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[mathjax] Question 1 A Write the first three terms of the following sequences defined by: t n = 3n + 1 Sol : Given: t n = 3n + 1 Taking n = 1, we get t 1 = 3(1) + 1 = 3 + 1 = 4 Taking n = 2, we get t...
[mathjax] Question 1 Divide 12 into two parts such that their product is 32. Sol : Let the first number be ‘X’, so the other number will be ’(12–X)’. ∵ X (12 – X) = 32 12X – X 2 = 32 X 2 – 12X + 32 =...
[mathjax] Question 1 A Write the discriminate of each of the following quadratic equation: x 2 + 4x + 3 =0 Sol : d = b 2 – 4ac d = (4) 2 – 4 (1) (3) d = 16 – 12 d = 4 Question 1 B Write the...
[mathjax] Question 1 Determine whether $x=\frac{3}{2}$ and $x=-\frac{4}{3}$ are the solutions of the equation 6x 2 -x-12=0 or not. Sol : Put both the values of x in the equation. When $x=\frac{3}{2}$...
[mathjax] Question 1 A Check whether the following are quadratic equations: (x − 2) (x + 1) = (x − 1) (x + 3) Sol : Given; (x − 2) (x + 1) = (x − 1) (x + 3) ⇒ x 2 + x − 2x − 2 = x 2 + 3x − x − 3 ⇒ x...
[mathjax] Question 1 A Which of the following is a quadratic polynomial? (i) 2 - 13x 2 (ii) x+ 1x√ (iii) x+ 1x (iv) x 2 +3 x−−√+2 Sol : (i) On solving the equations, 2−13x2 Re-writing in the format...
[mathjax] Question 1 The following distribution gives the daily income of 50 workers of a factory: Daily income (in Rs) 100-120 120-140 140-160 160-180 180-200 Number of workers 12 14 8 6 10 Convert...
[mathjax] Question 1 Find the median of the following data: Sol : Median $=$ size of $\frac{(\text { cumulative frequency }+1)^{\text {th }}}{2}$ item or $\frac{(n+1)^{t h}}{2}$ Median...
[mathjax] Question 1 Find mode of the following data: 64, 61, 62, 62, 63, 61, 63, 64, 64, 60, 65, 63, 64, 65, 66, 64 Sol : Here, we can see that 64 observation has the maximum frequency. Hence, Mode...
[mathjax] Question 1 The mean of 11 results is 30. If the mean of the first 6 results is 28 and that of last 6 results is 32, find the 6th result. Sol : Let the 6 th number be x Given that mean of 11...
[mathjax] Question 1 Sides of some triangles are given below. Determine which of them are right triangles (i) 8 cm, 15 cm, 17 cm (ii) (2a —1) cm, 22–√ cm and (2a + 1) cm (iii) 7 cm, 24 cm, 25 cm (iv)...
[mathjax] Question 1 In two similar triangles ABC and DEF, AC = 3 cm and DF = 5 cm. Find the ratio of the areas of the two triangles. Sol : Given: ΔABC ~ ΔDEF and AC = 3 cm and DF = 5 cm To find:...