# if there were 17 rows in the auditorium, how many seats will be there in the middle row?

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## The school auditorium was to be constructed to accommodate at least 1500 people.

The school auditorium was to be constructed to accommodate at least 1500 people.

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The school auditorium was to be constructed to accommodate at least 1500 people. The chairs are to be placed in concentric circular arrangement in such a way that each succeeding circular row has 10 seats more than the previous one.

If the first circular row has 30 seats, how many seats will be there in the 10th row?

For 1500 seats in the auditorium, how many rows need to be there?

OR

If 1500 seats are to be arranged in the auditorium, how many seats are still left to be put after the 10th row?

If there were 17 rows in the auditorium, how many seats will be there in the middle row?

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### SOLUTION

**i.**Since each row is increasing by 10 seats, so it is an AP with first term a = 30, and common difference d = 10.

So number of seats in 10th row = a10 = a+ 9d

= 30 + 9 × 10 = 120

**ii.**Sn =

n2(2a+(n-1)d) 1500 = n2(2×30+(n-1)10) 3000 = 50n + 10n2 n2 + 5n – 300 = 0

n2 + 20n – 15n – 300 = 0

(n + 20) (n – 15) = 0

Rejecting the negative value, n = 15

**OR**

No. of seats already put up to the 10th row = S10

S10 = 102

{2 × 30 + (10 – 1)10}

= 5(60 + 90) = 750

So, the number of seats still required to be put is 1500 – 750 = 750

**iii.**If no. of rows = 17

Then the middle row is the 9th row

a8 = a + 8d = 30 + 80 = 110 seats

Concept: Arithmetic Progression

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## [Case Based] If there were 17 rows in the auditorium, how many seats

Question 37 (iii) If there were 17 rows in the auditorium, how many seats will be there in the middle row? If total number of rows are 17 Middle row = 9th row We need to find how many seats will be there in the middle row i.e. we need to find a9 We know that an = a + (n − 1)d Putting n

**Check sibling questions**

## Question 37 (iii) - CBSE Class 10 Sample Paper for 2023 Boards - Maths Standard - Solutions of Sample Papers for Class 10 Boards

Last updated at March 16, 2023 by Teachoo

## If there were 17 rows in the auditorium, how many seats will be there in the middle row?

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### Transcript

Question 37 (iii) If there were 17 rows in the auditorium, how many seats will be there in the middle row? If total number of rows are 17 Middle row = 9th row We need to find how many seats will be there in the middle row i.e. we need to find a9 We know that an = a + (n − 1)d Putting n = 9, a = 30, d = 10 a8 = 30 + (9 − 1) × 10 = 30 + 8 × 10 = 30 + 80 = 110 Thus, there are 110 seats in the middle row

**Next**: Question 38 (i) [Case Based] Important →

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### Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

## CBSE Class 10 Math Standard Sample Paper 2022 Solutions

CBSE Class 10 Math Standard Sample Paper 2022 Questions and Answers Solution. CBSE Sample Paper 2022 - 23 Math Standard with Marking Scheme

## CBSE Class 10 Math Standard Sample Paper 2022 Solutions

Krishna September 17, 2022

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Advertisement **CBSE Class 10 Math Standard Sample Paper 2022 – 23 Solutions**

**CBSE Class 10 Math Standard Sample Paper 2022:**Central Board of Secondary Education(CBSE) has released the CBSE Class 10 Math Standard Sample Paper 2022 – 23 on its official website on 16th September 2022.

**1.) Let a and b be two positive integers such that a = p3q4 and b = p2q3 , where p and q are**

prime numbers. If HCF(a,b) = pmqn and LCM(a,b) = prqs, then (m+n)(r+s)=

(a) 15 (b) 30 (c) 35 (d) 72

**Ans- (c) 35**

**2.) Let p be a prime number. The quadratic equation having its roots as factors of p is**

(a) x2 –px +p=0 (b) x2–(p+1)x +p=0 (c) x2+(p+1)x +p=0 (d) x2 –px+p+1=0

**Ans- (b) x2–(p+1)x +p=0**

**3.) If α and β are the zeros of a polynomial f(x) = px2 – 2x + 3p and α + β = αβ, then p is**

(a)-2/3 (b) 2/3 (c) 1/3 (d) -1/3

Ans- (b) 2/3

**4.) If the system of equations 3x+y =1 and (2k-1)x +(k-1)y =2k+1 is inconsistent, then k =**

(a) -1 (b) 0 (c) 1 (d) 2

**Ans – (d) 2**

**5.) If the vertices of a parallelogram PQRS taken in order are P(3,4), Q(-2,3) and R(-3,-2), then the coordinates of its fourth vertex S are**

