3694 + Interview Questions in Maths in Class 10 Page 52 InterviewSolution

2551.	triangle ABC~triangle PQR. In triangle,AB=3.6 cm, BC=4 cm and AC=4.2 cm. The corresponding sides of triangle ABC and triangle PQR arein the ratio 2:3. Construct trianglePQR and triangle ABC.
Answer» ANSWER :`:.` In `TRIANGLE PQR`, pQ=5.4 CM, QR=6 cm, PR=6.3 cm

Discussion

2552.	Write all types of quadrilaterals.
Answer» Answer :PARALLELOGRAM, Rhombus, RECTANGLE, SQUARE, Trapezium, Kite.

Discussion

2553.	Solve 9m^2 -12 m +2 =0 by the method of completing square .
Answer» ANSWER :`(2+SQRT2)/(3) , (2- sqrt2)/(3)`

Discussion

2554.	The next term of 1/20 in the sequence 1/2,1/6, 1/12, 1/20 is……….
Answer» `1/24` `1/22` `1/30` `1/18` ANSWER :C

Discussion

2555.	State whether the followmg sets are finite or infinite. (i) The set of months in a year. (ii) {1,2,3, ..., 99, 100)
Answer» ANSWER :(i) FINITE (II) Finite

Discussion

2556.	It is required to make a plastering of sand and cement with 35 cm thick, surroundingfour cylindrical pillars, each of whose diameter is 175 cm. and height 3 m. If the ratio of sand and cement in the plaster material be 4:1 , then how many cubic, dcm of cement will be needed ?
Answer» SOLUTION :Diameter `= 17.5 cm = 1.75 dcm` `:.` Radius `= (1.75)/(2)` dcm `=0.875` dcm Thickness of each pillar `= 3.5 cm = 0.35 dcm` `:. ` Outer radius of the pillars after plastering will be `(0.875+0.35) dcm = 1.225` dcm `:.` Volume of MATERIALS `= (22)/(7) {(1.225)^(2)-(0.875)^(2)}xx30` cubic.dcm [ `:'3m=30 dcm`] `= (22)/(7) xx (1.225 + 0.875) (1.225-0.875)(1.225-0.875)xx30` cubic-dcm `= (22)/(7) xx 2.1 xx 0.35 xx 30` cubic - dcm `= 69.3` cubic . dcm `:. ` Volume of materials needed for 4 pillars `= 69.3xx4` cubic.dcm `= 277.2` cubic.dcm `:.` Volume of materials needed for 4 pillars `= 69.3xx 4` cubic.dcm ` = 277.2` cubic.dcm `:.` (a) 277.2 cubic.dcm plaster materials will be needed . (b) The RATIO of sand and cement is4:1 `:.` part of cement `= (1)/(4+1)=(1)/(5)`. Hence the required cement `= 277.2xx( 1)/(5)` cubic.dcm` = 55.44` cubic . dcm .

Discussion

2557.	In which of the following situations, does the list of numbers involved make an arithmetic progression, and why? (ii) The amount of air present in a cylinder when a vacuum pump removes 1//4^(th) of the air remaining in the cylinder at a time.
Answer» ANSWER :(i) AP, (II) Not AP, (III) AP, (IV) Not AP

Discussion

2558.	Given that x -2 and x + 1 are factors of f(x)=x^(3)+3x^(2)+ax+b, calculate the values of a and b. Hence, find all the factors of f(x).
Answer» ANSWER :a=-6l b=-8, (x+1) (x-2) (x+4)

Discussion

2559.	Write the number of real zeros of f(x) depicted by graphs shown below :
Answer» ANSWER :i] 2 ii] 2 iii] 2 iv]0

Discussion

2560.	If the cost of an apple is increased by Rs.1 per piece, then one can get 2 apples less for Rs. 840 . Find the original cost of one apple .
Answer» ANSWER :RS. 20

