A survey regarding the heights (in cm) of 50 girls of a class was conducted and the following data was obtained

(i) Mean height (in cm) of the girls is

(a) 146.8

(b) 147.8

(c) 148.8

(d) 149.8

(ii) The commutative frequency table is useful in determining the

(a) Mean

(b) Median

(c) Mode

(d) All of these

(iii) Lower limit of the median class is

(a) 130

(b) 140

(c) 150

(d) None of the above

(iv) Sum of lower limit of median class and modal class is

(a) 270

(b) 290

(c) 310

(d) None of these

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

Show that (2 + √3) is an irrational number.

The line segment XY is parallel to side AC of ΔABC and it divides the triangle into two parts of equal area. Prove that AX : XB = (√2 – 1) : 1.

OR

In a trapezium ABCD, O is the point of intersection of AC and BD, AB || CD and AB = 2 × CD. If the area of ΔAOB is 84 cm², find the area of ΔCOD.