| Question 121. Are there geometric figures which are always similar? by Ritika. Answered on Jan 16, 2007 at 8:20 p.m. |
| Answer 121. Yes. Circles, equilateral triangles and all other regular polygons are always similar. |
| Question 122. Find the sum of all two digit numbers which when divided by 9, yield 1 as remainder, by Nishajith. Answered on Jan 20, 2008 at 8:09 pm I.S.T |
| Answer 122. The Numbers of this type are 10, 19, 28, 37,...,91. First term = a = 10 common difference = d = 19 - 10 = 9 last term = Tn = 91 a + (n - 1)d = 91 10 + (n - 1)9 = 91 (n - 1)9 = 81 n - 1 = 9 n = 9 + 1 = 10 Sum = S10 = n/2 (a + l) = 10/2 ( 10 + 91) = 5 (101) = 505 |
| Question 123. Write a linear equation which passes through x = 2 and y = 3. How many such lines are possible.by Raman. Answered on Jan 21, 2007 at 10:21 pm I.S.T. |
| Answer 123. x + y = 5. Infinitely many lines are possible. |
| Question 124. How many tangents can be drawn to a circle from a point in its interior? by Shahnaz. Answered on Jan 25, 2008 at 10:43 pm I.S.T. |
| Answer 124. None. Tangents can be drawn from an exterior point or a point on the circle. |
| Question 125. The sum of ages of A and B is 49 years. A said to B, " I am twice as old as you were when I was as old as you are. Find their present ages by Ravi. Answered on Jan 31, 2007 at 9:14 pm I.S.T. |
| Answer 125. Let age of A = x years Let age of B = y years Difference of their ages = (x - y) years according to first condition x = 2 [ y - (x - y) ] x = 2 ( y - x + y ) x = 2 ( 2y - x ) x = 4y - 2x 3x = 4y ..............(i) according to second condition x + y = 49 x = 49 - y ............(ii) From i and ii 3 (49 - y) = 4y 147 - 3y = 4y 7y = 147 y = 21 Substituting in ii x = 28 Age of A = 28 years Age of A = 21 years |
| Question 126. Suppose you drop a dice in
a rectangular region with sides 6 m and 4 m. A circle is of |
| Answer 126. Area of rectangular region = 6 × 4 = 24 square metre Area of circle = pie/4 square metre Required probability = (pie/4)/24 = pie/96 |
| Question 127. prove that the area of triangle whose coordinates are (t,t-2),(t+23,t+2)and (t+3,t) is independent of t by Puneet Singh. Answered on Feb 10, 2007 at 11:11 pm |
| Answer 127. Area of triangle = 1/2 | t(t + 2 - t) + (t + 23)(t - t + 2) + (t + 3)(t - 2 - t - 2)| = 1/2 | 2t + 2t + 46 - 4t - 12| = 1/2 |34| = 17 square units So we see area of triangle does not contain t and hence is independent of t |
| Question 128. determine the ratio in which the line 2x+y-4=0 divides the line segment joining the points A(2,-2) and B(3,7) by Sukhmani Lamba. Answered on Feb 12, 2007 at 9:12 p.m. |
| Answer 128. Let the coordinates of point of intersection be (x,y) and let it divide the line segment AB in ratio k:1. So x = (2 + 3k)/(k+1) and y = (- 2 + 7k)/(k+1) Putting these values in the equation of given line we get 2(2 + 3k)/(k+1) + (- 2 + 7k)/(k+1) - 4 = 0 (4 + 6k)/(k+1) + (- 2 + 7k)/(k+1) - 4 = 0 (4 + 6k - 2 + 7k)/(k+1) = 4 (2 + 13k)/(k+1) = 4 2 + 13k = 4k + 4 9k = 2 k = 2/9 Required ratio = 2:9 |
| Question 129. (x-2) and (x-1/2) are the factorsof the polynomials qx^2+5x+r prove that q=r, by Arushi Gautam. Answered on Feb 14, 2007 at 9:37 pm I.S.T. |
| Answer 129. Let f(x) = qx^2+5x+r Since x - 2 is a factor therefore f(2) = 0 by factor theorem q(2^2) + 5(2) + r = 0 4q + r = - 10 ........(i) Since x - 1/2 is a factor therefore f(1/2) = 0 by factor theorem q(1/2)^2 + 5(1/2) + r = 0 q/4 + r = - 5/2 .....(ii) (i) - (ii) 4q - q/4 = - 10 + 5/2 (×4) 16q - q = - 40 + 10 15 q = - 30 q = - 2 Substituting in (i) 4(- 2) + r = - 10 r = - 10 + 8 r = - 2 Therefore p = q = -2 |
| Question 130. If 3cot A=4, check whether1-tan^2 A / 1+tan^2 A = cos^2 A - sin^2 A or not by Unnikrishnan. Answered on Feb 16, 2007 at 7:38pm I.S.T. |
| Answer 130.3cot A=4 or cot A = 4/3 = adjacent side/opposite side Let adjacent side = 4k and opposite side = 3k Hypotenuse = 5k L.H.S. = 1-tan^2 A / 1+tan^2 A = [1 - (3/4)^2]/ [1 + (3/4)^2] = [ 1 - 9/16]/[ 1 + 9/16] = [7/16]/[25/16] = 7/16 × 16/25 = 7/25 R.H.S. = cos^2 A - sin^2 A = [4/5]^2 - [3/5]^2 = 16/25 - 9/25 = 7/25 Therefore L.H.S. = R.H.S. |
| Question 131.A die is thrown once. Find probability of getting a composite or prime number by Parkash. Answered on Feb 17, 2008 at 8:19 pm I.S.T. |
| Answer 131. Favorable outcomes = 5 (2, 3, 4, 5, 6), Total outcomes = 6 (1, 2, 3, 4, 5, 6) Required Probability = Favorable outcomes/Total outcomes = 5/6 Note - 1 is neither composite nor Prime |
| Question 132. Sir, by when will the Maths (class X ) Mock test be available ? What about the answers? by Sukhman deep. Answered on Feb 23, 2008 at 1:08 a.m. I.S.T. |
| Answer 132. We plan to add two Mathematics class X Mock tests with answers. One has been already added today. The answers will be added in a few days. The second mock test we plan to add in March before Mathematics board exam. It is available here |
| Question 133.Explain why 7×11×13+13 is composite numbers by Surbhi Agarwal. Answered on Feb 25, 2007 at 11:39 pm I.S.T. |
| Answer 133. 7×11×13+13 = 13(7×11 + 1) = 13(78) Now this number has more than two factors. Therefore it is a composite number. |
| Question 134. Write the least even prime number. What are Prime numbers? by Vishnoo Prashanth. Answered on Feb 26, 2008 at 9:50 pm I.S.T. |
| Answer 134.The numbers which have exactly two factors are called prime numbers. These factors are 1 and the number itself. Least and the only even prime number is 2. |
| Question 135.Is [3^(1/2).x^2 + 5x -11]/[3.x^2 + 9] a rational expression? Why? by Surbhi Agarwal. Answered on Feb 28, 2008 at 7:12 pm I.S.T. |
| Answer 135. Yes. Because it is of the form polynomial/ polynomial and denominator not equal to zero. |