(i) Find ( \lim_x \to 2 f(x) ). (ii) Is ( f(x) ) continuous at ( x = 2 )? Justify. (iii) Redefine the function to make it continuous.
(i) Find the median class. (ii) Calculate the median monthly consumption. (iii) Why is median preferred over mean in such data?
(i) Find the slope of the line. (ii) Write the equation of the line in intercept form. (iii) Find the distance of this line from the origin. | Section | Marks per Q | No. of Qs | Total Marks | |---------|-------------|-----------|--------------| | A (MCQ) | 1 | 20 | 20 | | B (VSA) | 2 | 5 | 10 | | C (SA) | 3 | 6 | 18 | | D (LA) | 5 | 4 | 20 | | E (Case) | 4 | 3 | 12 | | Total | | 38 Qs | 80 | This paper covers all major 11th-grade topics , includes conceptual, calculation, proof, and application-based questions , and follows board exam pattern for effective preparation. 11th std maths guide
(i) Draw a neat diagram and represent the situation. (ii) Find the height of the tower. (iii) If the angle of elevation becomes 30°, how far is the point from the tower?
A tower stands vertically on the ground. From a point on the ground 15 m away from the foot of the tower, the angle of elevation of the top of the tower is found to be 60°. (i) Find ( \lim_x \to 2 f(x) )
A line passes through the points ( A(1,2) ) and ( B(3,6) ).
| Consumption (units) | 65–85 | 85–105 | 105–125 | 125–145 | 145–165 | 165–185 | 185–205 | |---------------------|-------|--------|---------|---------|---------|---------|---------| | No. of consumers | 4 | 5 | 13 | 20 | 14 | 8 | 4 | (iii) Redefine the function to make it continuous
The following frequency distribution gives the monthly consumption of electricity of 68 consumers: