At a DIWALI mela, a stall keeper in one of the food stalls has a large cylindrical vessel filled with orange juice and small cylindrical glasses.

(i). If the small cylindrical glass having base radius 2r and height h is open at the top, then total surface area is

(a) 2πr(r + h)

(b) 3πr(r + h)

(c) 4πr(r + h)

(d) None of the above

(ii) Volume of the large cylindrical vessel of radius R and height H is

(a) πR²H

(b) 1/3πR²H

(c) 4/3πR³

(d) 2/3πR³

(iii) If large cylindrical vessel has base radius = 15 cm, height = 32 cm and small cylindrical vessel has base radius = 3 cm, height = 8 cm. Then the number of small cylindrical vessel filled with juice out of a large cylindrical vessel is

(a) 500

(b) 100

(c) 150

(d) 200

(iv) If the stall keeper sold small glass of juice for Rs 3 each, amount received by the stall keeper by selling the juice completely is

(a) ₹ 250

(b) ₹ 275

(c) ₹ 300

(d) ₹ 325

PA and PB are two tangents drawn from an external point P to a circle with centre C and radius 4 cm. If PA ⊥ PB, then length of each tangent is _______.

Find the values of k for which the system of equations kx – y = 2, 6x – 2y = 3 has a unique solution.

Study the following graphs carefully and answer the following questions

(i) Number of Zeros of a polynomial is defined as the number of times the curve cut the

(a) X – axis

(b) Y – axis

(c) Both x and y axis

(d) None of the above

(ii) Number of zeroes of the polynomial in fig-A and fig-B

(a) 1, 2

(b) 2, 3

(c) 2, 1

(d) 3,2

(iii) Polynomial of the curve in fig-A

(a) x² + 3x – 4

(b) x² + 3x + 4

(c) x² - 3x – 4

(d) x² - 3x + 4

(iv) Polynomial of the curve in fig-B

(a) 2x³ – 4x

(b) 3x³ – 4x

(c) x³ + 4x

(d) x³ – 4x

Consider the points P(6, 4) and Q(–5, –3). Draw QS perpendicular to the x-axis. Also draw a perpendicular PT from the point P on QS (extended) to meet y-axis at the point R.

(i) Coordinates of point T is

(a) (-5, 5)

(b) (-5, 4)

(c) (-4, 5)

(d) (4, -5)

(ii) Equation of line PT is

(a) x = 4

(b) x + y = 0

(c) y = 4

(d) x – y = 0

(iii) Distance between points P and Q is

(a) 14 units

(b) 15 units

(c) 13.5 units

(d) None of the above

(iv) If S be any point in the 4th quadrant such that PTQS is the rectangle, then coordinates of point S is

(a) (6, -3)

(b) (5, -4)

(c) (6, -4)

(d) None of the above