3694 + Interview Questions in Maths in Class 10 Page 17 InterviewSolution

801.	Differentiate the following with respect to x using first principle method. sin^((1)/(3))x=root(3)(sinx).
Answer» Answer :`(COSX)/(3ROOT(3)(SIN^(2)x))`

Discussion

802.	Show that the locus of a point, equidistant from two intersecting lines in the plane, is a pair of lines bisecting the angles formed by the given lines.
Answer» Solution :Step-1 : We intially prove that any point equidistant from two given intersecting lines lies on one of the lines bisecting the angles formed by given lines. Given : `overline(AB) and overline(CD)` are two lines intersecting at O. P is the point on the plane such that `PM=PN`. Line L is the bisector of `angleBOD` and `angle AOC`. Line m is thebisector of `angle BOC and angle AOD`. RTP: P lies on either of line LOR lien m. Proof : In `Delta POM and Delta PON , PM=PN`. OP is common side and `angle PMO=angle PNO=90^@` `therefore` By RHS congruence PROPERTY , `angle POM approx Delta PON`. So, `anglePOM =angle PON`, i.e., P lies on the angle bisector of `angle BOD` As l is the bisector of angle BOD and `angle AOC` , P lies on the lien l. Similarly if P lies in any of the regions of `angle BOC , angle AOCor angleAOD`, such that it is equidistant from `overline (AB) and overline (CD)`, then we can conclude that P lies on the bisector l or on the angle bisector m . Step: 2 We prove that any point on the bisector of one of angles formed by two intersecting liens is equidistant FORM the liens. Given : Lines `overline(AB) and overline(CD)` intersect at O. Lines l and m are the angle bisectors. Proof : Let l be the angle bisector of `angle BOD` and `angle AOC`, and m be the angle bisector of `angle BOC` and `angle AOD`. Let P be a point on the angle bisector, l as shown in the figure. If P coincides with O, then P is eqidistant from the line `overline(AB) and overline(CD)`. Suppose P is different from O. Draw the perpendiculars `overline(PM) and overline(PN)` from the point P onto the lines `overline(AB) and overline(CD)` respectively. Then in `Delta POM and Delta PON, angle POM=angle PON, angle PON =angle PMO =90^@ and OP ` is a common side. `therefore` By AAS congurence propery `Delta POM approx Delta PON` So, `PN=PM` (`because` Corresponding sides) , i.e., P is equidistant from the lines `overline(AB) and overline (CD)`. Hence , from the steps 1 and 2 of the proof it can be said that the point which is equidistant from the two intersecting lines is the pair of the angle bisectors of the two pairs of vertically opposite angles formed by the lines.

Discussion

803.	Find the number zeroes of the given polynomials. And also find their values. p(x)=2x+1
Answer» ANSWER :`(-1)/(2)`

Discussion

804.	A well of diameter 14 m is dug 15 m deep. The earth taken out of it has been spread evenly to form circular embankment all around the wall of width 7 m. Find the height of the embankment.
Answer» ANSWER :5 m

Discussion

805.	What is the last digit of 6^(100) .
Answer» ANSWER :6

Discussion

806.	Draw a circle of radius 6 cm. From a pint 10 cm away from its centre, construct the pair of tangents to the circle and measure their lengths.
Answer» ANSWER :`8CM each`

Discussion

807.	A man invests a certain sum of money in 6% hundread rupee shares at 12rs premium. When the shares fell to 96rs he sold out all the shares bought and invested the proceed in 10% ten rupee shares at 8rs. If the change in his income is 540rs find the sum invested originally.
Answer» ANSWER :`10080rs`

Discussion

808.	Find the sum of (b) -3,1,5……….to 17 terms.
Answer»

Discussion

809.	A company declares 8 percent dividend to the share holders. If a man receives 2840rs as his dividend, find the nominal value of his shares.
Answer» ANSWER :`35500rs`

Discussion

810.	A metallic sphere of radius 4.2 cm is melted and recast into the sphape of cylinder of radius 6 cm. Findthe height of the cylinder.
Answer» ANSWER :`2.744 CM`

Discussion

811.	Which of the following points lies in the fourth quadrant ?
Answer» `(2,-7)` `(-3,5)` `(0,0)` `(-4,-7)` ANSWER :D

Discussion

812.	Find the number of squares in the figure given below :
Answer» SOLUTION :LET us try to count square without marking the points from small to big. Number of small squares = 8 Number of squares with 4 components = 7 There is one big (MAIN) given square = 1 `therefore ` Total number of squares = 8+7+1=16

Discussion

813.	Find the mean, median and mode of the following data :
Answer» ANSWER : mena=30, median=30.67 and MODE =32.01

Discussion

814.	The point which lies on the perpendicular bisector of the line sequent joining the points P(-2,0) and Q(2,5) is
Answer» `(0,0)` `(0,2)` `(2,0)` `(-2,0)` ANSWER :A

