RULEMATH | MATH ONLINE/DIRECT CLASS | MATH WEBSITE | SCIENCE CLASS 10, PHYSICS CLASS 11 AND 12

CLASS 5 REVISION TOPICS:    Number Names    Predecessor    Successor    Rounding off to 10, 100, 1000, 1000    Addition     Subtraction    Multiplication    Division    Prime Numbers     Composite Numbers    Hindu-Arabic, Roman Numerals       Factor Tree       HCF        LCM    Divisibility Tests    Factors     Multiples    Missing digits in                Addition and Subtraction                                                      1. W rite the names according to Indian System of Numeration: (i) 45789 (ii) 6879007 2. Write the names according to International System of Numeration: (...

SAMACHEER KALVI CLASS 10 ASSIGNMENT 3 COORDINATE GEOMETRY 1. Find the area of the triangle formed by the points: (i) (1,-1),  (-4, 6) and (-3, -5) 2. F ind the value of ‘a’ for which the given points are collinear. (i) (2,3), (4, a) and (6, -3) 3. Determine whether the sets of points are collinear? (i) (a, b+c), (b, c+a) and (c, a+b) 4.  Find the area of the quadrilateral whose vertices are at (i) (-9, 0), (-8,6), (-1, -2) and (-6, -3) 5. What is the slope of a line perpendicular to the line joining A(5,1) and P where P is the mid-point of the segment joining (4,2) and (-6,4). 6. If the three points (3, -1), (a, 3) and (1, -3) are collinear, find the value of a. 7. What is the inclination of a line whose slope is  0 ? 8. What is the slope of a line whose inclination with positive direction of x -axis is  90° ? 9. The line through the points (-2, 6) and (4, 8) is perpendicular to the line through the points (8,12) and (x, 24). Find the value of x. 10. Show that the gi...

 CLASS 11 ASSIGNMENT 7 SUMS - MOTION IN A STRAIGHT LINE 1. A body travels from A to B at 40 m/s and from B to A at 60 m/s.  Find the average speed and average velocity. 2. A car covers the first half of the distance between two places at a speed of 40 km/h and the second half at 60 km/h.  What is the average speed of the car? 3. The displacement of a particle varies with time t as x = 4t² - 15t + 25.  Find the position, velocity and acceleration of the particle at t=0.  When will the velocity of the particle become zero?  Can we call the motion of the particle as one with uniform acceleration? 4. The acceleration of a particle in m/s² is given by  a = 3t²+ 2t + 2, where time t is in second. If the particle starts with a velocity v=2 m/s at t=0, then find the velocity at the end of 2 s. 5.  A jet plane starts from rest with an acceleration of 3 m/s² and makes a run for 35 s before taking off.  What is the minimum length of the runway and what ...

  CLASS 10 CBSE QUADRATIC EQUATIONS ARITHMETIC PROGRESSION COORDINATE GEOMETRY 1. Check whether the following are quadratic equations: (i) (x + 1) 2  = 2(x – 3) (ii) x 2  – 2x = (–2) (3 – x) 2. Represent the following situations in the form of quadratic equations: (i) The area of a rectangular plot is 528 m 2 . The length of the plot (in metres) is one more than twice its breadth. We need to find the length and breadth of the plot. (ii) The product of two consecutive positive integers is 306. We need to find the integers. 3. Factorise (i) 2x 2  – x +1/8 = 0 (ii) 100x 2  – 20x + 1 = 0 4.  Find two consecutive positive integers, sum of whose squares is 365. 5. The altitude of a right triangle is 7 cm less than its base. If the hypotenuse is 13 cm, find the other two sides. 6. Find the roots of the quadratic equations by applying the quadratic formula. (i) 2x 2  – 7x + 3 = 0   (ii) 4x 2  + 4√3x + 3 = 0 7. For t...

CLASS 12 RELATIONS AND FUNCTIONS ADDITIONAL SUMS ONE-ONE AND ONTO FUNCTIONS 1. Prove that the function f:N →  N defined by f(x) = x²+ x + 1 is one - one but not onto. Let x, y ∊ N such that f(x) = f(y) x² +  x + 1  =     y²  + y + 1  x² - y² + x - y = 0 (x - y)(x + y) + (x - y) = 0 (x - y)(x + y + 1) = 0 Since x+y+1 ≠ 0, we have x - y = 0 x = y Therefore f is one-one. But, since f:N →N, f(x)  cannot take values 1 and 2.  Therefore f is not onto. 2. Show that the function f: R→ R defined by f(x)  = 2x³ - 7 is bijective. Let x, y ∊ R   such that f(x) = f(y) 2x³ - 7 = 2y³ - 7 2(x³ - y³) = 0 2(x-y)(x² + x y + y²) = 0 We know x² + x y + y² ≠ 0 we have x- y = 0 which implies x = y Therefore f is one-one. Let y = 2x³ - 7       x³ = (y + 7)/2       x  = ((y+7)/2) ^ 1/3  Therefore for all values of y ∊ R,  there exists x ∊ R and so f is onto. Hence f is bijective. 3. Show that the f...