IIT JEE , AIEEE Forum - Mathematics , Algebra

tarinbansal

So guys, here you go. Ur first challanging question of maths Q.BANK is coming up. Nudge me for solution.

Don't post the solution here. If you have done the question, its good. U R following the right path to IIT but don't post any solution here. And one more thing, please write the question in clearly understandable form using subscript,superscripts,appropriate symbols etc.

Also specify Difficulty level.

E-Easy

M-Medium

H-Hard

P.S.-Ek baat aur, agar lage ki the question was really good, then keep rating the authors of the questions taaki logon ka interest bana rahe yahan question post karne mai aur unhe rates bhi milte rahen.

C'mon guys, keep posting more and more good questions. 5 pointer for each question.

All The Best

Q.1- Find the minimum value of (u-v)² + [ (2- u²)^1/2 - 9/v²] for 0<u<

2, v>0?

Ans=8

Difficulty level-H

tarinbansal

Q.2- Let z₁,z₂ be roots of the equation z² + pz +q=0, where the coefficients p and q may be complex numbers. Let A and B represent z₁and z₂ in the argand plane. If AOB = @ ( @ not equal to 0) and OA=OB, where O is the origin, prove that p² = 4q cos²@/2.

Difficulty level-H

rhd92781

This is verrry easy but a good question. If u r gud at basics u'll find it very easy and enjoyable.

a,b,c are the cube roots of p, (p<0). Then for any permissible value of x,y,z which is given by

|xa+yb+zc| + (a₁²- 2b₁²) w + w²([x]+[y]+[z]) = 0

|xb+yc+za|

(where w is cube root of unity and a1,b1 are real positive number and b1 is prime number), find the value of [x+a₁] + [y+b₁] + [z], where [.] denotes the greatest integer function.

Ans: 6

lokeshsardana

If {2+ (3)^1/2}ⁿ=I+f where I and n are

+ve integers and 0<f<1,show that I is

an odd integer and (I+f)(1-f)=1

tarinbansal

A circle passing through (a,0), (0,b) on the ellipse x²/a²+y²/b² =1 cuts the curve again at P and Q. Show that the mid point of PQ lies on the line x/a+y/b=0.

P.S.-yeh question mujhse bhi nahi hua tha. Agar ho jaaye to nudge me.

tarinbansal

If a chord is drawn in the ellipse x²/a²+y²/b² =1 in a given direction, then show that the sum of the eccentric angles of the chord is constant.

Difficulty level-E

P.S.-Its an easy question provided the method strikes you.

tarinbansal

Show that the roots of the equation Zⁿ = (Z+1)ⁿ when represented on the Argand diagram are collinear points.

Difficulty level-H

tarinbansal

Alright guys, here's a determinant question. Again an easy question provided the method strikes you.

Prove that

| a² (s - a)² (s - a)² |

=|(s - b)² b² (s - b)² | = 2s³(s - a)(s - b)(s - c)

|(s - c)² (s - c)² c² |

where 2s=a+b+c.

Difficulty level-M

tarinbansal

In the figure given below, a unit square is given(each side=1 unit). A quadrilateral is formed inside the square by taking 4 points arbitrarily on 4 sides of square. The lengths of sides of quadrilateral are a,b,c,d.

Find the minimum value of a² + b² + c² + d² .

Ans = 2

Difficulty level-M

P.S.- Download the image for better view.

iitkgp_bipin

Dear GOIITians, this thread needs your support so come on and contribute.

Here goes my 1st question (an easy one) :

Take any three consecutive natural numbers. Prove that the sum of the cubes of the smaller of them can never be equal to the cube of the larger one.

All The Best.

budku007

I can prove it by principal of MI

tarinbansal

Well another easy question but is a great source of error.

The equation x² + y² + 4x + 6y + 13=0 represents a/an __________.

Difficulty level-E

P.S.- Nudge me to know the answer. I can't give the answer here otherwise question ka maza kirkira ho jaayega.

tarinbansal

All right guys,

Try this one-

If I_n = _{[/4 ]}

^{[/2 ]} cotⁿxdx, then (I₂ + I₄ ), (I₃ + I₅ ), (I₄ + I₆ ) are in-

A) A.P.

B) G.P.

C) H.P.

D) None of these

Answer- (C)

Difficulty level-M

P.S.-Nudge me to know the solution.

All the best.

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