WELCOME IN THE WORLD OF UNDERSTANDING

1.   Which term of the A.P. 3, 15, 27, 39, …… will be 120 more than its 21st term? 2.  Find c if the system of equations cx + 3y + (3 – c) = 0, 12x + cy – c = 0 has infinitely many solutions? 3.  A father’s age is three times the sum of the ages of his two children. After 5 years his age will be two times the sum of their ages. Find the present age of the father.  4.  Prove that (sin θ + cosec θ ) 2  + (cos θ + sec θ) 2  = 7 + tan 2  θ + cot 2  θ. 

  1.  Find the number of natural numbers between 101 and 999 which are divisible by both 2 and 5 .  2.   Solve the following pair of linear equations: 21x + 47y = 110 and 47x + 21y = 162   3. Prove that sin 6 θ + cos 6 θ + 3sin 2 θ cos 2 θ = 1   4. Explain the mechanism of photosynthesis 

  ( CBSE 2011)  1.  Find how many two-digit numbers are divisible by 6?  2.    Find an A.P. whose fourth term is 9 and the sum of its sixth term and the thirteenth term is 40.  3.  If pth, qth and rth terms of an A.P. are a, b, c respectively, then show that (a – b)r + (b – c)p + (c – a)q = 0. 4. I n Figure, an equilateral triangle has been inscribed in a circle of radius 6 cm. Find the area of the shaded region. [Use π = 3.14] 

 1. P and Q are the two points on the ground on either side of the pole. If the angle of elevation observed from point P and Q is 30 degrees and 60 degrees respectively the distance between the point P and Q is 84√3 find the height of Pole.  2.  Calculate the area bounded by the line x + y = 10 and both the co-ordinate axes. 3.  A man earns ₹600 per month more than his wife. One-tenth of the man’s salary and l/6 th  of the wife’s salary amount to ₹1,500, which is saved every month. Find their incomes. 4.  Atomic number of a few elements are given below 10, 20, 7, 14  (a) Identify the elements  (b) Identify the Group number of these elements in the Periodic Table  (c) Identify the Periods of these elements in the Periodic Table  (d) What would be the electronic configuration for each of these elements?  (e) Determine the valency of these elements

 1. Draw the graph of the pair of equations 2x + y = 4 and 2x – y = 4. Write the vertices of the triangle formed by these lines and the y-axis. Also find the area of this triangle. 2. 6/5, a , 4 are in Ap find the value of a  3. How many terms of the AP : 9, 17, 25, ... must be taken to give a sum 636?  4. The shadow of a tower standing on a level plane is found to be 50 m longer when Sun’s elevation is 30° than when it is 60°. Find the height of the tower

1. Write the balanced chemical equations for the following reactions and identify the type of reaction in each case (a) Nitrogen gas is treated with hydrogen gas in the presence of a catalyst at 773K to form ammonia gas. (b) Limestone is heated strongly to form quicklime and carbon dioxide gas is evolved 2. List the common food chain of a pond ecosystem 3. Why NaCl does not conduct electricity in a solid-state whereas it does conduct electricity in aqueous solution as well as in molten state 4. Solve the equations 5x – y = 5 and 3x – y = 3 graphically. 

 1. The Graph of Equation 5x - 2y + 1 = 0 and 4y -3x +5 = 0, Intersect at a Point (a,b). Write the value of (2a-3b)  2. Write all about Ozone  3. If Sn Denote the Sum of the  n term of AP Prove that S 12 = 3(S 8 -S 4 )  4.  Find the value of “x” in the polynomial 2a 2  + 2xa + 5a + 10 if (a + x) is one of its factors

 Date- 14 September 2020  1. The diameters of front and rear wheels of a tractor are 80 cm and 2 m respectively. Find the number of revolutions that rear wheel will make in covering a distance in which the front wheel makes 1400 revolutions.  2. The angles of a triangle are in AP. The greatest angle is twice the least. Find all the angles of the triangle. 3. Given that α + β = 90°, show that 4. Why do we store silver chloride in dark coloured bottles?

  13 September 2020  1.  If x= 4CosA + 5 Sin A and Y= 4sinA -5CosA then find the Value of x 2 + y 2 2.  In Fig a circle of radius 7.5 cm is inscribed in a square. Find the area of the shaded region (Use π = 3.14)                                                 Solution-  3 . In the equations shown below, a and b are unknown constants.        3ax + 4y = −2         2x+ by = 14  If (–3, 4) is the solution of the given equations, what are the values of a and b?  4.  The sum of n terms of an AP is 8558. If the 15 term is 97 and the 10th term is 32. What is the nth term?

12 September 2020  1. If sinθ = 1/3, the then find the value of  (9 cot 2 θ + 9) is  Solution 1 Solution 2                                        Solution 3 -  2. Which of the following can be the nth term of an AP? 3n + 1, 2n 2 + 3, n 3 + n. Give reasons. Hint -  put n=1,2,3 respectively in all the three equation then see which follow the rule of AP  3. If (x – 2) is a factor of x 3 +ax 2 +bx+16 and b = 4a, then find the values of a and b. 4. Find the sum of all two-digit natural numbers which are divisible by 7 Solution - 1  Solution- 2 

                                                                                                                                 11 September 2020  1.  If sin θ + cos θ = √3  , then prove that tan θ + cot θ = 1 Solution 1   Solution 2  2.  The lower window of a house is at a height of 2 m above the ground and its upper window is 4 m vertically above the lower window. At a certain instant, the angles of elevation of a balloon from these windows are observed to be 60 Degree and 30 Degree, respectively. Find the height of the balloon above the ground. 3. What is Joule’s heating effect? List its four applications in daily life.                                                                             4. What is electrical resistivity? In a series of an electrical circuit comprising a resistor made up of a metallic wire, the ammeter reads 5 A. The reading of the ammeter decreases to half when the length of the wire is doubled. Why?