The coefficient of x3 in (2x – 3y) (4x2 + 6xy + 9y2 ) is
A) 8
B) – 27
C) 12
D) 9
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Coefficient of variation of two distributions are 60 and 70, and their standard deviations are 21 and 16, respectively. What are their arithmetic mean
Correct Answer - 35,20
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उपयुक्त सर्वसमिकाएँ प्रयोग करके निम्नलिखित का गुणनखण्ड कीजिए : (i) `9x^(2)+6xy+y^(2)` (ii) `4y^(2)-4y+1` (iii) `x^(2)-(y^(2))/(100)`
Correct Answer - (i) `(3x+y)(3x+y)" (ii) " (2y-1)(2y-1)" (iii) " (x+(y)/(10))(x-(y)/(10))`
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The coefficient of static friction between a block of mass 0.25 kg and a horizontal surface is 0.4. Find the horizontal force applied to it.
Given: μS = 0.4, m = 0.25 kg, g = 9.8 m/s2 To find: Force (FL) Formula: FL = μSN = μS(mg) Calculation: From formula, FL = 0.4 × 0.25 × 9.8 = 0.98 N The horizontal force applied...
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In case of coefficient of static friction (µs), kinetic friction (µk) and rolling friction (µr), which of the following relation is true
Correct option is: (A) µs > µk > µr
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A wooden block of 50 kg is at rest on the table. A force of 70 N is required to just slide the block. The coefficient of static friction is
Correct option is: (D) \(\frac{1}{7}\)
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(i) Coefficient of linear expansion is same for all substances. (ii) Metals have high values for the coefficient of linear
1. False. Coefficient of linear expansion is different for different substances. 2. True.
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Do coefficient of areal expansion and coefficient of volume expansion depend upon nature of material?
Yes, coefficient of areal expansion and coefficient of volume expansion depend upon nature of material.
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The coefficient of x^3 in (2x – 3y) (4x^2 + 6xy + 9y^2 ) is
Correct option is (A) 8 \((2x-3y)\) \((4x^2+6xy+9y^2)\) \(\because\) \(x^3\) will get by multiplying 2x with \(4x^2.\) \(\therefore\) Coefficient of \(x^3\) in \((2x-3y)\) \((4x^2+6xy+9y^2)\) is \(2\times4=8.\)
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Simplify: (3x+2)(9x^2-6xy+4y^2)
a3−b3=(a−b)(a2+ab+b2) a3+b3=(a+b)(a2−ab+b2) Given, (3x+2y)(9x2−6xy+4y2) =(3x)3+(2y)3 =27x3+8y3
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A cruve is respresented by `C=21x^(2)-6xy+29y^(2)+6x-58y-151=0` The lengths of axes are
`24x^(2)-6xy+29y+6x-58y-151=0` `2(x-3y+3)^(2)+2(3x+y-1)^(2)=180` or `((x-3y+3)^(2))/(60)+((3x+y-1)^(2))/(90)=1` or `((x-3y+3)/(sqrt(1+3^(2))sqrt(6)))^(2)+((3x+y-1)/(3sqrt(1+3^(2))))=1` Thus, C is an ellipse whose lengths of axes are `6,2sqrt(6)`. The minor and the major axes are `x-3y+3=0 and 3x+y-1=0`, respectively. Their point...
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