Discussion

2561.	Draw a circle of radius 6cm. From a point 10cm away its centre, construct the pair of tangents to the circle and measure their lengths. Verify by using Pythogoras Theorem.
Answer» ANSWER :`2sqrt(5)CM`

Discussion

2562.	Which of the following points are collinear ?
Answer» `(2A,0),(3a,0),(a,2a)` `(3a,0),(0,3b),(a,2B)` `(3a,B),(a,2b),(-a,b)` `(a,-6),(-a,3b),(-2a,-2b)` ANSWER :B

Discussion

2563.	f : N to N : f (x) =2xis
Answer» ONE-one and onto one - one and onto many -one and onto many -one and into Answer :B

Discussion

2564.	Dinakar's salary is Rs.30,000 per month. He contributes Rs.27,000 towards GPF and Rs.30,000 towards LIC. He donates Rs.8,000 to a charitable trust (50%), Rs.10,000 towards National Relief Fund (100% relief). Calculate taxable income.
Answer» Rs.198,000 Rs.280,000 Rs.326,000 Rs.380,000 Solution :(i) TAXABLE INCOME is obtained when standard deduction, donations and saving are DEDUCTED. (II) Find the standard deduction. (iii) Taxable income = Annual salary-(SD+GPF+LIC+NRP+ `50%` of donations)

Discussion

2565.	Dinakar's salary is Rs.30,000 per month. He contributes Rs.27,000 towards GPF and Rs.30,000 towards LIC. He donates Rs.8,000 to a charitable trust (50%), Rs.10,000 towards National Relief Fund (100% relief). Find the rebate amount on his savings.
Answer» Rs.15,350 Rs.10,250 Rs.8550 Rs.20,000 Solution :(i) Refer the introduction for slab on rebate amount on SAVINGS. (ii) As his salary falls between Rs.150,000 and Rs. 500,000, rate of rebate is `15%` of his savings. (III) CALCULATE total savings and FIND `15%` of it.

Discussion

2566.	Hundread rupee shares of a company are available in the market at a premium of 20rs. Find the rate of dividend given by the company when a man's return on his investment is 15 percent.
Answer» ANSWER :`18%`

Discussion

2567.	A sports company was ordered to prepare 100 paper cylinders without caps for shuttle cocks. The required dimensions of the cylinder are 35 cm length / height and its radius is 7 cm. Find the required area of the thin paper sheet needed to make 100 cylinders.
Answer» ANSWER :`184800 cm^2`

Discussion

2568.	If a triangle is to be constructed similar to a given triangle ABC with scale factor 4/7, in what ratio should BC be divided internally ?
Answer» ANSWER :`4:3`

Discussion

2569.	Find the volume of right circular cone with radius 6 cm and height 7 cm.
Answer» ANSWER :264 c.c.

Discussion

2570.	Prove that the points A(1, 1) , B(-1, -1) and C(sqrt(3), -sqrt(3)) are the vertices of an equilateral triangle.
Answer» ANSWER :N/A

Discussion

2571.	Evaluate the following (sin theta +cos theta )^(2) +(sin theta -cos theta )^(2)
Answer» ANSWER :`2`

Discussion

2572.	The slant height of a frustum of a cone is 4cm and the perimeters of its circular ends are 18cm and 6cm . Find the curved surface areas of the frustum.
Answer» ANSWER :`48CM^(2)`

Discussion

2573.	Prove that: (tan theta)/(1 - cot theta) + (cot theta)/(1 - tan theta) = 1 sec theta "cosec" theta - 1 + tan theta + cot theta.
Answer» ANSWER :SEC `THETA `COSEC `theta` + 1

Discussion

2574.	Match the following:
Answer» (a) `ARARRP, BrarrQ, CrarrR, DrarrS` (B) `ArarrS, BrarrQ, CrarrR, DrarrP`C. `ArarrQ, BrarrS, CrarrR, DrarrP` ANSWER :A::B::C::D

