1847 + Interview Questions in Maths in Class 9 Page 32 InterviewSolution

1551.	The perimeter of a triangle is 32 cm and two of its sides measure 8 cm and 11 cm. Find the area of the triangle.
Answer» ANSWER :`8sqrt(30) CM^(2)`

Discussion

1552.	Factorise : 6x^(2) + 5x - 6
Answer» ANSWER :`(2x+3)(3x-2)`

Discussion

1553.	(i) How many lines can be drawn to pass through a given points ? (ii) How many lines can be drawn to pass through two given points? (iii) In how many points can the two lines at the most intersect? (iv) If A, B, Care three collinear points name all the line segments determined by them
Answer» Answer :(i)infinitely many (ii) ONE only (III) one POINT only(iv) `BAR(AB),bar(BC),bar(AC)`

Discussion

1554.	Three coins are tossed 30 times simultaneously. Each time the number of heads occurring was noted down as follows: Prepare a frequency distribution table for the data given above.
Answer» ANSWER :`(##NCERT_BEN_MAT_IX_C09_E01_003_A01##)`

Discussion

1555.	In what time will Rs 1,500 yield Rs 496,50 as compound interest at 20% per year compounded half-yearly ?
Answer» ANSWER :`1(1)/(2)` YEARS

Discussion

1556.	Find: (46656)^((-1)/(6))
Answer» ANSWER :`(1)/(6)`

Discussion

1557.	A village, having a population of 4000, requires 150litres of water per head per day. Ithas a tank measuring 20"\ "m"\ "xx"\ "15"\ "m"\ "xx"\ "6"\ "m. For how manydays will the water of this tanklast?
Answer» ANSWER :3 DAYS

Discussion

1558.	The mid-values of the class-intervals of a frequency distribution are respectively 15,20,25,30,…… The class interval of which the mid-value is 20 is
Answer» `12.5-17.5` `17.5-22.5` `18.5-21.5` `19.5-20.5` ANSWER :B

Discussion

1559.	If x ^(2) -x-6 and x ^(2) + 3x -18 have a common factor (x -a) then find the value of a.
Answer» ANSWER :`a =3`

Discussion

1560.	Find the remainder when p (x) = x ^(3) - 6x ^(2) + 14x -3 is divided b y g (x) =1-2x andverify the result by long division.
Answer» ANSWER :21/8

Discussion

1561.	What was the balance in her account as on 31-7-2006 ?
Answer» Rs 64000 Rs 44800 Rs 40320 none of the above SOLUTION :FIND the minimum BALACNE up to the MONTH of JULY

Discussion

1562.	Verify whether the following are zeroes of the polynomial, indicated against them : p(x) = 5x- pi, x = (4)/(5)
Answer» ANSWER :`(4)/(5)` is not a ZERO

Discussion

1563.	Simpilfy (2sqrt(5) + 3sqrt(2))
Answer» ANSWER :`(38+ 12SQRT(10))`

Discussion

1564.	Expand each of the following, using suitable identities (i) (x + 2y+ 4z) ^(2) (ii) (2a - 3b) ^(3) (iii) (-2a + 5b - 3c) ^(2) (iv) ((a)/(4) - (b)/(2) + 1) ^(2) (v) ( p +1) ^(3) (vi)(x - (2)/(3) y) ^(3)
Answer» Answer :(i) `x ^(2) + 4y ^(2) + 16 z ^(2) + 4xy + 16yz + 8xz` (ii) `8a ^(2) - 36a ^(2) b + 54 ab ^(2) - 27b ^(3)` (iii) `4a ^(2) + 25 b ^(2) + 9x^(2) - 20ab - 30 bc + 12 ac` (iv) `(a^(2))/(16) + (b ^(2))/(4) +1 - (ab)/(4) -b + a/2` (v) ` p ^(3) + 3P^(2) + 3p +1` (vi)` x ^(3) -2x ^(2) y + 4/3 xy ^(2) - (8)/(27) y ^(3)`

Discussion

1565.	State true or false .A circle divides the plane on which it lies into three parts.
Answer» ANSWER :1

Discussion

1566.	…………..should be added to x^(3) - 5x^(2) + x-8, so that the result is exactly divisible by (x-5).
Answer» 2 `-2` `-3` 3 Answer :C

