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

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

The document WBJEE Subjective Mathematics Sample Paper I Notes | Study WBJEE Sample Papers, Section Wise & Full Mock Tests - JEE is a part of the JEE Course WBJEE Sample Papers, Section Wise & Full Mock Tests.
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Question: 1. The harmonic mean of two numbers is 4. Their arithemetic mean A and the geometric mean G satisfy the relation 2A + G2 = 27. find the numbers.
Ans: 
 (3, 6)
Solution:  Let the number be a, b
WBJEE Subjective Mathematics Sample Paper I Notes | Study WBJEE Sample Papers, Section Wise & Full Mock Tests - JEE
WBJEE Subjective Mathematics Sample Paper I Notes | Study WBJEE Sample Papers, Section Wise & Full Mock Tests - JEE



Question: 2  If the area of a rectangle is 64 sq. unit, find the minimum value possible for its perimeter.
Ans:
32
Solution: Let the dimesions be a, b
Area = ab
Paimeter = 2(a + b)
WBJEE Subjective Mathematics Sample Paper I Notes | Study WBJEE Sample Papers, Section Wise & Full Mock Tests - JEE
Perimeter as function of a
WBJEE Subjective Mathematics Sample Paper I Notes | Study WBJEE Sample Papers, Section Wise & Full Mock Tests - JEE
for maxima or minimum
WBJEE Subjective Mathematics Sample Paper I Notes | Study WBJEE Sample Papers, Section Wise & Full Mock Tests - JEE
P (8) is minimum
Minimum P (8) = 2 ( 8 + 8) = 32


Question: 3. Find the image of the point (–8, 12) with respect to the line 4x + 7y + 13 = 0
Ans: 
(–16, –2)
Solution:   
WBJEE Subjective Mathematics Sample Paper I Notes | Study WBJEE Sample Papers, Section Wise & Full Mock Tests - JEE
WBJEE Subjective Mathematics Sample Paper I Notes | Study WBJEE Sample Papers, Section Wise & Full Mock Tests - JEE
WBJEE Subjective Mathematics Sample Paper I Notes | Study WBJEE Sample Papers, Section Wise & Full Mock Tests - JEE

⇒ 4k – 48 = 75 + 56
4k – 7h = 104 ........(ii)
Solving (i) & (ii)
Equation (i) × 7 + Equation (ii) × 4
WBJEE Subjective Mathematics Sample Paper I Notes | Study WBJEE Sample Papers, Section Wise & Full Mock Tests - JEE
A′ (– 16, –2) is the image of (–8, 12)


Question:  4. How many triangles can be formed by joining 6 points lying on a circle ?
Ans: 20
Solution: 
Number of triangle
  WBJEE Subjective Mathematics Sample Paper I Notes | Study WBJEE Sample Papers, Section Wise & Full Mock Tests - JEE


Question:  5. If r2 = x2 + y2 + z2 , then prove that
WBJEE Subjective Mathematics Sample Paper I Notes | Study WBJEE Sample Papers, Section Wise & Full Mock Tests - JEE
Ans:    WBJEE Subjective Mathematics Sample Paper I Notes | Study WBJEE Sample Papers, Section Wise & Full Mock Tests - JEE
WBJEE Subjective Mathematics Sample Paper I Notes | Study WBJEE Sample Papers, Section Wise & Full Mock Tests - JEE

Question:  6. Determine the sum of imaginary roots of the equation
WBJEE Subjective Mathematics Sample Paper I Notes | Study WBJEE Sample Papers, Section Wise & Full Mock Tests - JEE
Ans:  WBJEE Subjective Mathematics Sample Paper I Notes | Study WBJEE Sample Papers, Section Wise & Full Mock Tests - JEE
Solution:  Put 2x2 + x = y
⇒ (4 – 1) (24 – 3) = 6, on solving
WBJEE Subjective Mathematics Sample Paper I Notes | Study WBJEE Sample Papers, Section Wise & Full Mock Tests - JEE

Question:  7. If cos A + cos B + cos C = 0, prove that  cos 3A + cos 3B + cos 3C = 12 cos A cos B cos C
Ans: 

WBJEE Subjective Mathematics Sample Paper I Notes | Study WBJEE Sample Papers, Section Wise & Full Mock Tests - JEE
WBJEE Subjective Mathematics Sample Paper I Notes | Study WBJEE Sample Papers, Section Wise & Full Mock Tests - JEE
= 12 cos A . cos B. cos C

Question: 8.  Let IR be the set of real numbers and f : IR → IR  be such that for all x, y ∈IR, |f(x) – f(y)| ≤ | x – y|3 . Prove that f is a constant function.
Ans:  
WBJEE Subjective Mathematics Sample Paper I Notes | Study WBJEE Sample Papers, Section Wise & Full Mock Tests - JEE
= |f′ (x) | ≤ | 0 | ⇒ |f′ (x)| = 0
⇒ f (x) = constant


Question: 9. Find the general solution of (x + logy) dy + y dx = 0
Ans. xy + y lny – y = 0
Solution:  x dy + y dx + log y dy = 0
WBJEE Subjective Mathematics Sample Paper I Notes | Study WBJEE Sample Papers, Section Wise & Full Mock Tests - JEE
xy + y lny – y = 0
 

Question: 10.  Prove that  WBJEE Subjective Mathematics Sample Paper I Notes | Study WBJEE Sample Papers, Section Wise & Full Mock Tests - JEE
Ans.  WBJEE Subjective Mathematics Sample Paper I Notes | Study WBJEE Sample Papers, Section Wise & Full Mock Tests - JEE
WBJEE Subjective Mathematics Sample Paper I Notes | Study WBJEE Sample Papers, Section Wise & Full Mock Tests - JEE

The document WBJEE Subjective Mathematics Sample Paper I Notes | Study WBJEE Sample Papers, Section Wise & Full Mock Tests - JEE is a part of the JEE Course WBJEE Sample Papers, Section Wise & Full Mock Tests.
All you need of JEE at this link: JEE

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