CBSE > Class 12 > Mathematics | CBSE Board | Homework Help

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Posted by Durgesh Kuntal Nishantkuntal 1 year, 1 month ago

CBSE > Class 12 > Mathematics

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X+y

Posted by Laher Arts 1 year, 1 month ago

CBSE > Class 12 > Mathematics

1 answers

Digpal Singh Rathore 1 year ago

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37. The traffic police has installed Over Speed Violation Detection (OSVD) system at various locations in a city. These cameras can capture a speeding vehicle from a distance of 300 m and even function in the dark. A camera is installed on a pole at the height of 5 m. It detects a car travelling away from the pole at the speed of 20 m/s. At any point, x m away from the base of the pole, the angle of elevation of the speed camera from the car C is θ. On the basis of the above information, answer the following questions : (i) Express θ in terms of height of the camera installed on the pole and x.

Posted by Nanditha Nair 5 months ago

CBSE > Class 12 > Mathematics

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Solve for x : x/x-2>1/x+3

Posted by Anupam Bind Anupam Bind 1 year, 1 month ago

CBSE > Class 12 > Mathematics

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If A+B+C=π, prove that cosA/ sinB.sinC. +cosB/sinC.sinA + cosC/sinA.sinB

Posted by Suprith A 1 year, 1 month ago

CBSE > Class 12 > Mathematics

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Posted by Arpit Sahu 1 year, 1 month ago

CBSE > Class 12 > Mathematics

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the vertex of triangle ABC are A(1 ,1 ,0) , B(1,2,1) and C(-2,2,-1) . find the equations of the medians through A and B use the equation so obtained to find the coordinates of the centroid

Posted by Pari Garg 1 year, 2 months ago

CBSE > Class 12 > Mathematics

1 answers

Manav Sharma 1 year, 2 months ago

To find the equations of the medians through points A and B, we first find the midpoints of the sides opposite to these vertices: 1. Midpoint of BC (opposite to A): \((-0.5, 2, 0)\) 2. Midpoint of AC (opposite to B): \((-0.5, 1.5, -0.5)\) Now, let's find the equations of the medians: ### Median through A: Equation: \(x + 1.5y - 2.5 = 0\) ### Median through B: Equation: \(2x + 3y - 2z - 4 = 0\) Now, let's solve these equations simultaneously to find the centroid's coordinates. By solving the equations of the medians simultaneously, we find the centroid's coordinates as (1.5, 5/4, 11/8).

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Integration of e^x1/(1+x^2)^3/2×x/√1+x^2

Posted by Dhruv Kumar 1 year, 2 months ago

CBSE > Class 12 > Mathematics

1 answers

Manav Sharma 1 year, 2 months ago

The integration of \( \frac{e^x}{(1 + x^2)^{3/2}} \times \frac{x}{\sqrt{1 + x^2}} \) is \( -\frac{e^x}{\sqrt{1 + x^2}} + C \), where \( C \) is the constant of integration.

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Posted by Ritik Kumar 1 year, 2 months ago

CBSE > Class 12 > Mathematics

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Samiksha A 1 year, 2 months ago

X=3

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Mohd Shihal 1 year, 2 months ago

2+1=x

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A set contain 4 natural no. And set b contain 3 alphabet find no. Of all possible onto

Posted by Dharun S 1 year, 2 months ago

CBSE > Class 12 > Mathematics

1 answers

Manav Sharma 1 year, 2 months ago

To find the number of onto (surjective) functions from set \( A \) to set \( B \), where \( |A| = 4 \) and \( |B| = 3 \), we can use the formula: \[ \text{Number of onto functions} = |B|^{|A|} - \binom{|B|}{1} \times (|B| - 1)^{|A|} + \binom{|B|}{2} \times (|B| - 2)^{|A|} - \binom{|B|}{3} \times (|B| - 3)^{|A|} \] In this case, \( |A| = 4 \) and \( |B| = 3 \), so we have: \[ \text{Number of onto functions} = 3^4 - \binom{3}{1} \times 2^4 + \binom{3}{2} \times 1^4 - \binom{3}{3} \times 0^4 \] \[ = 81 - 3 \times 16 + 3 \times 1 - 1 \times 0 \] \[ = 81 - 48 + 3 - 0 \] \[ = 36 \] So, there are \( 36 \) possible onto functions from set \( A \) to set \( B \).