Discussion

1567.	Construct a triangle whose sides are 3.6 cm , 3.0 cm and 4.8 cm. Bisect the smallest angle and measure each part.
Answer» Solution :To construct a triangle ABCin which `AB = 3.6cm , AC = 3.0cm and BC= 4.8cm` , use the following STEPS. (i) Draw a line segment BC of length `4.8cm`. (ii) From B, point A is at a distance of `3.6cm` . So having B as centre, draw an arc of radius `3.6cm`. (III) From C, point A is at a distance of 3cm. So, having C as centre, draw an arc of radius 3cm which intersect previous arc at A. (iv) Join AB and AC. Thus, `DeltaABC` is the required triangle. Here, angle B is smallest , as AC is the smallest side . To DIRECT angle B, we use the following steps. (i) Taking B as centre, we draw an are intersecting AB and BC at D and E, respectively. (ii) Taking D and E as centres we draw ARCS intersecting at P. (iii) Joining BP, we obtain angle bisector of `angleB`. (iv) Here, `angleABC = 39^(@)` Thus, `angleABD = angleDBC = (1)/(2)xx139^(@)= 19.5^(@)`

Discussion

1568.	The angle of elevation of the sun, when the length of the shadow of a tree (1/sqrt3) times the height of the tree is____
Answer» ANSWER :`(AB)/(a^2+b^2)(X^(a/b)+x^(b/a))=(a/b)^((a^2+b^2)/(a^2-b^2))`

Discussion

1569.	The volume of a hemisphere is 89""5/6cm^(3). Find its diameter.
Answer» ANSWER :7 CM

Discussion

1570.	The students of a class like at least one of the games out of Chess, Caroms and Judo. The number of students who like only Chess and Caroms, only Caroms and Judo, only Chess and Judo and the number of those who like all the three are equal. The number of students who like only Chess, only Caroms, only Judo and the number of those who like all the three are equal. A possible value of the number of students in the class is
Answer» 30 40 50 70 Solution :(i) Use VENN DIAGRAM (ii) GIVEN data can be expressed as (iii) Total number of STUDENTS is 7x.

Discussion

1571.	Express each of the following linear equations in two variables in the standard form ax + by +c = 0 and in each case state the values of a, b and c : 1/(6)x =1/4y+3
Answer» ANSWER :`a = 1/6, B = -1/4 , C = -3`

Discussion

1572.	Express each of the following linear equations in two variables in the standard form ax + by +c = 0 and in each case state the values of a, b and c : 5x -3y = 2.bar(8)
Answer» ANSWER :`a = 5, B = -3 , C = -2.bar8`

Discussion

1573.	Express each of the following linear equations in two variables in the standard form ax + by +c = 0 and in each case state the values of a, b and c : 4x = 5y +2
Answer» Answer :`a = 4, B = -5 , C = -2`

Discussion

1574.	Express each of the following linear equations in two variables in the standard form ax + by +c = 0 and in each case state the values of a, b and c : 3y=15
Answer» ANSWER :`a = 0, b = 3 , C = -15`

Discussion

1575.	Express each of the following linear equations in two variables in the standard form ax + by +c = 0 and in each case state the values of a, b and c : 4x-8=0
Answer» Answer :`a = 4, B = 0 , c = -8`

Discussion

1576.	Express each of the following linear equations in two variables in the standard form ax + by +c = 0 and in each case state the values of a, b and c : 2x-3y=0
Answer» ANSWER :`a = 2, B = -3 , C = -2`

Discussion

1577.	Express each of the following linear equations in two variables in the standard form ax + by +c = 0 and in each case state the values of a, b and c : 5y=3x
Answer» Answer :`a = 3, b = -5 , C = 0`

Discussion

1578.	Express each of the following linear equations in two variables in the standard form ax + by +c = 0 and in each case state the values of a, b and c : -3x+4y=12
Answer» ANSWER :`a = -3, b = 4 , c = -12`

Discussion

1579.	Express each of the following linear equations in two variables in the standard form ax + by +c = 0 and in each case state the values of a, b and c : 3x=7-2y
Answer» Answer :`a = 3, B = 2 , C = -7`

Discussion

1580.	Express each of the following linear equations in two variables in the standard form ax + by +c = 0 and in each case state the values of a, b and c : y=4x-1
Answer» ANSWER :`a = 4, B = -1 , C = -1`

Discussion

1581.	If x^(2) + mx - 28 = (x-7)(x+4), then m = ……… .
Answer» 3 `-3` 11 `-11` ANSWER :C

Discussion

1582.	If 4cos^(2)x=3 and x is an acute angle, find the value of : x
Answer» ANSWER :`x=30^(@)`

Discussion

1583.	A company manufactures car batteries of particular type. The life (in years) of 40 batteries was recorded as follows: Construct a grouped frequency distribution table with exclusive classes for this data, using class intervals of size 0.5 starting from the interval 2-2.5.
Answer» ANSWER :`(##NCERT_GUJ_MAT_IX_C09_E01_009_A01##)`

