Explore topic-wise InterviewSolutions in .

This section includes InterviewSolutions, each offering curated multiple-choice questions to sharpen your knowledge and support exam preparation. Choose a topic below to get started.

1801.

An organization selected 2400 families at random and surveyed them to determine a relationship between level and the number of vehicles in a family. The information gathered is listed in the table below Suppose a family is chosen. Find the probability that the family chosen is : (i) earning Rs 10000-13000 per month and owing exactly 2 vehicles. (ii) earning Rs 16000 ro more per month and owning exactly 2 vehicle. (iii) earning less than Rs 7000 per month and odes not own andy vehicle. (iv) earning Rs 13000-16000 per month and owning more than 2 vehicles. (v) owning not more than 1 vehicles.

Answer»


Answer :(i) `P(A) = (29)/(2400)`
(II) `(193)/(800)`
(iii) `1/(240)`
(IV) `1/(96)`
(V) 2062
1802.

The value of an article decreased for two years at the rate of 10% per year and then in the third year it increased by 10%. Find the original value of the article, if its value at the end of 3 years is Rs40,095

Answer»


ANSWER :RS 45,000
1803.

The radius and slant height of a cone are 21 cm and 35 cm respectively. Find the volume of the cone.

Answer»


ANSWER :12,936 `CM^(3)`
1804.

Verify whether the following are zeros of the polynomial , Indicted against them , or not, (i)p(x) =2x-1, x=(1)/(2)(ii)p(x) =x^(3) -1 , x=1 (iii)p(x) =ax +b, x = (-b) /( a )(iv)p(x) =( x+3) (x-4) , x = -3 ,x =4

Answer»


Answer :(i) YES (II) No (iii) Yes (iv) No, Yes (V) Yes (VI) Yes (vii) Yes,No(viii) Yes,No
1805.

Find the value of k, if x-1 is a factor of p(x) in each of the following cases : p(x) = 2x^(2) + kx + sqrt(2)

Answer»


ANSWER :`K = -(2 + SQRT(2))`
1806.

A tent is cylindrical to a height of 4.8 m .and conical above it. The radius of the base is 4.5 m. and total height of the tent is 10.8 m . Find the canvas required for the tent in square meters.

Answer»


ANSWER :` 241.84 m^(2) ` (APPROXIMATE)
1807.

Evaluate each of the following using proper identity : (123)^(3)

Answer»


ANSWER :15129
1808.

Construct a DeltaABC in which AB = 5 cm, AC + BC = 8 cm and angleB = 60^(@).

Answer»

SOLUTION :Steps of construction :
1. Draw `AB = 5 cm`.
2. Construct `angleABP = 60^(@)` and cut `BP = 8 cm. `
3. Join `AP`.
4. Draw the perpendicular bisector of `AP` which intersect `BP` at `C`.
5. Join`AC`.
`therefore DeltaABC` is the required triangle.
1809.

Find zero of the polynomialp (x) = 3x +1

Answer»


ANSWER :`3X +1`
1810.

Find the remainder when x^(3) + 3x^(2) + 3x+1 is divided by : x-(1)/(2)

Answer»


ANSWER :`(27)/(8)`
1811.

The side faces of a pyramid are

Answer»

TRIANGLES
squares
TRAPEZIUMS
polygons

Solution :The SIDE FACES of a pyramid are triangles
1812.

Nikita invests Rs 6,000 for two years at a certain rate of interest compounded annually. At the end of first year it amounts to Rs 6,720. Calculatethe amount at the end of the second year.

Answer»


ANSWER :RS 7,526.40
1813.

Nikita invests Rs 6,000 for two years at a certain rate of interest compounded annually. At the end of first year it amounts to Rs 6,720. Calculate the rate percent (i.e. rate of growth)

Answer»


ANSWER :0.12
1814.

State for any acute angle theta whether : costheta increases or decreases as theta increases.

Answer»


ANSWER :DECREASING
1815.

Calculate the value of A, if : (sinA-1)(2cosA-1)=0

Answer»


ANSWER :`90^(@) and 60^(@)`
1816.

Rohit invested in two types of shares, P and Q, of a company. He purchased P at x% discount and Q at x% premium. If the total market value of each is equal, find the rate of effective discount (in per cent).