Discussion

2575.	Mahima has a recurring deposite accountin a bookfor 3 years at 8 %P.a. if she gets rupes 3,996as interestat the time of maturity of the scheme ,find :the monthly instalment (ii)the maturity amount.
Answer» Answer :rupes 900 (ii) 36, 396 `

Discussion

2576.	Find the curved surface area of a cone of base radius r and height h .
Answer» Answer :`PI r SQRT(r^(2)+h^(2))`

Discussion

2577.	State True or False Justify. (i) The n^(th) term of any A.P. is of the form pn + q where p and q are some constants. (ii) The sum to nth term of any A.P. is of the form pn^(2) + qn +r, where p,q,r are some constants.
Answer» ANSWER :(i) TRUE, (II) FALSE

Discussion

2578.	If(x-2)and(x-3) are two factors off(x)=x^(3)+ax+b,then find the remainder when f(x) is divided byx-5.
Answer» 1 0 5 4 Solution :Since the COEFFCIENT of `X^(2)` is zero , the SUM of the ROOTS is zero.

Discussion

2579.	A dealer A in Bihar an article for Rs. 5,000 from a dealer B in Punjab. The dealer A sells this artic,e for Rs. 6,000 to a dealer C in the same state. If the rate of GST at each stage is 18%, find : the price (including GST) paid by the dealer A.
Answer» ANSWER :5900

Discussion

2580.	A dealer A in Bihar buys an article for Rs. 5,000 from a dealer B in Punjab. The dealer A sells this artic,e for Rs. 6,000 to a dealer C in the same state. If the rate of GST at each stage is 18%, find : the price (including GST) paid by the dealer C.
Answer» ANSWER :7080

Discussion

2581.	Represent the following situations in the form of quadratic equations : The product of two consecutive positive integers is 306. We need to find the Integers.
Answer» ANSWER :`X^(2)+x-306=0`(x=Smaller INTEGER)

Discussion

2582.	If 3x + 7y =-1 and 4y - 5x +14=0, find the values of 3x - 8y and y/x -2.
Answer» ANSWER :`14, -5/2`

Discussion

2583.	12 dfective pens are accidently mixed with 132 good ones. It is not possible to just look at a pen and tell whether or not it is defective. One pen is taken at radom from the lot. Determine the probability that the pentaken out is a good pen.
Answer» ANSWER :`11/12`

Discussion

2584.	For the G.P. (1)/(27),(1)/(9),(1)/(3), . . . . . .. . . . .. ,81, find the product of fourth term from the beginning and the fourth term from the beginning and the fourth term from the end.
Answer» ANSWER :3

Discussion

2585.	Linear equation 5x+2y=16 and 7x-4y=2 will have :
Answer» MANY solutions No solution A UNIQUE solution Two solutions. Answer :C

Discussion

2586.	The sum of the 4th and the 8th terms of an A.P. is 24 and the sum of the 6th and the 10th terms of the same A.P. is 44. Find the first three terms of the A.P.
Answer» ANSWER :`-1/2, 2 9/2`

Discussion

2587.	The shape of solid iron rod is cylinderical Its height is 11 cm and base diameter si 7 cm Then find the total volume of 50 such rods.
Answer» ANSWER :`21,175 cm^3`

Discussion

2588.	Consider the following distribution of daily wages of 50 workers of a factory. Find the mean daily wages of the workers of factory by using an appropriate method.
Answer» ANSWER :`Rs1455.2`

Discussion

2589.	Formulate the following problems as a pair of equations and then find their solutions. i. A boat goes 30km upstream and 44 km downstream in 10 hours. In 13 hours. In 13 hours it can go 40 km upstream and 55 km downstream. Determine the speed of the stream and that of the boat in still water.
Answer» ANSWER :SPEED of boat = 8 km/h ; Speed of stream = 3 km/h

