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If the distance between the points (4, k) and (1, 0) is 5, then what can be the possible value of k?
Concept: Distance Formula
If a ≠ b ≠ 0, prove that the points (a, a2), (b, b2) (0, 0) will not be collinear.
Concept: Distance Formula
If the distances of P(x, y) from A(5, 1) and B(–1, 5) are equal, then prove that 3x = 2y
Concept: Distance Formula
Find the distance of a point P(x, y) from the origin.
Concept: Distance Formula
Read the following passage:
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Use of mobile screen for long hours makes your eye sight weak and give you headaches. Children who are addicted to play "PUBG" can get easily stressed out. To raise social awareness about ill effects of playing PUBG, a school decided to start 'BAN PUBG' campaign, in which students are asked to prepare campaign board in the shape of a rectangle: One such campaign board made by class X student of the school is shown in the figure.
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Based on the above information, answer the following questions:
- Find the coordinates of the point of intersection of diagonals AC and BD.
- Find the length of the diagonal AC.
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- Find the area of the campaign Board ABCD.
OR - Find the ratio of the length of side AB to the length of the diagonal AC.
- Find the area of the campaign Board ABCD.
Concept: Distance Formula
If 4 tan θ = 3, evaluate `((4sin theta - cos theta + 1)/(4sin theta + cos theta - 1))`
Concept: Trigonometric Ratios
Prove the following trigonometric identities.
sec A (1 − sin A) (sec A + tan A) = 1
Concept: Trigonometric Identities (Square Relations)
If cos A = `4/5`, then the value of tan A is ______.
Concept: Trigonometric Ratios
Proved that `(1 + secA)/secA = (sin^2A)/(1 - cos A)`.
Concept: Trigonometric Identities (Square Relations)
sec θ when expressed in term of cot θ, is equal to ______.
Concept: Trigonometric Identities (Square Relations)
Prove that `(cot A - cos A)/(cot A + cos A) = (cos^2 A)/(1 + sin A)^2`
Concept: Trigonometric Identities (Square Relations)
Prove that (sec θ + tan θ) (1 – sin θ) = cos θ
Concept: Trigonometric Identities (Square Relations)
With the help of an appropriate example, justify that some of the chemical reactions are determined by the evolution of a gas.
Give a chemical equation for the reaction involved in the above case.
Concept: Chemical Equations
With the help of an appropriate example, justify that some of the chemical reactions are determined by a change in colour.
Give a chemical equation for the reaction involved in the above case.
Concept: Chemical Equations
With the help of an appropriate example, justify that some of the chemical reactions are determined by a change in temperature.
Give a chemical equation for the reaction involved in the above case.
Concept: Chemical Equations
State the change in colour observed in the following case, mentioning the reason:
Silver chloride is exposed to sunlight.
Concept: Types of Chemical Reactions > Decomposition Reaction
Bronze is an alloy of ______.
Concept: Corrosion of Metals
Answer the following question.
2 g of silver chloride is taken in a china dish and the china dish is placed in sunlight for some time. What will be your observation in this case? Write the chemical reaction involved in the form of a balanced chemical equation. Identify the type of chemical reaction.
Concept: Types of Chemical Reactions > Decomposition Reaction
Answer the following question.
What is observed when 2 mL of dilute hydrochloric acid is added to 1 g of sodium carbonate taken in a clean and dry test tube? Write a chemical equation for the reaction involved.
Concept: Chemical Equations
In a double displacement reaction such as the reaction between sodium sulphate solution and barium chloride solution:
- exchange of atoms takes place
- exchange of ions takes place
- a precipitate is produced
- an insoluble salt is produced
The correct option is:
Concept: Types of Chemical Reactions > Double Displacement Reaction