Answer»

`0.1%`
`(x^(2))/(400)%`
`(x^(2))/(200)%`
`(x^(2))/(100)%`

Solution :(i) `"Effective DISCOUNT"=("Total discount")/("Total MARKET value")XX100`
(ii) LET the market value of each share be m.
(iii) `FV_(1)=(100m)/(100+x)and FV_(2)=(100m)/(100-x)`
(iv) Find the total face value which is LESS than the total market value.
(v) Effective discount.
`=("(Total FV"-"Total MV)")/("Total FV")xx100`.
1817.

Evaluate 105 xx 106 without multiplying directly.

Answer»


ANSWER :11130
1818.

State whether the statements are True or False. (i) Every parallelogram is a trapezium ( )

Answer»


ANSWER :1
1819.

Express 3.28 in the form of (p)/(q) (where p and q are intgers, q ne0).

Answer»


ANSWER :`(82)/(25)`
1820.

Monika and Vasu have the same weight, if they both gain weight by 2kg, how will their new weight be compared? (a) What mathematical concept has been converted in this question?

Answer»


ANSWER :EUCLID's SECOND AXIOM
1821.

If the mean of the following frequency distribution is 7.2 find value of 'K'.

Answer»


ANSWER :K=10
1822.

Solve for theta(0^(@) lt theta lt 90^(@)) : tan^(2)theta+3=3sectheta.

Answer»


ANSWER :`theta=60^(@)`
1823.

The median of 21, 17, 13, 33, 19, 23 is......

Answer»

19
20
21
23

Answer :B
1824.

Express the following rational numbers in decimal form. (242)/(1000)

Answer»


ANSWER :0.242
1825.

A circle divides the plane, on which it lies, in ________ parts.

Answer»


ANSWER :1
1826.

State True or False, if 'false' write correct statement. In the Cartesian plane the horizontal line is called Y-axis.

Answer»


ANSWER :FALSE
1827.

Use the Factor Theorem to determine whether g (x) is factor of f(x) in each of the following cases: (i) f (x) = 5x ^(3) + x ^(2)-5x -1, g (x)=x +1 (ii) f (x) = x ^(3) + 3x ^(2) + 3x +1 , g(x) =x +1 (iii) f (x) =x ^(3) - 4x ^(2) +x + 6, g (x) =x -2 (iv) f (x) = 3x ^(3) - 20x + 12, g (x) = 3x -2 (v)f (x) = 4x ^(3) + 20 x ^(2) + 33 x +18, g (x) =2x +3

Answer»


Answer :(i) YES (II) Yes (III) Yes (IV) Yes (v) Yes
1828.

State true or false .The longest of all chords of a circle is called a diameter.

Answer»


ANSWER :1
1829.

Subtract 5sqrt3+7sqrt5 from 3sqrt5-7sqrt3

Answer»


ANSWER :`-(4sqrt5+12sqrt3)`
1830.

How many pages of NCERT class IX Mathematics book of English medium contains ? A page is selected of at random . What is the probability that the page number contains . (i) 9 at one's place. (ii) multiple of 4 (iii) perfect square

Answer»


Answer :(i)`(32)/(323)`(II)`(80)/(323)`(III)`(17)/(323)`
1831.

Answer the following by a number or a word or a sentence : What is the sum of opposite angles of a cyclic quadrilateral ?

Answer»


ANSWER :`108^(@)`
1832.

Find the square root of the expression (1)/(xyz) (x^(2) + y^(2) + z^(2)) + 2((1)/(x) + (1)/(y) + (1)/(z))

Answer»

`(x + y + z)/(xyz)`
`sqrt((yz)/(x)) + sqrt((zx)/(y)) + sqrt((XY)/(z))`
`sqrtx + sqrty + sqrtz`
`sqrt((x)/(yz)) + sqrt((y)/(xz)) + sqrt((z)/(xy))`

Solution :(i) Use ALGEBRAIC identities to factorize the given POLYNOMIAL
(II) Multiply the first three terms with xyz
(III) Now express the expression in `(a +b +c)^(2)` form
1833.