Discussion

2590.	Without using trignometric tables, prove that : (i) sin 53^@cos 37^@+cos 53^@sin 37^@=1 (ii) cos 54^@cos 36^@-sin 54^@sin 36^@=0 (iii) sec 35^@sin 20^@+cos 20^@cosec 70^@=2 (iv) sin 35^@sin 55^@-cos 35^@cos 55^@=0 (v) (sin 72^@+cos 18^@)(sin 72^@-cos 18^@)=0 (vi) tan 48^@tan 23^@tan 42^@tan 67^@=1
Answer» SOLUTION :`(IV) LHS =sin 35^@sin(90^@-35^@)-COS 35^@cos(90^@-35^@)=sin 35^@cos 35^@-sin 35^@cos 35^@=0` `(V) LHS =sin^2 72^@-cos^2 18^@=sin ^2 72^@-cos^2(90-72^@)=sin^2 72^@-sin ^2 72^@=0`.

Discussion

2591.	In a certain code, MENTION is written as LNEITNO. How is PATTERN written in that code?
Answer» APTTREM PTAETNR OTAETNR OTAETRN Solution :Clearly, to obtain the CODE, the first LETTER of the word is moved one step backward and the remaining letters are moved in REVERSE order taking two at a time

Discussion

2592.	Volume of a frustrum of a cone is …….
Answer» `(PIH)/3(R^(2)+r^(2)+R.r)` `pi/3(R^(2)+r^(2))` `(pih)/3(R^(2)+r^(2))` none Answer :A

Discussion

2593.	Find the mean median of the following frequency distrbution : Also, find the mode of the following data.
Answer» Solution :We have Let assumed `A=55 ,h=10. sumf= 50 and sumfu=-27` `"Mean"barx=A+[hxx(sum(fu))/(sumf)]` `barx=55+(10xx(-27)/(50))` `barx=55-5.4` `barx=49.6` Here, N=50 `rarr (N)/(2)=(50)/(2)=25` Cumulative FREQUENCY just greater than 25 is 36 and the corresponding class is 50-60 `:. l_(1)=50,f=12ml_(2)=60,C=24,i=60-50=10` Now, `"MEDIAN"(M)=l_(1)+(((N)/(2)-C))/(f)XXI` `=50+(10)/(12)(25-24)=50+(10)/(12)` `=50+0.83=50.83` Mode =3(Median)-2(Mean) Mode = `3xx50.83-2xx49.60` `=152.49-99.20=53.29`

Discussion

2594.	Statements: 1. Most teachers are boys 2. Some boys are students Conclusions: 1. Some students are boys 2. Some teachers are students
Answer» if only conclusion 1 follows, if only conclusion 2 follows, if either conclusion 1 or 2 follows, if NEITHER conclusion 1 nor 2 follows, ANSWER :A

Discussion

2595.	Find the ratio in which the line segment joining the points (-3, 10) and (6, -8) is divided by (-1, 6) .
Answer» ANSWER :0.088194444444444

Discussion

2596.	Show that the points (-4, -7), (-1, 2), (8, 5) and (5, -4) taken in order are the vertices of a rhombus. Find its area. (Hint : Area of rhombus = (1)/(2)xx product of its diagonals)
Answer» Answer :AB = BC = CD = DA = `sqrt(90)` , AC `ne` BD (vertices of a thombus), 72 Sq. UNITS

Discussion

2597.	If the geometic progressions 162, 54, 18,….. And 2/81, 2/27, 2/9,……. Have there nth term equal. Find the value of n.
Answer» ANSWER :5

Discussion

2598.	Solve the following simultaneous equations graphically. 3x - 4 y = 7, 5x - 2y = 0
Answer» ANSWER :X = 1 , y = 2.5

Discussion

2599.	State the co-ordinates of the following points under reflection in origin: (i) (-2,-4)(ii) (-2, 7) (iii)(0, 0)
Answer» ANSWER :(i) (2,4)(ii) (2, -7) (iii)(0, 0)

Discussion

2600.	The sum of two digit number and the number obtained by reversing the digits is 66. If the digits of the number differ by 2, Find the number. How many such numbers are there?
Answer» ANSWER :42 and 24

Discussion

Explore topic-wise InterviewSolutions in .

triangle ABC~triangle PQR. In triangle,AB=3.6 cm, BC=4 cm and AC=4.2 cm. The corresponding sides of triangle ABC and triangle PQR arein the ratio 2:3. Construct trianglePQR and triangle ABC.

