All questions

• Q.3 (B)(iv) In a general store the prices of different articles and its demand is shown in the following frequency distribution table. Find the Median of the prices.Price in RupeesNo. of ArticlesLess than 2014020—4010040—608060—806080—10020 Answer: Median price = ₹ 32 Treat \"less than 20\" as 0–20. Cumulative frequencies: 140, 240, 320, 380, 400. N = 400, N/2 = 200. The cumulat... Statistics 1 answer
• Q.4 (i) Find the value of ‘m’ if the quadratic equation \((m - 12)x^2 + 2(m - 12)x + 2 = 0\) has real and equal roots. Answer: m = 14 a = m – 12, b = 2(m – 12), c = 2. For real and equal roots, b² - 4ac = 0 : 4(m-12)² - 8(m-12) = 0 4(m-12) [(m-12) - 2] = 0 4(... Quadratic Equations 1 answer
• Q.4 (ii) A farmer borrows ₹ 1,000 and agrees to repay with a total interest of ₹ 140, in 12 instalments. Each instalment being less than the preceding instalment by ₹ 10. What should be the amount of his first and last instalment ? Answer: First instalment ₹ 150, last instalment ₹ 40 Total amount repaid = 1000 + 140 = ₹ 1140. The instalments form an A.P. with n = 12, d... Arithmetic Progression 1 answer
• Q.4 (iii) The following table shows the marks of 180 students in Mathematics.MarksNo. of Students0—102510—20x20—303030—402x40—5065Find the value of ‘x’ and draw histogram. Answer: x = 20 25 + x + 30 + 2x + 65 = 180, so 3x + 120 = 180, 3x = 60, x = 20. Frequencies: 0–10: 25, 10–20: 20, 20–30: 30, 30–40: 40, 40–5... Statistics 1 answer
• Q.5 (i) Draw the graphs representing the equation 2x = y + 2 and 4x + 3y = 24 on the same graph paper. Find the area of the triangle formed by these lines and the X-axis. Answer: Area = 10 square units 2x = y + 2, i.e. y = 2x – 2: points (1, 0), (0, –2), (3, 4). 4x + 3y = 24: points (6, 0), (0, 8), (3, 4). Plo... Linear Equations in Two Variables 1 answer
• Q.5 (ii) The following pie-diagram shows percentage of persons according to blood group in a blood group checking camp. Answer the following questions :[Pie diagram: O – 45%, B – 30%, A – 20%, AB – 5%](a) Find the measure of central angle for each bl… Answer: (a) O = 162°, B = 108°, A = 72°, AB = 18°; (b) 2000 persons (a) Central angle = percentage/100 × 360^° : O: 45/100 × 360 = 162^° ; B... Statistics 1 answer
• Q.1 (A)(i) \(\begin{vmatrix} 1 & 2 \\ 3 & 4 \end{vmatrix}\). Write the degree of the given determinant. Answer: B. 2 Answer: (B) 2 The determinant has 2 rows and 2 columns, so it is a determinant of order (degree) 2. Linear Equations in Two Variables 1 answer
• Q.1 (A)(ii) From the following equations which one is the quadratic equation ? Answer: B. x(x + 5) = 2 Answer: (B) x(x+5)=2 x(x+5)=2 ⇒ x²+5x-2=0 , a polynomial equation of degree 2. (A) gives x³+3x-5=0 (degree 3), (C) i... Quadratic Equations 1 answer
• Q.1 (A)(iii) Find the common difference of the following A.P. : 4, 4, 4, ... Answer: D. 0 Answer: (D) 0 d = t₂ - t₁ = 4 - 4 = 0 . Every term is the same, so the common difference is 0. Arithmetic Progression 1 answer
• Testnwiw s s kw s skw a am Chapter 1 Relations and Functions no answer
• The general solution of \(\frac{dy}{dx}+\frac yx=x^2\) is Answer: B. xy=x⁴/4+C I.F. =e^(∫ dx/x)=x ; d/dx(xy)=x³⇒ xy=x⁴/4+C . Differential Equations 1 answer
• A bacterial population grows at a rate proportional to its size and doubles in 2 hours. The time in which it becomes 8 times the original is Answer: B. 6 hours N=N₀e^kt , e^2k=2 . 8=2³⇒ t=3×2=6 h. Differential Equations 1 answer
• A random variable \(X\) has \(P(X=x)=kx\) for \(x=1,2,3,4\). Then \(E(X)\) is Answer: C. 3 k(1+2+3+4)=1⇒ k=frac110 ; E(X)=1+4+9+16/10=3 . Probability Distributions 1 answer
• The p.d.f. of \(X\) is \(f(x)=kx^2\) for \(0\le x\le3\) and 0 otherwise. Then \(P(X\le1)\) is Answer: C. frac127 ∫₀³kx²dx=9k=1⇒ k=1/9 ; P(X≤1)=1/9·1/3=frac127 . Probability Distributions 1 answer
• A fair coin is tossed 6 times. The probability of getting exactly 3 heads is Answer: C. 5/16 binom63(1/2)⁶=20/64=frac516 . Binomial Distribution 1 answer
• The mean and variance of a binomial distribution are 4 and 3 respectively. The number of trials n is Answer: D. 16 q=3/4⇒ p=1/4 ; n=4/1/4=16 . Binomial Distribution 1 answer
• The value of \((1+i)^8\) is Answer: C. 16 (1+i)²=2i⇒(1+i)⁸=(2i)⁴=16 . Complex Numbers 1 answer
• If \(\omega\) is a complex cube root of unity, then \((1+\omega-\omega^2)^3=\) Answer: D. −8 1+ω=-ω²⇒(-2ω²)³=-8ω⁶=-8 . Complex Numbers 1 answer
• The number of distinct arrangements of the letters of the word BANANA is Answer: C. 60 6!/3! 2!=60 (A repeated 3 times, N twice). Permutations and combinations 1 answer
• A committee of 5 is to be formed from 6 men and 4 women. The number of ways in which it contains at least 3 women is Answer: B. 66 binom43binom62+binom44binom61=60+6=66 . Permutations and combinations 1 answer
• The distance between the parallel lines \(3x+4y=5\) and \(6x+8y=25\) is Answer: B. 3/2 Write the second as 3x+4y=12.5 : d=|12.5-5|/5=1.5 . Straight Line 1 answer
• The centre and radius of the circle \(x^2+y^2-6x+8y=0\) are Answer: B. (3,-4) and 5 Centre (-g,-f)=(3,-4) , r=√(9+16)=5 . Circle 1 answer
• The eccentricity of the hyperbola \(\frac{x^2}{16}-\frac{y^2}{9}=1\) is Answer: D. 5/4 e=√(1+b²/a²)=sqrt1+frac916=5/4 . Conic Sections 1 answer
• The length of the latus rectum of the ellipse \(\frac{x^2}{25}+\frac{y^2}{16}=1\) is Answer: A. 32/5 2b²/a=2×16/5=32/5 . Conic Sections 1 answer