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Q) If the length of a rectangle is reduced by 5 cm and its breadth is increased by 2 cm, then the area of the rectangle is reduced by 80 cm². However, if we increase the length by 10 cm and decrease the breadth by 5 cm, its area is increased by 50 cm². Find […]
If the length of a rectangle is reduced by 5 cm and its breadth is increased by 2 cm, Read More »
Q) Can the number (15n), n being a natural number, end with the digit 0 ? Ans:Â For any number to end with the digit 0, it will be divisible by 10 Since 10 = 2 x 5, therefore, a number ending with digit 0 will be divisible by 2 and 5 both. Next, since
Can the number (15n), n being a natural number, end with the digit 0? Give reasons. Read More »
Q) 22. Find the type of triangle ABC formed whose vertices are A(1, 0), B(-5, 0) and C(-2, 5). Ans: Step 1: Let’s plot the points on the graph: Step 2:Â Given vertices are A(1, 0), B(- 5, 0) and C(- 2, 5). Let’s find out lengths of all the sides: We know that the
Find the type of triangle ABC formed whose vertices are A(1, 0), B(-5, 0) and C(-2, 5). Read More »
Q) If 2 sin (A + B) = √3 and cos (A – B) = 1 , then find the measures of angles A and B. 0 <= A B, (A + B) <= 90 deg Ans: Let’s take each of the given values one by one: 2 sin(A + B) = √3 ∴ sin (A
Q) Evaluate: 2 sin2 300 sec 600 + tan2 600 Ans: We need to find the value of: 2 sin2 300 sec 600 + tan2 600 We know that sin 300 = , sec 600 = 2, tan 600 = √3 by substituting these values in the given expression, we get: 2 sin2 300 sec 600 + tan2 600 = 2 (
Q) In the given figure, AB and CD are tangents to a circle centred at O. Is angle BAC = angle DCA ? Justify your answer. Ans:Â VIDEO SOLUTION STEP BY STEP SOLUTION Step 1: Let’s connect center O with points A and C Step 2: Since BA is the tangent to the circle and
Q) In what ratio is the line segment joining the points (3, – 5) and (- 1, 6) divided by the line y = x ? Ans:Â Method 1: Step 1:Â Â Now, by section formula, coordinates of point P (X, Y) which lies between two points (x1, y1), (x2, y2) will be given by: P (X,Y)
Q) A(3, 0), B(6, 4) and C(-1, 3) are vertices of a triangle ABC. Find length of its median BE. Ans:Â Let’s plot the points on the graph: Step 1:Â Â To draw median BE, point E lies on AC Let’s consider the coordinates of E are (x, y) Since E is the midpoint of A C, we
Q) If the sum of first m terms of an A.P. is same as sum of its first n terms (m ≠n), then show that the sum of its first (m + n) terms is zero. Ans: Step 1: We know that the sum of first m terms of an AP is given by: Sm
Q) In an A.P., the sum of three consecutive terms is 24 and the sum of their squares is 194. Find the numbers. Ans:Â Step 1:Â Let’s consider that the middle term is A, first term is A – D and third term is A + D, here D is the common difference. By given 1st