Write all types of quadrilaterals.

Solve 9m^2 -12 m +2 =0 by the method of completing square .

The next term of 1/20 in the sequence 1/2,1/6, 1/12, 1/20 is……….

State whether the followmg sets are finite or infinite. (i) The set of months in a year. (ii) {1,2,3, ..., 99, 100)

It is required to make a plastering of sand and cement with 3*5 cm thick, surroundingfour cylindrical pillars, each of whose diameter is 17*5 cm. and height 3 m. If the ratio of sand and cement in the plaster material be 4:1 , then how many cubic, dcm of cement will be needed ?

In which of the following situations, does the list of numbers involved make an arithmetic progression, and why? (ii) The amount of air present in a cylinder when a vacuum pump removes 1//4^(th) of the air remaining in the cylinder at a time.

Given that x -2 and x + 1 are factors of f(x)=x^(3)+3x^(2)+ax+b, calculate the values of a and b. Hence, find all the factors of f(x).

Write the number of real zeros of f(x) depicted by graphs shown below :

If the cost of an apple is increased by Rs.1 per piece, then one can get 2 apples less for Rs. 840 . Find the original cost of one apple .

Draw a circle of radius 6cm. From a point 10cm away its centre, construct the pair of tangents to the circle and measure their lengths. Verify by using Pythogoras Theorem.

Which of the following points are collinear ?

f : N to N : f (x) =2xis

Dinakar's salary is Rs.30,000 per month. He contributes Rs.27,000 towards GPF and Rs.30,000 towards LIC. He donates Rs.8,000 to a charitable trust (50%), Rs.10,000 towards National Relief Fund (100% relief). Calculate taxable income.

Dinakar's salary is Rs.30,000 per month. He contributes Rs.27,000 towards GPF and Rs.30,000 towards LIC. He donates Rs.8,000 to a charitable trust (50%), Rs.10,000 towards National Relief Fund (100% relief). Find the rebate amount on his savings.

Hundread rupee shares of a company are available in the market at a premium of 20rs. Find the rate of dividend given by the company when a man's return on his investment is 15 percent.

A sports company was ordered to prepare 100 paper cylinders without caps for shuttle cocks. The required dimensions of the cylinder are 35 cm length / height and its radius is 7 cm. Find the required area of the thin paper sheet needed to make 100 cylinders.

If a triangle is to be constructed similar to a given triangle ABC with scale factor 4/7, in what ratio should BC be divided internally ?

Find the volume of right circular cone with radius 6 cm and height 7 cm.

Prove that the points A(1, 1) , B(-1, -1) and C(sqrt(3), -sqrt(3)) are the vertices of an equilateral triangle.

Evaluate the following (sin theta +cos theta )^(2) +(sin theta -cos theta )^(2)

The slant height of a frustum of a cone is 4cm and the perimeters of its circular ends are 18cm and 6cm . Find the curved surface areas of the frustum.

Prove that: (tan theta)/(1 - cot theta) + (cot theta)/(1 - tan theta) = 1 sec theta "cosec" theta - 1 + tan theta + cot theta.

Match the following:

Mahima has a recurring deposite accountin a bookfor 3 years at 8 %P.a. if she gets rupes 3,996as interestat the time of maturity of the scheme ,find :the monthly instalment (ii)the maturity amount.

Find the curved surface area of a cone of base radius r and height h .

State True or False Justify. (i) The n^(th) term of any A.P. is of the form pn + q where p and q are some constants. (ii) The sum to nth term of any A.P. is of the form pn^(2) + qn +r, where p,q,r are some constants.

