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Rutherford’s a-particle scattering experiment showed that (i) electrons have negative charge. (ii) the mass and positive charge of the atom is concentrated in the nucleus. (iii) neutron exists in the nucleus. (iv) most of the space in an atom is empty. Which of the above statements are correct?
(b) The experiment did not say anything about the charge of electrons, the neutrons were not discovered by that time. https://www.tiwariacademy.com/ncert-solutions/class-9/science/chapter-4/
(b) The experiment did not say anything about the charge of electrons, the neutrons were not discovered by that time.
https://www.tiwariacademy.com/ncert-solutions/class-9/science/chapter-4/
See lessThe optimal value of the objective function is obtained at the points
The optimal value of the objective function in LPP is always obtained at the corner points of the feasible region. This is because the objective function is linear, and at one of the corner points due to the property of linear programming, the maximum or minimum occurs. Check this for more: https://Read more
The optimal value of the objective function in LPP is always obtained at the corner points of the feasible region.
This is because the objective function is linear, and at one of the corner points due to the property of linear programming, the maximum or minimum occurs.
Check this for more:
See lesshttps://www.tiwariacademy.com/ncert-solutions/class-12/maths/#chapter-12
Corner points of the feasible region determined by the system of linear constraints are (0, 3), (1,1) and (3, 0). Let Z = px + qy, where p, q > 0. Condition on p and q so that minimum value of Z occurs at (3, 0) and (1,1) is
To find the condition on p and q, we substitute the coordinates of the corner points 1, 1 and 3, 0 into the objective function Z = px + qy. 1. For point (1, 1): Z = p(1) + q(1) = p + q 2. For point (3, 0) Z = p(3) + q(0) = 3p For the minimum value of Z to occur at (3, 0) and (1, 1), the objective fuRead more
To find the condition on p and q, we substitute the coordinates of the corner points 1, 1 and 3, 0 into the objective function Z = px + qy.
1. For point (1, 1):
Z = p(1) + q(1) = p + q
2. For point (3, 0)
Z = p(3) + q(0) = 3p
For the minimum value of Z to occur at (3, 0) and (1, 1), the objective function value at (1, 1) must be greater than at (3, 0). So we require,
p + q ≥ 3p
q ≥ 2p
Therefore, the constraint on p and q is q = 2p.
See lessIf z = 1 – cos 2 θ + i sin 2 θ, then ∣ z ∣
Choice (c) is correct. Here, z = 1 - cos 2 θ + i sin 2 θ ∣ z ∣ = ∣1 - cos 2 θ + i sin 2 θ∣ = √(1 - cos 2θ)² + (sin 2θ)² = √ 1 -2 cos 2 θ + sin² 2θ = √1 - 2 cos2θ + 1 = √2 -2 cos 2 θ = √2(1- cos 2θ ) = √2(2 sin² θ) = 2 ∣ sin θ ∣ This question related to Chapter 4 maths Class 11th NCERT. From the ChRead more
Choice (c) is correct.
Here, z = 1 – cos 2 θ + i sin 2 θ
∣ z ∣ = ∣1 – cos 2 θ + i sin 2 θ∣ = √(1 – cos 2θ)² + (sin 2θ)²
= √ 1 -2 cos 2 θ + sin² 2θ = √1 – 2 cos2θ + 1
= √2 -2 cos 2 θ = √2(1- cos 2θ ) = √2(2 sin² θ) = 2 ∣ sin θ ∣
This question related to Chapter 4 maths Class 11th NCERT. From the Chapter 4: Complex Numbers and Quadratic Equations. Give answer according to your understanding.
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For the following LPP Maximise Z = 3x + 4y subject to constraints x – y ≥ – 1, x ≤ 3 x ≥ 0, y ≥ 0 The maximum value is
To solve the LPP, we first plot the constraints: 1. x - y ≥ -1 ⟹ y ≤ x + 1 2. x ≤ 3 3. x ≥ 0 4. y ≥ 0 Now, we find the corner points of the feasible region: - From x = 0 and y = 0, the point is (0, 0). - For the line x = 3 and y = x + 1, when x = 3, y = 4. So the point is (3, 4). - From the intersecRead more
To solve the LPP, we first plot the constraints:
1. x – y ≥ -1 ⟹ y ≤ x + 1
2. x ≤ 3
3. x ≥ 0
4. y ≥ 0
Now, we find the corner points of the feasible region:
– From x = 0 and y = 0, the point is (0, 0).
– For the line x = 3 and y = x + 1, when x = 3, y = 4. So the point is (3, 4).
– From the intersection of x = 3 and y = x + 1, we get (3, 4).
Now, evaluate Z = 3x + 4y at the corner points:
– At (0, 0), Z = 3(0) + 4(0) = 0
– At (3, 4), Z = 3(3) + 4(4) = 9 + 16 = 25
The maximum value of Z occurs at (3, 4) and is 25.
Check this for more solutions:
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