ধরা যাক x হল 25.6 এবং 32.4 এর গড় সমানুপাতিক এবং y হল 32 এবং 48 এর তৃতীয় সমানুপাতিক।

Let x be the mean proportional of 25.6 and 32.4 and y be the third proportional of 32 and 48. Then, 3x:2y=_____ मान लीजिए कि x, 25.6 और 32.4 का मध्यानुपाती है और y, 32 एवं 48 का तृतीयानुपाती है | तब 3x:2y=_____

Directions (Questions 1 to 5): Study the given table carefully and answer the questions that follow: Number of candidates appeared and qualified for a test (in hundreds) in 6 different years from 5 different zones. Year P Q R S T App. Qual. App. Qual. App. Qual. App. Qual. App. Qual. 2005 3.2 2.5 3.5 1.4 3.8 2.2 4.2 2.4 6.2 2.6 2006 4.6 3.4 6.9 4.2 6.9 4.4 7.4 3.3 6.2 4.8 2007 6.5 4.9 7.7 4.5 5.9 4.8 8.3 5.6 6.4 4.2 2008 7.4 5.7 5.4 3.4 7.2 3.2 9.3 6.4 7.8 6.2 2009 8.8 4.8 6.6 5.2 8.6 6.8 11.4 5.2 9.9 6.9 2010 9.2 5.6 10.6 6.4 10.3 7.4 14.2 11.4 11.8 9.4 Note: Here App. means Appeared and Qual. means Qualified. In which years was in zones the difference between the appeared candidates and qualified candidates the second lowest? (a) 2005 (b) 2007 (c) 2008 (d) 2009 (e) 2010

It x\ a n d\ y vary inversely, fill in the following blanks: (i) x 12 16 ... 8 ... y ... 6 4 ... 0.25 (ii) x 16 32 8 128 y 4 ... ... 0.25 (iii) x, 9, ..., 81, 243 y, 27, 9, ..., 1

Directions (Questions 6 to 10): Study the following table carefully and answer the questions that follow: Semester Fees (in Rs thousands) For Five Different Courses in 6 Different Years Years Course B.Tech M.Sc. B.Ed. M.Phil Diploma 2005 11.5 5.8 7.5 4.7 1.8 2006 14.5 6.4 11.6 5.8 3.2 2007 20.0 10.2 13.9 8.6 4.8 2008 22.2 14.6 15.8 12.7 5.6 2009 35.8 17.7 18.5 25.1 12.5 2010 50.7 20.9 22.6 18.9 14.9 What was the approximate per cent increase in the semester fees of B.Ed. course in the year 2007 as compared to the previous year? (a) 26% (b) 30% (c) 20% (d) 16% (e) 10%

Objective question . i. A certains compound has the molecular formula X_(4) O_(6) . If 10 g of X_(4) O_(6) has 5.72 g X , then atomic mass of X is: a. 32 amu b. 42 amu c. 98 amu d. 37 amu ii. For 109% labelled oleum, if the number of moles of H_(2)SO_(4) and free SO_(3) be p and q , respectively, then what will be the value of (p - q)/(p + q) a. 1//9 b. 9 c. 18 d. 1//3 iii. Hydrogen peroxide in aqueous solution decomposes on warming to give oxygen according to the equation, 2H_(2) O_(2) (aq) rarr 2 H_(2) O (l) + O_(2) (g) Under conditions where 1 mol gas occupies 24 dm^(3), 100 cm^(3) of X M solution of H_(2) O_(2) produces 3 dm^(3) of O_(2) . Thus, X is a. 2.5 b. 0.5 c. 0.25 d. 1 iv. 4 g of sulphur is burnt to form SO_(2) which is oxidised by Cl_(2) water. The solution is then treated with BaCl_(2) solution. The amount of BaSO_(4) precipitated is: a. 0.24 mol b. 0.5 mol c. 1 mol d. 0.125 mol v. A reaction occurs between 3 moles of H_(2) and 1.5 moles of O_(2) to give some amount of H_(2) O . The limiting reagent in this reaction is a. H_(2) and O_(2) both b. O_(2) c. H_(2) d. Neither of them vi. 4 I^(ɵ) + Hg^(2+) rarr HgO_(4)^(-) , 1 mole each of Hg^(2+) and I^(ɵ) will form: a. 1 mol of HgI_(4)^(2-) b. 0.5 mol of HgI_(4)^(-2) 0.25 mol of HgI_(4)^(2-) 2 mol of HgI_(4)^(-2)

The ratio of coins 75, 50 paise and 25 paise is 4:5:6 . If total cost of all coins is 764, then the number of coins of 25 paise is. Options are (A) 48 (B) 40 (C) 32 (D) None of these.

In a triangle ABC if the equation of the medians AD and BE are 2x + 3y - 6=0 and 3x-2y-10=0 respectively and AD = 6, BE = 11, then find the area of the Triangle ABC : (A) 32 (B) 38 (C) 44 (D) 48

A tangent having slope of -4/3 to the ellipse (x^2)/(18)+(y^2)/(32)=1 intersects the major and minor axes at point Aa n dB , respectively. If C is the center of the ellipse, then the area of triangle A B C is 12s qdotu n i t s (b) 24s qdotu n i t s 36s qdotu n i t s (d) 48s qdotu n i t s

Factorise the expressions and divide them as directed. (y 2 y 10) 5) ll) (m 14m 32) (m 2) (ii) (5p 25p 20) (p -1) (iv) 4yz(z (v) 5pq (p2 -q2) 2p(p q) -98) 26y (5y 7) (vi) 12ry(9x2 16y2) 4xy (3x 4y) (vii 39y (50y