Discussion

815.	Compute the mode of the following data :
Answer» ANSWER :`24.17`

Discussion

816.	The surface area of two sphere are in the ratio of 9:25 then their volume are in the ratio …….. .
Answer» `81:625` `729:15625` `27:75` `27:125` ANSWER :D

Discussion

817.	Evaluate the (tan 45^(@))/("cosec" 30^(@)) + (sec 60^(@))/(cot 45^(@)) - (3 sin 90^(@))/(2 cos 0^(@)) .
Answer» ANSWER :1

Discussion

818.	If in a certain language, MACHINE is coded as LBBIHOD, which would be coded as SLT-MFNB?
Answer» RKSLEMA TKULGMC RMSNEOA TMUNGOC Solution :In the CODE, we have ALTERNATELY ONE LETTER one step behind and the other one step AHEAD of the coresponding letter in the word

Discussion

819.	Find the area of the canvas required to make a conical tent 14 m high and 96 m in diameter. Given that: (i) 20% of the canvas is used in folds and stitchings. (il) canvas used in folds and stitchings is 20% of the curved surface area of the tent.
Answer» ANSWER :`3/7 m ^(2)`

Discussion

820.	Rajat invested Rs 24,000 in 7% hundred rupee shares at 20% discount. After one year, he sold these shares at Rs 75 each and invested the proceeds (including dividend of first year) in 18% twenty five rupee shares at 64% premium. Find : his gain or loss after one year.
Answer» ANSWER :RS 2,100 GAIN

Discussion

821.	find the equation of cicle in each of the following cases ) (c)touches both the coordinate axes inthrid quadrant and having rasius
Answer» ANSWER :C`(x+3)^(2)+(y+3)^(2)=9`

Discussion

822.	Given [{:(,x,y+2),(,3,z-1):}] =[{:(,3,1),(,3,2):}] find x,y and z.
Answer» ANSWER :x=3, y=-1 and z=3

Discussion

823.	If the number of zeroes between the decimal point and the first non-zero digit of a number is 2, then the characteristic of logarithm of that number is ______.
Answer» ANSWER :`BAR(3)`

Discussion

824.	In the format of GSTIN there are ......alpha-numberals.
Answer» 15 10 16 9 Answer :A

Discussion

825.	ABCD is a cyclic quadrilateral , Sides AB and DC produced meet at point E ,whereas sides BC and AD produced meet at point F.Ifangle DCF : angle F : angle E =3 : 5 : 4find the angles of the cyclic quadrilateral ABCD.
Answer» ANSWER :` ANGLE A = 36^(@) , angle B = 84^(@) , angle C = 144^(@) and angle D = 96^(@) `

Discussion

826.	P and Q have co-ordinates (0, 5) and (-2, 4). Write the co-ordinates of the image of Q, obtained by reflecting it in the origin followed by reflection in x-axis.
Answer» ANSWER :(2,4)

Discussion

827.	A cone of height 24 cm and radius of base 6 cm is made up of modelling clay. A child moulds it in the form of a sphere. Find the radius of the shape.
Answer» ANSWER :the RADIUS of the SPHERE is 6 CM.

Discussion

828.	Two cars start together in the same direction from the same place. The first car goes at uniform speed of 10 km h^(-1). The second car goes at a speed of 8 km h^(-1) in the first hour and thereafter increasing the speed by 0.5 km h^(-1). each succeeding hour. After how many hours will the two cars meet ?
Answer» ANSWER :9 HOURS

Discussion

829.	A woodern article was made by scooping out a hemisphere from each end of a soid cylinder is 12 cm and its base is of radius 4.2 cm find the total suface area of the article. Also find the volume of the wood left in the article.
Answer» Solution :RADIUS of the hemisphere r= 4.2 CM Radius of the cylinder r= 4.2 cm Height of the cylinder , h= 12 cm Total surface area of the article = curved surface area of cylinder + curved surface area of 2 hemispheres `= 2pi r h + 2 xx 2pi r^2 = 2pi RH + 4 pi r^2 ` `=2pir(h+2r)=[2xx22/7xx4.2 xx(12-4/3xx4.2)]cm^2` `= (26.4 xx 20.4)cm^3= 354.816 cm^3` Total volume of the wood left in the article = volume of the cylinder - volume of 2 hemispheres `pi r^2h -2 xx 2/3pi r^3= pi r^2(h-4/3r)` `[ 22/7xx 4.2 xx 4.2 xx(12 - 4/3xx 4.2)]cm^3 ` `=(55.44 xx 6.4 )cm^2= 354.816 cm^3` (`##RSA_MATH_X_C17_S01_020_S01.png" width="80%">