If(x-2)and(x-3) are two factors off(x)=x^(3)+ax+b,then find the remainder when f(x) is divided byx-5.

A dealer A in Bihar an article for Rs. 5,000 from a dealer B in Punjab. The dealer A sells this artic,e for Rs. 6,000 to a dealer C in the same state. If the rate of GST at each stage is 18%, find : the price (including GST) paid by the dealer A.

A dealer A in Bihar buys an article for Rs. 5,000 from a dealer B in Punjab. The dealer A sells this artic,e for Rs. 6,000 to a dealer C in the same state. If the rate of GST at each stage is 18%, find : the price (including GST) paid by the dealer C.

Represent the following situations in the form of quadratic equations : The product of two consecutive positive integers is 306. We need to find the Integers.

If 3x + 7y =-1 and 4y - 5x +14=0, find the values of 3x - 8y and y/x -2.

12 dfective pens are accidently mixed with 132 good ones. It is not possible to just look at a pen and tell whether or not it is defective. One pen is taken at radom from the lot. Determine the probability that the pentaken out is a good pen.

For the G.P. (1)/(27),(1)/(9),(1)/(3), . . . . . .. . . . .. ,81, find the product of fourth term from the beginning and the fourth term from the beginning and the fourth term from the end.

Linear equation 5x+2y=16 and 7x-4y=2 will have :

The sum of the 4th and the 8th terms of an A.P. is 24 and the sum of the 6th and the 10th terms of the same A.P. is 44. Find the first three terms of the A.P.

The shape of solid iron rod is cylinderical Its height is 11 cm and base diameter si 7 cm Then find the total volume of 50 such rods.

Consider the following distribution of daily wages of 50 workers of a factory. Find the mean daily wages of the workers of factory by using an appropriate method.

Formulate the following problems as a pair of equations and then find their solutions. i. A boat goes 30km upstream and 44 km downstream in 10 hours. In 13 hours. In 13 hours it can go 40 km upstream and 55 km downstream. Determine the speed of the stream and that of the boat in still water.

Without using trignometric tables, prove that : (i) sin 53^@cos 37^@+cos 53^@sin 37^@=1 (ii) cos 54^@cos 36^@-sin 54^@sin 36^@=0 (iii) sec 35^@sin 20^@+cos 20^@cosec 70^@=2 (iv) sin 35^@sin 55^@-cos 35^@cos 55^@=0 (v) (sin 72^@+cos 18^@)(sin 72^@-cos 18^@)=0 (vi) tan 48^@tan 23^@tan 42^@tan 67^@=1

In a certain code, MENTION is written as LNEITNO. How is PATTERN written in that code?

Volume of a frustrum of a cone is …….

Find the mean median of the following frequency distrbution : Also, find the mode of the following data.

Statements: 1. Most teachers are boys 2. Some boys are students Conclusions: 1. Some students are boys 2. Some teachers are students

Find the ratio in which the line segment joining the points (-3, 10) and (6, -8) is divided by (-1, 6) .

Show that the points (-4, -7), (-1, 2), (8, 5) and (5, -4) taken in order are the vertices of a rhombus. Find its area. (Hint : Area of rhombus = (1)/(2)xx product of its diagonals)

If the geometic progressions 162, 54, 18,….. And 2/81, 2/27, 2/9,……. Have there nth term equal. Find the value of n.

Solve the following simultaneous equations graphically. 3x - 4 y = 7, 5x - 2y = 0

State the co-ordinates of the following points under reflection in origin: (i) (-2,-4)(ii) (-2, 7) (iii)(0, 0)

The sum of two digit number and the number obtained by reversing the digits is 66. If the digits of the number differ by 2, Find the number. How many such numbers are there?

It is required to make a plastering of sand and cement with 35 cm thick, surroundingfour cylindrical pillars, each of whose diameter is 175 cm. and height 3 m. If the ratio of sand and cement in the plaster material be 4:1 , then how many cubic, dcm of cement will be needed ?