(a) (-2,-1) (b) (-2,-3) (c) (2,-1) (d) (1,2)

**Ans- (c) (2,-1)**

**6.) ∆ABC~∆PQR. If AM and PN are altitudes of ∆ABC and ∆PQR respectively and AB2: PQ2 = 4 : 9, then AM: PN =**

(a) 3:2 (b) 16:81 (c) 4:9 (d) 2:3

**Ans – (d) 2:3**

**7.) If x tan**

**60°cos60°**

**= sin**

**60°cot60°**

**, then x =**

(a) cos30° (b) tan30° (c) sin30° (d) cot30°

**Ans – (b) tan30**

**°**

**8.) If sinθ + cosθ =**

**√2**

**, then tanθ + cot θ =**

(a) 1 (b) 2 (c) 3 (d) 4

**Ans- (b) 2**

**9.) In the given figure, DE ∥ BC, AE = a units, EC =b units, DE =x units and BC = y units. Which of the following is true?**

(a) x= a+b/ (b) y= ax/a+b (c) x= ay/a+b d) x/y =a/b

**Ans – (c) x= ay/a+b**

**10.) ABCD is a trapezium with AD**

**∥**

**BC and AD = 4cm. If the diagonals AC and BD intersect each other at O such that AO/OC = DO/OB =1/2, then BC =**

(a) 6cm (b) 7cm (c) 8cm (d) 9cm

**Ans – (c) 8cm**

**11.) If two tangents inclined at an angle of 60ᵒ are drawn to a circle of radius 3cm, then the length of each tangent is equal to**

a) 3√3 cm (b) 3cm (c) 6cm (d) 3√3cm

**Ans – (d) 3√3cm**

**12.) The area of the circle that can be inscribed in a square of 6cm is**

(a) 36π cm2 (b) 18π cm2 (c) 12 π cm2 (d) 9π cm2

**Ans – (d) 9π cm2**

**13.) The sum of the length, breadth and height of a cuboid is 6√3cm and the length of its diagonal is 2√3cm. The total surface area of the cuboid is**

(a) 48 cm2 (b) 72 cm2 (c) 96 cm2 (d) 108 cm2

**Ans – (c) 96 cm2**

**14.) If the difference of Mode and Median of a data is 24, then the difference of median and mean is**

(a) 8 (b) 12 (c) 24 (d) 36

**Ans – (b) 12**

**15.) The number of revolutions made by a circular wheel of radius 0.25m in rolling a distance of 11km is**

(a) 2800 (b) 4000 (c) 5500 (d) 7000

**Ans – (d) 7000**

**16.) For the following distribution,**

**Class**0-5 5-10 10-15 15-20 20-25

**Frequency**10 15 12 20 9

the sum of the lower limits of the median and modal class is

(a) 15 (b) 25 (c) 30 (d) 35

**Ans – (b) 25**

**17.) Two dice are rolled simultaneously. What is the probability that 6 will come up at least once?**

(a)1/6 (b) 7/36 (c) 11/36 (d) 13/36

Ans – (c) 11/36

**18.) If 5 tanβ =4, then 5 sinβ – 2 cosβ /5 sinβ + 2 cosβ =**

(a) 1/3 (b) 2/5 (c) 3/5 (d) 6

**Ans –**

**(a) 1/3**

**19.) DIRECTION:**In the question number 19 and 20, a statement of

**assertion (A)**is followed by a statement of

**Reason (R)**.

Choose the correct option

**Statement A (Assertion):**If product of two numbers is 5780 and their HCF is 17, then their LCM is 340

**Statement R( Reason)**

**:**HCF is always a factor of LCM

a.) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A)

b.) Both assertion (A) and reason (R) are true and reason (R) is not the correct explanation of assertion (A)

Guys, does anyone know the answer?