the distance Pφ.

6. i) Find the value of k, if the lines 2x-3y+k=0, 3x-4y-13=0 and 8x-11y-33=0 are concurrent.

ii) Find the value of p, if the lines 3x + 4y = 5 , 2x + 3y = 4 and Px + 4y = 6 are concurrent.

7. Show that f(x) = {Cosax-cosbx/x² and ½ (b²-a²)}, if x ≠ 0 and x = 0, respectively. Where a and b are real constants, and is continuous at x=0.

8. Check the continuity of 'f' given by f(x) = { x²-9)/(x²-2x-3) if 0<x<5 and x≠3 and 1.5 if x = 3, at the point x=3

9. Find the derivative of the following functions from the first principles w.r.t x
a) Sin2x
b) cos²x

10. Find the derivative of the following functions from the first principles w.r.t x
a) xSinx
b) cotx

11. Find the equations of the tangent and normal to the curve xy = 10 at (2,5)

12. Show that the tangent at any point θ on the curve x = csecθ, y = ctanθ is
ySinθ = x - c cosθ

13. A container in the shape of an inverted Cone has height 8m and radius 6m at the top. If it is filled with water at the rate of 2m³/ min, how fast is the height of the water changing when the level is 4m?

14. The distance-time formula for the motion of a particle along a straight line t3-9t²+24t-18, then find when and where the velocity is zero.

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