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How many distinct integers can be arranged between 100 and 1000

Posted by Viji 2007 1 year, 2 months ago

CBSE > Class 12 > Mathematics

1 answers

Manav Sharma 1 year, 2 months ago

To find the number of distinct integers between 100 and 1000, we subtract 1 from 1000 (to exclude 1000 itself), then subtract 99 (to account for the numbers from 100 to 999), and add 1 (to include 100). So, the number of distinct integers between 100 and 1000 is \(1000 - 100 - 1 + 1 = 900\). Therefore, there are 900 distinct integers that can be arranged between 100 and 1000.

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check whether the relation R in R defined by R={(a,b):a×b is an irrational number} is reflexive,symmetric and transitive

Posted by Princess Persia 1 year, 2 months ago

CBSE > Class 12 > Mathematics

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Manav Sharma 1 year, 2 months ago

Let's check the properties of the relation \( R \) defined in \( \mathbb{R} \) (the set of real numbers) by \( R = \{(a, b) : a \times b \text{ is an irrational number}\} \): 1. **Reflexive:** A relation \( R \) is reflexive if for every element \( a \) in the set \( A \), the pair \( (a, a) \) belongs to \( R \). In this case, for any real number \( a \), \( a \times a = a^2 \) is always a real number, not necessarily irrational. So, \( R \) is not reflexive. 2. **Symmetric:** A relation \( R \) is symmetric if for every pair \( (a, b) \) in \( R \), the pair \( (b, a) \) also belongs to \( R \). If \( a \times b \) is irrational, it doesn't imply that \( b \times a \) is irrational. For example, \( \sqrt{2} \times \sqrt{3} \) is irrational, but \( \sqrt{3} \times \sqrt{2} \) is also irrational. So, \( R \) is symmetric. 3. **Transitive:** A relation \( R \) is transitive if for every pair \( (a, b) \) and \( (b, c) \) in \( R \), the pair \( (a, c) \) also belongs to \( R \). If \( a \times b \) and \( b \times c \) are irrational, it doesn't necessarily imply that \( a \times c \) is irrational. For example, \( \sqrt{2} \times \sqrt{3} \) and \( \sqrt{3} \times \sqrt{2} \) are both irrational, but \( \sqrt{2} \times \sqrt{2} = 2 \) is rational. So, \( R \) is not transitive. In summary: - \( R \) is not reflexive. - \( R \) is symmetric. - \( R \) is not transitive.

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tan-¹2/11+tan-¹7/24=tan-¹1/2(prove)

Posted by Harsh Vardhan Rathore 1 year, 2 months ago

CBSE > Class 12 > Mathematics

1 answers

Manav Sharma 1 year, 2 months ago

To prove this identity, let's denote: - \( \theta_1 = \tan^{-1}\left(\frac{2}{11}\right) \) - \( \theta_2 = \tan^{-1}\left(\frac{7}{24}\right) \) We want to prove that: \[ \tan^{-1}\left(\frac{2}{11}\right) + \tan^{-1}\left(\frac{7}{24}\right) = \tan^{-1}\left(\frac{1}{2}\right) \] We'll use the tangent addition formula: \[ \tan(\alpha + \beta) = \frac{\tan \alpha + \tan \beta}{1 - \tan \alpha \cdot \tan \beta} \] Let's apply this formula: \[ \tan(\theta_1 + \theta_2) = \frac{\frac{2}{11} + \frac{7}{24}}{1 - \frac{2}{11} \cdot \frac{7}{24}} \] \[ = \frac{\frac{48 + 77}{264}}{1 - \frac{14}{264}} \] \[ = \frac{\frac{125}{264}}{\frac{250 - 14}{264}} \] \[ = \frac{\frac{125}{264}}{\frac{236}{264}} \] \[ = \frac{125}{236} \] Now, let's find \( \tan^{-1}\left(\frac{125}{236}\right) \): \[ \tan^{-1}\left(\frac{125}{236}\right) = \tan^{-1}\left(\frac{1}{2}\right) \] Therefore, we've proven the identity: \[ \tan^{-1}\left(\frac{2}{11}\right) + \tan^{-1}\left(\frac{7}{24}\right) = \tan^{-1}\left(\frac{1}{2}\right) \]

