Question

Section B consists of 5 questions of 2 marks each. 21. If the system of equations \( 2 x+3 y=7 \) and \( (a+b) x+(2 a-b) y=21 \) has infinitely many solutions, then find \( a \) and \( b \). OR Sumit is 3 times as old as his son. Five years later, he shall be two and a half time as old as his son. How old is Sumit at present? 22. Write the coordinates of a point on \( x \)-axis which is equidistant from the points \( (-3,4) \) and \( (2,5) \). 23. \( X \) is a point on the side \( B C \) of \( \triangle A B C . X M \) and \( X N \) are drawn parallel to \( A B \) and \( A C \) respectively meeting \( A B \) in \( N \) and \( A C \) in \( M . M N \) produced meets \( C B \) produced at \( T \). Prove that \( T X^{2}=T B \times T C \). 24. Find the length of the tangent from an external point \( P \) at a distance of 20 cm from the centre of a circle of radius 12 cm . OR Two concentric circles are of radii 8 cm and 5 cm . Find the length of the chord of the larger circle which touches the smaller circle. 25. The probability of selecting a blue marble at random from a jar that contains only blue, black and green marbles is \( \frac{1}{5} \). The probability of selecting a black marble at random from the same jar is \( \frac{1}{4} \). If the jar contains 11 green marbles, find the total number of marbles in the jar.

          Section B consists of 5 questions of 2 marks each.
21. If the system of equations \( 2 x+3 y=7 \) and \( (a+b) x+(2 a-b) y=21 \) has infinitely many solutions, then find \( a \) and \( b \).

OR
Sumit is 3 times as old as his son. Five years later, he shall be two and a half time as old as his son. How old is Sumit at present?
22. Write the coordinates of a point on \( x \)-axis which is equidistant from the points \( (-3,4) \) and \( (2,5) \).
23. \( X \) is a point on the side \( B C \) of \( \triangle A B C . X M \) and \( X N \) are drawn parallel to \( A B \) and \( A C \) respectively meeting \( A B \) in \( N \) and \( A C \) in \( M . M N \) produced meets \( C B \) produced at \( T \). Prove that \( T X^{2}=T B \times T C \).
24. Find the length of the tangent from an external point \( P \) at a distance of 20 cm from the centre of a circle of radius 12 cm .

OR
Two concentric circles are of radii 8 cm and 5 cm . Find the length of the chord of the larger circle which touches the smaller circle.
25. The probability of selecting a blue marble at random from a jar that contains only blue, black and green marbles is \( \frac{1}{5} \). The probability of selecting a black marble at random from the same jar is \( \frac{1}{4} \). If the jar contains 11 green marbles, find the total number of marbles in the jar.

Section B consists of 5 questions of 2 marks each.
21. If the system of equations 2 x+3 y=7 and (a+b) x+(2 a-b) y=21 has infinitely many solutions, then find a and b.

OR
Sumit is 3 times as old as his son. Five years later, he shall be two and a half time as old as his son. How old is Sumit at present?
22. Write the coordinates of a point on x-axis which is equidistant from the points (-3,4) and (2,5).
23. X is a point on the side B C of A B C . X M and X N are drawn parallel to A B and A C respectively meeting A B in N and A C in M . M N produced meets C B produced at T. Prove that T X^2=T B × T C.
24. Find the length of the tangent from an external point P at a distance of 20 cm from the centre of a circle of radius 12 cm .

OR
Two concentric circles are of radii 8 cm and 5 cm . Find the length of the chord of the larger circle which touches the smaller circle.
25. The probability of selecting a blue marble at random from a jar that contains only blue, black and green marbles is (1)/(5). The probability of selecting a black marble at random from the same jar is (1)/(4). If the jar contains 11 green marbles, find the total number of marbles in the jar.

Added by Joel W.

Question

Please give Ace some feedback