Q70.A triangle is formed by X -axis, Y -axis and the line 3x + 4y = 60 . Then the number of points P(a, b) which lie strictly inside the triangle, where a is an integer and b is a multiple of a, is _____ .
What This Question Tests
This question involves finding integer points strictly inside a triangle formed by coordinate axes and a line, with an additional constraint that the y-coordinate must be a multiple of the x-coordinate. It combines coordinate geometry with number theory.
Concepts Tested
Formulas Used
ax + by = c
Area = (1/2) * base * height
📚 NCERT Sections This Tests
2.2 — A Regular Hexagon Of Side 10 Cm Has A Charge 5 Mc At Each Of Its
Physics Class 11 · Chapter 2
2.2 A regular hexagon of side 10 cm has a charge 5 mC at each of its vertices. Calculate the potential at the centre of the hexagon.
2.1 — Two Charges 5 × 10–8 C And –3 × 10–8 C Are Located 16 Cm Apart. At
Physics Class 11 · Chapter 2
2.1 Two charges 5 × 10–8 C and –3 × 10–8 C are located 16 cm apart. At what point(s) on the line joining the two charges is the electric potential zero? Take the potential at infinity to be zero.
9.17 — (A) Sin I¢C = 1.44/1.68 Which Gives I¢C = 59°. Total Internal Reflection
Physics Class 12 · Chapter 9
9.17 (a) sin i¢c = 1.44/1.68 which gives i¢c = 59°. Total internal reflection takes place when i > 59° or when r < rmax = 31°. Now, (sin i /sin r max max ) = 1.68 , which gives imax ~ 60°. Thus, all incident rays of angles in the range 0 < i < 60° will suffer total internal reflections in the pipe. (If the length of the pipe is finite, which it is in practice, there will be a lower limit on i determined by the ratio of the diameter to the length of the pipe.) (b) If there is no outer coating, i¢c = sin–1(1/1.68) = 36.5°. Now, i = 90° will have r = 36.5° and i¢ = 53.5° which is greater than i¢c. Thus, all incident rays (in the range 53.5° < i < 90°) will suffer total internal reflections.
📋 Question Details
- Chapter
- Straight Lines
- Topic
- Points inside a triangle
- Year
- 2023
- Shift
- 25 Jan Shift 2
- Q Number
- Q70
- Type
- Numerical
- NCERT Ref
- Class 11 Mathematics Ch 10: Straight Lines
More from this Chapter
Q91.Let A(h, k), B(1, 1) and C(2, 1) be the vertices of a right angled triangle with AC as its hypotenuse. If the area of the triangle is 1 , then the set of values which ' k ' can take is given by (1) {1, 3} (2) {0, 2} (3) {−1, 3} (4) {−3, −2}
Q92.Let P = (−1, 0), Q = (0, 0) and R = (3, 3√3) be three points. The equation of the bisector of the angle PQR (1) √3x + y = 0 (2) x + √32 y = 0 (3) √3 x + y = 0 (4) x + √3y = 0 2
Q93.If one of the lines of my2 + (1 −m2)xy −mx2 = 0 is a bisector of the angle between the lines xy = 0 , then m is JEE Main 2007 JEE Main Previous Year Paper (1) −1/2 (2) −2 (3) 1 (4) 2
Q66.The lines p (p2 + 1)x −y + q = 0 and (p2 + 1)2x + (p2 + 1)y + 2q = 0 are perpendicular to a common line for (1) no value of p (2) exactly one value of p (3) exactly two values of p (4) more than two values of p