Discussion

830.	Find the sum of G.P. : sqrt(3)+(1)/(sqrt(3))+(1)/(3sqrt(3))+ . . . . . . . . to n terms.
Answer» ANSWER :`(3sqrt(3))/(2)(1-(1)/(3^(N)))`

Discussion

831.	Construct a triangle similar to a given triangle ABC with its sides equal to (3)/(4)th of the corresponding sides of the Delta ABC For this construction, which of the following statements are true?
Answer» The REQUIRED `triangle` A'BC' is LESS than `triangle` ABC The required `triangle A' BC'` is GREATER than `triangle` ABC The required `triangle A' BC'` is equal to `Delta ABC` None of the above Answer :A

Discussion

832.	In what ratio is the line segment joining the point (-2,-3) and (3,7) divided by y-axis ?
Answer» `(-2,3)` `(-3,2)` `(2,3)` `(6,0)` ANSWER :C

Discussion

833.	The outer radius and the inner radius of a 30 cm long cylindrical gold pipe are 14 cm and 7 cm respectively. It is filled with bronze. The densitiesof gold and bronze are 20gm/cm^(3) and 30gm/cm^(3) respectively. Find the weight of the cylinder formed. (in gm)
Answer» `66150pi` `99225pi` `132300pi` `198450pi` Solution :Volume of the pipe `=pi (14^(2)-7^(2))(30)cm^(3)` ` :. " Volume of the gold "=pi (14^(2)-7^(2))(30)cm^(3)` Volume of the bronze in the pipe `=pi (7)^(2)(30) cm^(3)` WEIGHT of the pipe (in gms) = Weight of gold in it (in gm) + WEIGHTOF bronze in it (in gm) `=[pi (14^(2)-7^(2))(30)][20]+[pi(7)^(2)(30)][30]` `=30pi[(196-49)(20)+(49)(30)]` `=30pi [2940 + 1470]=132300 pi gm.`

Discussion

834.	The mean of x_(1),x_(2)....... x_(50) is M, if every x_ị, i = 1, 2 ..... 50is replaced by x_(i)//50then the mean is
Answer» M `M+(1)/50` `50/M` `M/50` ANSWER :D

Discussion

835.	If sec theta +tan theta =p,then what is the value ofsec theta -tan theta ?
Answer» <P> ANSWER :`(1)/(p) `

Discussion

836.	Mr. Tiwari invested 29040rs in 15% 100rs shares quoted at a premium of 20%. Calculate (i) the number of shares bought by Mr. Tiwari (ii) Mr. Tiwari income from the investment (iii) the percentage return on his investment
Answer» ANSWER :`(i) 242 (II) 3630rs (III) 12.5%`

Discussion

837.	A copper wire of diameter 6 mm is evenly wrapped on a cylinder of length 18 cm and diameter 49 cm to vover its whole surface. Find the length and the volume of the wire. If the density of copper be 8.8 g per cu-cm, find the weight of the wire.
Answer» ANSWER :`46.2 m, 1306.8 CM^(3)`, 11.5 KG

Discussion

838.	Find the common difference of an AP in which a_(25) - a_(12) = -52.
Answer» ANSWER :`-4`

Discussion

839.	Can (x - 2) be the remainder on division of a polynomial p(x) by (x + 3)?
Answer» ANSWER :No, as DEGREE (X - 2) = degree (x + 3)

Discussion

840.	If a parallelogram circumscribes a circle then prove that it must be a rhombus.
Answer» Solution :Given a parallelogram, say ABCD, Let this parallelogram TOUCH the circle at the point P, Q, R and S. As AP and AS are tangents to the circle drawn from an EXTERNAL point A. `AP=AS""…(1)` SIMILARLY,`""BP=BQ""…(2)` `CR=CQ""...(3)` `DR=DS""...(4)` Circles Adding (1), (2), (3) and (4), we get `implies""AP+BP+CR+DR=AS+BQ+CQ+DS` `implies""(AP+BP)+(CR+DR)=(AS+DS)+(BQ+CQ)` `implies""AB+CD=AD+BC` `implies""AB+AB=AD+AD` (CD=AB, DB=AD, opposite sides of a parallelogram) `implies""2AB=2AD` `implies""AB=AD` Hence, ABCD is a RHOMBUS. (`because` adjacent sides of a parallelogram are equal) Hence Proved.