Discussion

1584.	Express each of the following decimal numbers in (p)/(q) form 3.127bar(7)
Answer» ANSWER :`(563)/(180)`

Discussion

1585.	It is required to make a closed cylindrical tank of height 1 m and base diameter 140 cm from a metal sheet. How many square metres of the sheet are required for the same ?
Answer» Answer :7.48 `m^(2)` SHEET is REQUIRED to MAKE the closed cyclindrical TANK

Discussion

1586.	Write whether the following statements are True or False. Justify your answer (i) A binomial has two terms (ii) Every polynomial is a binomial (iii) A binomial may have degree 3 (iv) Degree of zero polynomial is zero (v) The degree of x ^(2) + 2xy + y ^(2)is 2 (vi) pi r ^(2) is a monomial.
Answer» ANSWER :(i) True (ii) FALSE (III) True (iv) False (v)True (VI) True

Discussion

1587.	An overhead water tanker is in the shape of a cylinder has capacity of 61.6 m^3. The diameter of the tank is 5.6 m. Find the height of the tank.
Answer» ANSWER :` H= 2.5 m .`

Discussion

1588.	Draw a flowchart to pick the smallest among the two number
Answer»

Discussion

1589.	Dividing 2x^(3) + 6x^(2) + x + 5 by (x+3), the remainder is ……….. .
Answer» 2 3 1 0 Answer :B

Discussion

1590.	Simplify the following expressions : (sqrt5-sqrt3)(sqrt5+sqrt3)
Answer» ANSWER :2

Discussion

1591.	The value of a machine, purchased two years ago, depreciates at the annual rate of 10%. If its present value is Rs 97,200, find its value when it was purchased.
Answer» ANSWER :RS 1,20,000

Discussion

1592.	The value of a machine, purchased two years ago, depreciates at the annual rate of 10%. If its present value is Rs 97,200, findit value after 2 years
Answer» ANSWER :RS 78,732

Discussion

1593.	The mean of 200 items was 50. Later on, it was discovered that two items were misread as 92 and 8 instead of 192 and 88. Find the correct mean.
Answer» ANSWER :`50*9`

Discussion

1594.	How many litres of milk can a hemispherical bowl of diameter 10.5 cm hold ?
Answer» ANSWER :0.303 LITERS

Discussion

1595.	A spinner was spun 1000 times and the frequency of outcomes was recorded as in given table: Find (a) List the possible outcomes that you can see in the spinner(b) Compute the probability of each outcome. (c) Find the ratio of each outcome to the total number of times that the spinner spun (use the table)
Answer» ANSWER :0.2, 0.185

Discussion

1596.	5 conical tents with diameter 8 m and height 3 m are to be made. How many metres of 2 m wide tarpaulin will be required to make these 5 tents ? (pi=3.14)
Answer» ANSWER :157 m

Discussion

1597.	If secA=cosecA" and "0^(@) le A le 90^(@), state the value of A.
Answer» ANSWER :`45^(@)`

Discussion

1598.	If 2 (a ^(2) + b ^(2)) = (a+b)^(2), then show that a =b
Answer» Answer :(i) `3x (X-2) (x +2)` (ii) 4 (3Y +5) (y-1)`

Discussion

1599.	A child playingwith building blocks, which are of the shape of cubes, has built a structureas shown in Fig. 13.25. If the edge of each cube is 3 cm, find the volume ofthe structure built by the child.
Answer» Answer :The VOLUME of the STRUCTURE = 405 `cm^(3)`

Discussion

1600.	Evaluate the following uing suitable identities : (99)^(3)
Answer» ANSWER :9,70,299

Discussion

Explore topic-wise InterviewSolutions in .

The perimeter of a triangle is 32 cm and two of its sides measure 8 cm and 11 cm. Find the area of the triangle.

Factorise : 6x^(2) + 5x - 6

(i) How many lines can be drawn to pass through a given points ? (ii) How many lines can be drawn to pass through two given points? (iii) In how many points can the two lines at the most intersect? (iv) If A, B, Care three collinear points name all the line segments determined by them

Three coins are tossed 30 times simultaneously. Each time the number of heads occurring was noted down as follows: Prepare a frequency distribution table for the data given above.

In what time will Rs 1,500 yield Rs 496,50 as compound interest at 20% per year compounded half-yearly ?

Find: (46656)^((-1)/(6))

A village, having a population of 4000, requires 150litres of water per head per day. Ithas a tank measuring 20"\ "m"\ "xx"\ "15"\ "m"\ "xx"\ "6"\ "m. For how manydays will the water of this tanklast?

The mid-values of the class-intervals of a frequency distribution are respectively 15,20,25,30,…… The class interval of which the mid-value is 20 is

If x ^(2) -x-6 and x ^(2) + 3x -18 have a common factor (x -a) then find the value of a.

Find the remainder when p (x) = x ^(3) - 6x ^(2) + 14x -3 is divided b y g (x) =1-2x andverify the result by long division.

