Class 11th

Choose the incorrect statement about the two circles whose equations are given below:
x² + y² - 10x - 10y + 41 = 0 and x² + y² - 16x - 10y + 80 = 0

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Contributor-Level 10

Circle S? : x² + y² - 10x - 10y + 41 = 0.
Center C? = (5, 5). Radius r? = √ (5² + 5² - 41) = √ (25 + 25 - 41) = √9 = 3.
Circle S? : x² + y² - 16x - 10y + 80 = 0.
Center C? = (8, 5). Radius r? = √ (8² + 5² - 80) = √ (64 + 25 - 80) = √9 = 3.
The solution checks if the center of one circle lies on the other.
Put C? (8, 5) into S? : 8² + 5² - 10 (8) - 10 (5) + 41 = 64 + 25 - 80 - 50 + 41 = 130 - 130 = 0. So C? lies on S?
Put C? (5, 5) into S? : 5² + 5² - 16 (5) - 10 (5) + 80 = 25 + 25 - 80 - 50 + 80 = 130 - 130 = 0. So C? lies on S?
This means both circles pass through the center of each other. So statement (D) is co

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7 months ago

In a triangle PQR, the co-ordinates of the points P and Q are (-2, 4) and (4, -2) respectively. If the equation of the perpendicular bisector of PR is 2x - y + 2 = 0, then the centre of the circumcircle of the ΔPQR is:

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Contributor-Level 10

By property of triangle image of vertex of P is Q about the perpendicular side bisector of triangle Hence according to question X - Y = 0 is a perpendicular side bisector of PQ
Hence solving X - Y = 0 and 2X - y + 2= 0
o (-2, -2)

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7 months ago

Suppose you have taken a dilute solution of oleic acid in such a way that its concentration becomes 0.01cm³ of oleic acid per cm³ of the solution. Then you make a thin film of this solution (monomolecular thickness) of area 4cm² by considering 100 spherical drops of radius ³√(3/(40π)) * 10⁻³ cm. Then the thickness of oleic acid will be x * 10⁻¹⁴ m. Where x is ______.

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Contributor-Level 10

4t = 100 * (4/3)π * (40π * 10? * 0.01)³
t = 2.5 * 10? ¹¹ cm = 2.5 * 10? ¹³ m

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7 months ago

In a school, there are three types of games to be played. Some of the students play two types of games, but none play all the three games. Which Venn diagrams can justify the above statement?

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Contributor-Level 10

P, Q, R represents some students which play all three games. Hence no any option is correct.

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7 months ago

A boy of mass 4 kg is standing on a piece of wood having mass 5 kg. If the coefficient of friction between the wood and the floor is 0.5, the maximum force that boy can exert on the rope so that the piece of wood does not move from its place is _____ N. (Round off to the Nearest Integer) [Take g = 10 ms?²]

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Class 11th Units and Measurement

Contributor-Level 10

Assuming the rope in the boy's hand is vertical and using a Free Body Diagram (FBD):
f? = T
R + T = 90 ⇒ R = 90 - T
For the piece of wood not to move, f? ≤ µR:
T ≤ 0.5 (90 - T) ⇒ T ≤ 30N

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7 months ago

The time period of a simple pendulum is given by T = 2π√(l/g). The measured value of the length of pendulum is 10cm known to a 1 mm accuracy. The time for 200 oscillations of the pendulum is found to be 100 second using a clock of 1 s resolution. The percentage accuracy in the determination of 'g' using this pendulum is 'x'. The value of 'x' to the nearest integer is,

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Raj Pandey

Contributor-Level 9

l = 10.0 ± 0.1cm.
T = (100 ± 1) / 200 = 0.5 ± 0.005

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7 months ago

Class 11th Inverse Trigonometric Functions

If cot⁻¹(α) = cot⁻¹2 + cot⁻¹8 + cot⁻¹18 + cot⁻¹32 + . upto 100 terms, then α is:

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Contributor-Level 10

Kindly consider the following figure

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7 months ago

The disc of mass M with uniform surface mass density σ is shown in the figure. The centre of mass of the quarter disc (the shaded area) is at the position (xa/3π, xa/3π) where x is---------. (Round off to the Nearest integer) [a is an area as shown in the figure]

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Contributor-Level 10

The x and y coordinates of the center of mass are given by:
x? = y? = 4a / 3π

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7 months ago

A body of mass 1 kg rests on a horizontal floor with which it has a coefficient of static friction 1/√3. It is desired to make the body move by applying the minimum possible force F N. The value of F will be ______. (Round off to Nearest Integer) [Take g = 10 ms?²]

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Contributor-Level 10

The minimum force F? is calculated as:
F? = (μmg) / √* (1 + μ²)* = ( (1/√3) * 1 * 10 ) / √* (1 + (1/√3)²) = 5N

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7 months ago

The inverse of y = 5^logx is:

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