Ahemispherical bowl has a radius of 3.5 cm. What would be the volume of waterit would contain?

Answer»


ANSWER :89.8 `CM^(3)`
1834.

Answer the following: (i) How many dimensions a solid has? (ii) How many books are there in Euclid's Elements? (iii) Write the numbers of faces of a cube and cuboid? (iv) What is sum of interior angles of a triangle? (v) Write three un-defined terms of geometry?

Answer»


Answer :(i) 3, (ii) 13, (iii) 6, (iv) `180^(@)` , (V) POINT, Plane, Line
1835.

Find p(0), p(1) and p(2) for each of the following polynomials : p(t) = 2 + t + 2t^(2)- t^(3)

Answer»


ANSWER :2,4,4
1836.

Sides of a triangle are in the ratio of 12 : 17 : 25 and its perimeter is 540 cm. Find its area.

Answer»


ANSWER :9000 `CM^(2)`
1837.

If the point (3,4) lies on the graph of the equation 3y = ax + 7. find the value of a .

Answer»


ANSWER :`a = 5/3`
1838.

Construct an equilateral triangle whose altitude is 4 cm. Give justification for your construction.

Answer»

Solution :STEPS OF CONSTRUCTION
(i) Draw a LINE `XY`.
(ii) Mark any point `D` on `XY`.
(iii) From `D`, draw `DE bot XY`.
(IV) From `D`, set off `DA=4` cm, cutting `DE` at`A.`
(v) Construct `angleDAB=30^(@)` and `angleDAC=30^(@)` meeting `XY` at `B` and `C` RESPECTIVELY.
Then, `Delta ABC` is the required equilateral triangle.
Verification :
On measuring, we find that
`angleA=angleB=angleC=60^(@)`
and `AB=BC=CA=4.5` cm
Justification:
In `Delta DAB`, we have
`angleABD+angleBDA+angleDAB=180^(@) implies angleABD+90^(@)+30^(@)=180^(@)`
`implies angleABD=180^(@)-120^(@)=60^(@)`
In `Delta DAC`, we have
`angleACD+angleCDA+angleDAC=180^(@) implies angleACD+90^(@)+30^(@)=180^(@)`
`implies angleACD=180^(@)-120^(@)=60^(@)`.
In `Delta ABC`, we have `angleA=angleB=angleC=60^(@)`.
Hence, `Delta ABC` is an equilateral triangle.
1839.

State whether the statements are True or False. (iv) A square is a rhombus ( )

Answer»


ANSWER :1
1840.

Factorise 27 x ^(3) + y ^(3) + z ^(3)-9 xyz using identitiy.

Answer»


ANSWER :`(3x+y+Z) (9X ^(2) +y ^(2) +z ^(2) -3zy-yz-3xz)`
1841.

Number of integral values of x that do not satisfy the inequation (x -7)/(x -9) gt 0 is ____

Answer»

4
3
2
0

Solution :If `(a)/(B) GT 0 " then " a gt 0, b gt 0 (or) a LT 0 , b lt 0`
1842.

If the mean of 12, 13, x, 17, 18 and 20 is 16, then x = ...........

Answer»

8
4
16
32

Answer :A
1843.

A residential colony has a population of 5400 and 60 litres of water is required per person per day. For the effective utilization of rain water, a group of people decided to the WATER HARVESTING. They constructed a water reservoir measuring 48mxx27mxx25m to collect the rain water.For How many days the water of this tank is sufficient if during rain, the height of water level is 5m ?

Answer»


ANSWER :20DAYS
1844.

The mean weight of 60 students in a class is 40 kg. The mean weight of boys is 50 kg while that of girls is 30 kg. Find the number of boys and girls in the class.

Answer»


ANSWER :30 and 30
1845.

An Olympic swimming pool isin the shape of a cuboid of dimensions 50m. Long and 25 m. wide. If it is 3m . Deep throughout , how many liters of water does it hold? ( 1cu.m =1000 liters)

Answer»


ANSWER :` 3750000` LITERS
1846.

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_GUJ_MAT_IX_C09_E01_003_A01##)`
1847.

Find the mean of first six natural numbers.

Answer»


ANSWER :`3*5`