What was the balance in her account as on 31-7-2006 ?

Verify whether the following are zeroes of the polynomial, indicated against them : p(x) = 5x- pi, x = (4)/(5)

Simpilfy (2sqrt(5) + 3sqrt(2))

Expand each of the following, using suitable identities (i) (x + 2y+ 4z) ^(2) (ii) (2a - 3b) ^(3) (iii) (-2a + 5b - 3c) ^(2) (iv) ((a)/(4) - (b)/(2) + 1) ^(2) (v) ( p +1) ^(3) (vi)(x - (2)/(3) y) ^(3)

State true or false .A circle divides the plane on which it lies into three parts.

…………..should be added to x^(3) - 5x^(2) + x-8, so that the result is exactly divisible by (x-5).

Construct a triangle whose sides are 3.6 cm , 3.0 cm and 4.8 cm. Bisect the smallest angle and measure each part.

The angle of elevation of the sun, when the length of the shadow of a tree (1/sqrt3) times the height of the tree is____

The volume of a hemisphere is 89""5/6cm^(3). Find its diameter.

Express each of the following linear equations in two variables in the standard form ax + by +c = 0 and in each case state the values of a, b and c : 1/(6)x =1/4y+3

Express each of the following linear equations in two variables in the standard form ax + by +c = 0 and in each case state the values of a, b and c : 5x -3y = 2.bar(8)

Express each of the following linear equations in two variables in the standard form ax + by +c = 0 and in each case state the values of a, b and c : 4x = 5y +2

Express each of the following linear equations in two variables in the standard form ax + by +c = 0 and in each case state the values of a, b and c : 3y=15

Express each of the following linear equations in two variables in the standard form ax + by +c = 0 and in each case state the values of a, b and c : 4x-8=0

Express each of the following linear equations in two variables in the standard form ax + by +c = 0 and in each case state the values of a, b and c : 2x-3y=0

Express each of the following linear equations in two variables in the standard form ax + by +c = 0 and in each case state the values of a, b and c : 5y=3x

Express each of the following linear equations in two variables in the standard form ax + by +c = 0 and in each case state the values of a, b and c : -3x+4y=12

Express each of the following linear equations in two variables in the standard form ax + by +c = 0 and in each case state the values of a, b and c : 3x=7-2y

Express each of the following linear equations in two variables in the standard form ax + by +c = 0 and in each case state the values of a, b and c : y=4x-1

If x^(2) + mx - 28 = (x-7)(x+4), then m = ……… .

If 4cos^(2)x=3 and x is an acute angle, find the value of : x

A company manufactures car batteries of particular type. The life (in years) of 40 batteries was recorded as follows: Construct a grouped frequency distribution table with exclusive classes for this data, using class intervals of size 0.5 starting from the interval 2-2.5.

Express each of the following decimal numbers in (p)/(q) form 3.127bar(7)

It is required to make a closed cylindrical tank of height 1 m and base diameter 140 cm from a metal sheet. How many square metres of the sheet are required for the same ?

Write whether the following statements are True or False. Justify your answer (i) A binomial has two terms (ii) Every polynomial is a binomial (iii) A binomial may have degree 3 (iv) Degree of zero polynomial is zero (v) The degree of x ^(2) + 2xy + y ^(2)is 2 (vi) pi r ^(2) is a monomial.

An overhead water tanker is in the shape of a cylinder has capacity of 61.6 m^3. The diameter of the tank is 5.6 m. Find the height of the tank.

Draw a flowchart to pick the smallest among the two number

Dividing 2x^(3) + 6x^(2) + x + 5 by (x+3), the remainder is ……….. .

Simplify the following expressions : (sqrt5-sqrt3)(sqrt5+sqrt3)

The value of a machine, purchased two years ago, depreciates at the annual rate of 10%. If its present value is Rs 97,200, find its value when it was purchased.

The value of a machine, purchased two years ago, depreciates at the annual rate of 10%. If its present value is Rs 97,200, findit value after 2 years

The mean of 200 items was 50. Later on, it was discovered that two items were misread as 92 and 8 instead of 192 and 88. Find the correct mean.

How many litres of milk can a hemispherical bowl of diameter 10.5 cm hold ?

5 conical tents with diameter 8 m and height 3 m are to be made. How many metres of 2 m wide tarpaulin will be required to make these 5 tents ? (pi=3.14)

If secA=cosecA" and "0^(@) le A le 90^(@), state the value of A.

If 2 (a ^(2) + b ^(2)) = (a+b)^(2), then show that a =b

A child playingwith building blocks, which are of the shape of cubes, has built a structureas shown in Fig. 13.25. If the edge of each cube is 3 cm, find the volume ofthe structure built by the child.

Evaluate the following uing suitable identities : (99)^(3)