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WBJEE Subjective Mathematics Sample Paper II Notes | Study WBJEE Sample Papers, Section Wise & Full Mock Tests - JEE

Document Description: WBJEE Subjective Mathematics Sample Paper II for JEE 2022 is part of WBJEE Sample Papers, Section Wise & Full Mock Tests preparation. The notes and questions for WBJEE Subjective Mathematics Sample Paper II have been prepared according to the JEE exam syllabus. Information about WBJEE Subjective Mathematics Sample Paper II covers topics like and WBJEE Subjective Mathematics Sample Paper II Example, for JEE 2022 Exam. Find important definitions, questions, notes, meanings, examples, exercises and tests below for WBJEE Subjective Mathematics Sample Paper II.

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Question: 1. Prove that the equation cos2x + a sinx = 2a – 7 possesses a solution if   WBJEE Subjective Mathematics Sample Paper II Notes | Study WBJEE Sample Papers, Section Wise & Full Mock Tests - JEE
Ans: ⇒ cos2x + a sinx = 2a – 7
⇒ 2sin2x – asinx + (2a – 8) = 0
Since sin ∈IR   WBJEE Subjective Mathematics Sample Paper II Notes | Study WBJEE Sample Papers, Section Wise & Full Mock Tests - JEE
∴ Given equation has solution of WBJEE Subjective Mathematics Sample Paper II Notes | Study WBJEE Sample Papers, Section Wise & Full Mock Tests - JEE

Question: 2. Find the values of x, (–S < x < S, x ≠ 0) satisfying the equation,  WBJEE Subjective Mathematics Sample Paper II Notes | Study WBJEE Sample Papers, Section Wise & Full Mock Tests - JEE
Ans: WBJEE Subjective Mathematics Sample Paper II Notes | Study WBJEE Sample Papers, Section Wise & Full Mock Tests - JEE
WBJEE Subjective Mathematics Sample Paper II Notes | Study WBJEE Sample Papers, Section Wise & Full Mock Tests - JEE

Question: 3.  Prove that the centre of the smallest circle passing through origin and whose centre lies on y = x + 1 is  WBJEE Subjective Mathematics Sample Paper II Notes | Study WBJEE Sample Papers, Section Wise & Full Mock Tests - JEE
Ans: 
Let centre be c(h, h + 1) , 0(0, 0)
WBJEE Subjective Mathematics Sample Paper II Notes | Study WBJEE Sample Papers, Section Wise & Full Mock Tests - JEE

Question: 4. Prove by induction that for all n∈ N, n2 + n is an even integer (n ≥ 1)
Ans:  x = 1, x2 + x = 2 is an even integer
Let for n = k, k2 + k is even
Now for n = k + 1, (k + 1)2 + (k + 1) – (k2 + k)
= k2 + 2k + 1 + k + 1 – k2 – k = 2k + 2 which is even integer also k2 + k is even integer
Hence (k + 1)2 + (k + 1) is also an even integer
Hence n2 + n is even integer for all n∈ N.
 

Question: 5. If A, B are two square matrices such that AB = A and BA = B, then prove that B2 = B
Ans:  B2 = B.B = (BA)B = B (AB) = B(A) = BA = B (Proved)
 

Question: 6.  WBJEE Subjective Mathematics Sample Paper II Notes | Study WBJEE Sample Papers, Section Wise & Full Mock Tests - JEE

Ans:  WBJEE Subjective Mathematics Sample Paper II Notes | Study WBJEE Sample Papers, Section Wise & Full Mock Tests - JEE
WBJEE Subjective Mathematics Sample Paper II Notes | Study WBJEE Sample Papers, Section Wise & Full Mock Tests - JEE

Question: 7. Use the formula  WBJEE Subjective Mathematics Sample Paper II Notes | Study WBJEE Sample Papers, Section Wise & Full Mock Tests - JEE
Ans:   WBJEE Subjective Mathematics Sample Paper II Notes | Study WBJEE Sample Papers, Section Wise & Full Mock Tests - JEE
WBJEE Subjective Mathematics Sample Paper II Notes | Study WBJEE Sample Papers, Section Wise & Full Mock Tests - JEE

Question: 8.  WBJEE Subjective Mathematics Sample Paper II Notes | Study WBJEE Sample Papers, Section Wise & Full Mock Tests - JEE  prove that,  WBJEE Subjective Mathematics Sample Paper II Notes | Study WBJEE Sample Papers, Section Wise & Full Mock Tests - JEE   where A is constant
Ans:   WBJEE Subjective Mathematics Sample Paper II Notes | Study WBJEE Sample Papers, Section Wise & Full Mock Tests - JEE
WBJEE Subjective Mathematics Sample Paper II Notes | Study WBJEE Sample Papers, Section Wise & Full Mock Tests - JEE

Question: 9. Evaluate the following integral   WBJEE Subjective Mathematics Sample Paper II Notes | Study WBJEE Sample Papers, Section Wise & Full Mock Tests - JEE
Ans:   WBJEE Subjective Mathematics Sample Paper II Notes | Study WBJEE Sample Papers, Section Wise & Full Mock Tests - JEE
WBJEE Subjective Mathematics Sample Paper II Notes | Study WBJEE Sample Papers, Section Wise & Full Mock Tests - JEE
WBJEE Subjective Mathematics Sample Paper II Notes | Study WBJEE Sample Papers, Section Wise & Full Mock Tests - JEE

Question: 10.  WBJEE Subjective Mathematics Sample Paper II Notes | Study WBJEE Sample Papers, Section Wise & Full Mock Tests - JEE
Ans:   WBJEE Subjective Mathematics Sample Paper II Notes | Study WBJEE Sample Papers, Section Wise & Full Mock Tests - JEE
= g'(a) f(a) – g(a) f'(a)
= (2)(2) – (–1) (1) = 4 + 1 = 5

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