JEE WBJEE Subjective Sample Paper III 2026 PDF Download

Question: 1. A train moving with constant acceleration takes t seconds to pass a certain fixed point and the front and back end of the train pass the fixed point with velocities u and v respectively. Show that the length of the trai is 
Ans: v = u + at       

 
Question: 2. Show that​ 

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Question: 3. If x = sin t, y = sin 2t, prove that

Ans:  




Question: 4. Show that, for a positive integer n, the coefficient of x^k (0 ≤ K ≥ n) in the expansion of
  
Ans: 
Coefficient of      Coefficient of  

Question: 5. If m, n be integers, then find the value of 
Ans:  
                  (Odd .....)


Question: 6. Find the angle subtended by the double ordinate of length 2a of the parabola y² = ax at its vertex
Ans:  

y² = ax, a² = ax, a = x    [ put y = a]
A (a, a), B(a, –a)


Question: 7.  If f is differentiable at x = a, find the value of 

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Question: 8. Find the values of ‘a’ for which the expression x² – (3a – 1)x + 2a² + 2a – 11 is always positve.
Ans: x² – (3a – 1) x + 2a² + 2a – 11 > 0
D < 0
(3a – 1)² – 4 (2a² + 2a –11) < 0
9a² – 6a + 1 – 8a2 – 8a + 44 < 0
a² – 14a + 45 < 0
(a – 9) (a – 5) < 0
5 < a < 9

Question: 9. Find the sum of the first n terms of the series 0.2 + 0.22 + 0.222 + ..........
Ans: 



Question: 10. The equation to the pairs of opposite sides of a parallelogram are x² – 5x + 6 = 0 and y² – 6y + 5. Find the equations of its diagonals.
Ans: x = 2 ......(i)
x = 3 ...... (ii)
y = 1 .... (iii)
y = 5 ..... (iv)
A (2, 1), B (3, 1), C (3, 5), D(2, 5)
Equation of AC

4x – 8 = y – 1, 4x – y – 7 = 0
Equation of BD  

4x + y – 13 = 0