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WBJEE Subjective Mathematics Sample Paper III | WBJEE Sample Papers, Section Wise & Full Mock Tests 2024 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  WBJEE Subjective Mathematics Sample Paper III | WBJEE Sample Papers, Section Wise & Full Mock Tests 2024
Ans: v = u + at        WBJEE Subjective Mathematics Sample Paper III | WBJEE Sample Papers, Section Wise & Full Mock Tests 2024
WBJEE Subjective Mathematics Sample Paper III | WBJEE Sample Papers, Section Wise & Full Mock Tests 2024

 
Question: 2. Show that​ 
WBJEE Subjective Mathematics Sample Paper III | WBJEE Sample Papers, Section Wise & Full Mock Tests 2024
Ans:  WBJEE Subjective Mathematics Sample Paper III | WBJEE Sample Papers, Section Wise & Full Mock Tests 2024
WBJEE Subjective Mathematics Sample Paper III | WBJEE Sample Papers, Section Wise & Full Mock Tests 2024
WBJEE Subjective Mathematics Sample Paper III | WBJEE Sample Papers, Section Wise & Full Mock Tests 2024

Question: 3. If x = sin t, y = sin 2t, prove that
WBJEE Subjective Mathematics Sample Paper III | WBJEE Sample Papers, Section Wise & Full Mock Tests 2024
Ans:  
WBJEE Subjective Mathematics Sample Paper III | WBJEE Sample Papers, Section Wise & Full Mock Tests 2024
WBJEE Subjective Mathematics Sample Paper III | WBJEE Sample Papers, Section Wise & Full Mock Tests 2024
WBJEE Subjective Mathematics Sample Paper III | WBJEE Sample Papers, Section Wise & Full Mock Tests 2024

Question: 4. Show that, for a positive integer n, the coefficient of xk (0 ≤ K ≥ n) in the expansion of
   WBJEE Subjective Mathematics Sample Paper III | WBJEE Sample Papers, Section Wise & Full Mock Tests 2024
Ans:  WBJEE Subjective Mathematics Sample Paper III | WBJEE Sample Papers, Section Wise & Full Mock Tests 2024
Coefficient of    WBJEE Subjective Mathematics Sample Paper III | WBJEE Sample Papers, Section Wise & Full Mock Tests 2024  Coefficient of   WBJEE Subjective Mathematics Sample Paper III | WBJEE Sample Papers, Section Wise & Full Mock Tests 2024

Question: 5. If m, n be integers, then find the value of  WBJEE Subjective Mathematics Sample Paper III | WBJEE Sample Papers, Section Wise & Full Mock Tests 2024
Ans:  

WBJEE Subjective Mathematics Sample Paper III | WBJEE Sample Papers, Section Wise & Full Mock Tests 2024                  (Odd .....)
WBJEE Subjective Mathematics Sample Paper III | WBJEE Sample Papers, Section Wise & Full Mock Tests 2024

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

WBJEE Subjective Mathematics Sample Paper III | WBJEE Sample Papers, Section Wise & Full Mock Tests 2024
y2 = ax, a2 = ax, a = x    [ put y = a]
A (a, a), B(a, –a)
WBJEE Subjective Mathematics Sample Paper III | WBJEE Sample Papers, Section Wise & Full Mock Tests 2024

Question: 7.  If f is differentiable at x = a, find the value of 
WBJEE Subjective Mathematics Sample Paper III | WBJEE Sample Papers, Section Wise & Full Mock Tests 2024
Ans:  
WBJEE Subjective Mathematics Sample Paper III | WBJEE Sample Papers, Section Wise & Full Mock Tests 2024
WBJEE Subjective Mathematics Sample Paper III | WBJEE Sample Papers, Section Wise & Full Mock Tests 2024

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:  WBJEE Subjective Mathematics Sample Paper III | WBJEE Sample Papers, Section Wise & Full Mock Tests 2024
WBJEE Subjective Mathematics Sample Paper III | WBJEE Sample Papers, Section Wise & Full Mock Tests 2024
WBJEE Subjective Mathematics Sample Paper III | WBJEE Sample Papers, Section Wise & Full Mock Tests 2024

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
WBJEE Subjective Mathematics Sample Paper III | WBJEE Sample Papers, Section Wise & Full Mock Tests 2024
4x – 8 = y – 1, 4x – y – 7 = 0
Equation of BD  WBJEE Subjective Mathematics Sample Paper III | WBJEE Sample Papers, Section Wise & Full Mock Tests 2024
WBJEE Subjective Mathematics Sample Paper III | WBJEE Sample Papers, Section Wise & Full Mock Tests 2024
4x + y – 13 = 0
 

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FAQs on WBJEE Subjective Mathematics Sample Paper III - WBJEE Sample Papers, Section Wise & Full Mock Tests 2024

1. What are the topics covered in the WBJEE Mathematics Exam?
Ans. The WBJEE Mathematics Exam covers various topics such as algebra, trigonometry, calculus, coordinate geometry, probability, and statistics.
2. How many questions are there in the WBJEE Mathematics Exam?
Ans. The WBJEE Mathematics Exam consists of 75 questions in total.
3. Are there negative markings in the WBJEE Mathematics Exam?
Ans. Yes, there is a provision for negative marking in the WBJEE Mathematics Exam. For each incorrect answer, 0.25 marks will be deducted.
4. How much time is allowed to complete the WBJEE Mathematics Exam?
Ans. The WBJEE Mathematics Exam has a duration of 2 hours. Candidates need to manage their time efficiently to attempt all the questions within the given time frame.
5. Is there any specific syllabus for the WBJEE Mathematics Exam?
Ans. Yes, there is a specific syllabus provided for the WBJEE Mathematics Exam. Candidates must refer to the official WBJEE website or the exam brochure to get the detailed syllabus for mathematics.
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