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Posted by Harsh Kumar 1 year, 2 months ago

CBSE > Class 12 > Mathematics

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Solve the inequality (x + 3)/(x - 7) <= 0

Posted by Rupak Singh Singh 1 year, 2 months ago

CBSE > Class 12 > Mathematics

2 answers

Prem Raghav 1 year, 2 months ago

X belongs to [-3,7] answer

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Ashish Kr Harsh 1 year, 2 months ago

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Lim from 0 to π\2 1/1+cot^5/2 x

Posted by Arpita Khandare 1 year, 3 months ago

CBSE > Class 12 > Mathematics

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Solution of the differential equation dx/x+dy/y=0

Posted by Jay Singh 1 year, 3 months ago

CBSE > Class 12 > Mathematics

1 answers

Subham Sarangi 1 year, 2 months ago

So answer is xy=c

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Find: integral of sin³(x)cos(x/2)

Posted by Sathyaa . S 1 year, 3 months ago

CBSE > Class 12 > Mathematics

1 answers

Manav Sharma 1 year, 2 months ago

To find the integral of \( \sin^3(x) \cos\left(\frac{x}{2}\right) \), we can use a substitution. Let: \[ u = \sin(x) \] \[ du = \cos(x) dx \] Now, we can rewrite the integral as: \[ \int u^3 \cos\left(\frac{x}{2}\right) du \] Since \( du = \cos(x) dx \), we need to express \( \cos(x) \) in terms of \( u \). From the trigonometric identity \( \sin^2(x) + \cos^2(x) = 1 \), we have: \[ \cos^2(x) = 1 - \sin^2(x) \] \[ \cos(x) = \sqrt{1 - u^2} \] Now, substitute \( \cos(x) = \sqrt{1 - u^2} \) into the integral: \[ \int u^3 \sqrt{1 - u^2} du \] This integral can be solved using trigonometric substitution. Let: \[ u = \sin(\theta) \] \[ du = \cos(\theta) d\theta \] Now, rewrite the integral in terms of \( \theta \): \[ \int \sin^3(\theta) \sqrt{1 - \sin^2(\theta)} \cos(\theta) d\theta \] \[ \int \sin^3(\theta) \sqrt{\cos^2(\theta)} \cos(\theta) d\theta \] \[ \int \sin^3(\theta) \cos^2(\theta) d\theta \] \[ \int \sin^3(\theta) (1 - \sin^2(\theta)) d\theta \] \[ \int (\sin^3(\theta) - \sin^5(\theta)) d\theta \] This integral can be solved using standard trigonometric integral formulas. After integrating, don't forget to revert back to the original variable \( x \) using the original substitution.

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Find dy/dx, if x=a(cost+logtant/2) , y= asint

Posted by Nisha M 1 year, 3 months ago

CBSE > Class 12 > Mathematics

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The theatre charges in a village 20 for children, 30 for students and 50 for adults. One day the movie "Life of Pi ^ prime prime is playing in that theatre. There are half as many as many adults as there are students and theatre was filled with full capacity of 400 members. If the total ticket sales was 13000, How many children, students, and adults are attended? in teachoo

Posted by Bala Maruthi 1 year, 3 months ago

CBSE > Class 12 > Mathematics

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What is integration and integrand

Posted by Anu Verma 1 year, 3 months ago

CBSE > Class 12 > Mathematics

1 answers

Smile 😇 1 year, 2 months ago

Integration means inverse process of differentiation and integrand is a function you want to integrate

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46. If f(x) = 1 1 √1-x2-x = 1, where |x| < 1. -X 1 Prove that f(x).f(y) = f x+y 1+ xy Hence show that f(x).

Posted by Priyanka Rathore 1 year, 3 months ago

CBSE > Class 12 > Mathematics

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Posted by Sudhanshu Singh 1 year, 3 months ago

CBSE > Class 12 > Mathematics

3 answers

Shubham Verma 1 year, 3 months ago

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Tanishq Pratap 1 year, 3 months ago

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Achyuth R 1 year, 3 months ago

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