Please select a subject first
Advertisements
Advertisements
Find a and b so that the numbers a, 7, b, 23 are in A.P.
Concept: General Term of an Arithmetic Progression
Find the sum of first 20 terms of an A.P. whose nth term is given as an = 5 – 2n.
Concept: Sum of First ‘n’ Terms of an Arithmetic Progressions
Assertion (A): a, b, c are in A.P. if and only if 2b = a + c.
Reason (R): The sum of first n odd natural numbers is n2.
Concept: Sum of First ‘n’ Terms of an Arithmetic Progressions
The x-coordinate of a point P is twice its y-coordinate. If P is equidistant from Q(2, –5) and R(–3, 6), find the coordinates of P.
Concept: Distance Formula
If A(5, 2), B(2, −2) and C(−2, t) are the vertices of a right angled triangle with ∠B = 90°, then find the value of t.
Concept: Distance Formula
If the point A(0, 2) is equidistant from the points B(3, p) and C(p, 5), find p. Also, find the length of AB.
Concept: Distance Formula
If the distance between the points (4, k) and (1, 0) is 5, then what can be the possible values 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
A line intersects the y-axis and x-axis at the points P and Q respectively. If (2, –5) is the mid-point of PQ, then find the coordinates of P and Q.
Concept: Co-ordinate Geometry
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
If the points A(k + 1, 2k), B(3k, 2k + 3) and C(5k − 1, 5k) are collinear, then find the value of k
Concept: Co-ordinate Geometry
Find the distance of a point P(x, y) from the origin.
Concept: Distance Formula
If A(–2, 1), B(a, 0), C(4, b) and D(1, 2) are the vertices of a parallelogram ABCD, find the values of a and b. Hence find the lengths of its sides
Concept: Co-ordinate Geometry
The distance of the point (–1, 7) from x-axis is ______.
Concept: Co-ordinate Geometry
Read the following passage:
|
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.
|
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.
-
- 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)
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)
