Q) PA and PB are tangents drawn to a circle of centre O from an external point P. Chord AB makes and angle of 30 with the radius at the point of contact. If length of the chord of 6 cm, find the length of the tangent PA and the length of the radius OA. Ans: […]
September 2023
Q) Solve :- = 2; = – 1, x, y > o Ans: Let’s consider, = A and = B therefore the given equations will be: Equation = 2 will become: 2 A + 3 B = 2 ………. (i) Similarly, = – 1 will become: 4 A – 9 B = -1
Solve 2 by root x + 3 by root y = 2 ; 4 by root x – 9 by root y = -1, x, y > o Read More »
Q) The sum of a two digit number and the number obtained by reversing the digits is 66. If the digits of the number differ by 2, find the number. How many such numbers are there? Ans: Let’s consider X and Y are the digits of the given number. Hence the given number is 10 X
The sum of a two digit number and the number obtained by reversing the digits is 66. Read More »
Q) If 𝛼, β are zeroes of quadratic polynomial 5×2 + 5x + 1, find the value of1. 𝛼2 + 𝛽22. 𝛼‾1 + 𝛽‾1 Ans: Given polynomial equation 5×2 + 5x + 1 = 0 The roots of the polynomial be α and β. We know that sum of roots (α + β) = α + β
Q) National Art convention got registrations from students from all parts of the country, of which 60 are interested in music, 84 are interested in dance and 108 students are interested in handicrafts. For optimum cultural exchange, organisers wish to keep them in minimum number of groups such that each group consists of students interested
National Art convention got registrations from students from all parts of the country Read More »
Q) Find the area of the unshaded region shown in the given figure. Ans: Let’s redraw the diagram: As we can see in the diagram, in the center area: diameter of semicircle (2R) = side of the inside square (S) or S = 2R ………………. (i) Also we see that Side of larger square = Gap
Find the area of the unshaded region shown in the given figure. Read More »
Q) With vertices A, B and C of Δ ABC as centres, arcs are drawn with radii 14 cm and the three portions of the triangle so obtained are removed. Find the total area removed from the triangle. Ans: We know that the area made by an arc of θ angle is given by = r2
Q) Find the value of X if 2 cosec2 300 + X sin2 600 – (3\4) tan2 300 = 10 Ans: Given that,
Find the value of x if 2 cosec2 30 + x sin2 60 – 3/4 tan2 30 = 10 Read More »
Q) If tan (A + B) = √3 and tan (A – B) = ; 0° < A + B < 90°; A > B, find A and B. Ans: Given that, tan (A + B) = √3 = tan 60° Hence, A + B = 60° ………… (i) Next, its given that, tan (A –
If tan (A + B) = √3 and tan (A – B) = 1/(√3) ; 0° < A + B B, find A and B. Read More »
Q) From an external point P, two tangents, PA and PB are drawn to a circle with centre O. At a point E on the circle, a tangent is drawn to intersect PA and PB at C and D, respectively. If PA = 10 cm, find the perimeter of ∆PCD. Ans: Let’s draw a diagram and