Discussion

841.	Find the area of that triangle whose vertices are(1,1),(-1,4)and(3,2).
Answer» ANSWER :4 SQUARE UNITS

Discussion

842.	Ratio of two supplementary angles is 7:2. Find measure of each angle.
Answer» ANSWER :`140^@`,`40^@`

Discussion

843.	Do the line segments joining the points (-6, 2), (-2, -2) and (1,1) form a triangle ? If so name the type of triangle so formed
Answer» ANSWER :`DeltaABC` is a right ANGLED TRIANGLE, right angled at B

Discussion

844.	Describe the locus of points at distances greater than 4 cm from a given point.
Answer» ANSWER :4 CM

Discussion

845.	A is a manufacturer fo T.V. sets in Delhi. He manufactures a particular brand of T.V. set and marks it at Rs. 75,000. He then sells this T.V. set to a wholesaler B in Punjab at a discount of 30%. The wholesaler B raises the marked price of the T.V. set bought by 30% and then sells it to dealer C in Delhi. If the rate of GST =5%, find tax (under GST) paid by wholesaler B to the government.
Answer» ANSWER :RS. 2,250

Discussion

846.	Name the type of quadrilateral formed, if any, by the points, and give reasons for your answer. (-1, -2), (1, 0), (-1, 2), (-3, 0)
Answer» ANSWER :SQUARE

Discussion

847.	The volumes of two spheres are in the ratio 27:8. Find the ratio of their diameters.
Answer» ANSWER :`3:2`

Discussion

848.	x^(3)-2x+5 find coefficient of x^2,x^1,x^0.
Answer»

Discussion

849.	Draw a line segment of length 7cm. Find a point P on it which divides it in the ratio 3:5.
Answer» Solution :Steps of construction 1. Draw a line segment AB=7 cm. 2. Draw a ray AX , making an acute `angleBAX`. 3. Along AX, MARK 3+5=8 points `A_(1),A_(2),A_(3),A_(4),A_(5),A_(6),A_(6),A_(7),A_(8)` such that `A A_(1)=A_(1)A_(2)=A_(2)A_(3)=A_(3)A_(4)=A_(4)A_(5)=A_(5)A_(6)=A_(6)A_(7)=A_(7)A_(8)` 4. Join `A_(8)B`. From `A_(3)`, draw `A_(3)C\|\|A_(8)` B meeting AB at C. [ by making an angle equal to `angleBA_(8)A " at " A_(3)`] Then, C is the point on AB which divides it in the RATIO 3:5. Thus, AC:CB=3:5 JUSTIFICATION Let `A A_(1)=A_(1)A_(2)=A_(2)A_(3)=A_(3)A_(4)= ....=A_(7)A_(8)=x` In `DeltaABA_(8)` , we have `A_(3)C\|\|A_(8)B` `:. (AC)/(CB)=(A A_(3))/(A_(3)A_(8))=(3x)/(5x)=(3)/(5)` Hence, `AC:CB=3:5`

Discussion

850.	If the roots of the equation q^(2)x^(2)+p^(2)x+r^(2)=0 are the squares of the roots of the equation qx^(2)+px+r=0 then q, p, r are in___.
Answer» A.P. G.P. Both A.P. and G.P. None of these Answer :B

Discussion

Explore topic-wise InterviewSolutions in .

Differentiate the following with respect to x using first principle method. sin^((1)/(3))x=root(3)(sinx).

Show that the locus of a point, equidistant from two intersecting lines in the plane, is a pair of lines bisecting the angles formed by the given lines.

Find the number zeroes of the given polynomials. And also find their values. p(x)=2x+1

A well of diameter 14 m is dug 15 m deep. The earth taken out of it has been spread evenly to form circular embankment all around the wall of width 7 m. Find the height of the embankment.

What is the last digit of 6^(100) .

Draw a circle of radius 6 cm. From a pint 10 cm away from its centre, construct the pair of tangents to the circle and measure their lengths.

A man invests a certain sum of money in 6% hundread rupee shares at 12rs premium. When the shares fell to 96rs he sold out all the shares bought and invested the proceed in 10% ten rupee shares at 8rs. If the change in his income is 540rs find the sum invested originally.

Find the sum of (b) -3,1,5……….to 17 terms.

A company declares 8 percent dividend to the share holders. If a man receives 2840rs as his dividend, find the nominal value of his shares.

A metallic sphere of radius 4.2 cm is melted and recast into the sphape of cylinder of radius 6 cm. Findthe height of the cylinder.

Which of the following points lies in the fourth quadrant ?

Find the number of squares in the figure given below :

Find the mean, median and mode of the following data :

The point which lies on the perpendicular bisector of the line sequent joining the points P(-2,0) and Q(2,5) is

Compute the mode of the following data :

The surface area of two sphere are in the ratio of 9:25 then their volume are in the ratio …….. .

Evaluate the (tan 45^(@))/("cosec" 30^(@)) + (sec 60^(@))/(cot 45^(@)) - (3 sin 90^(@))/(2 cos 0^(@)) .

If in a certain language, MACHINE is coded as LBBIHOD, which would be coded as SLT-MFNB?

Find the area of the canvas required to make a conical tent 14 m high and 96 m in diameter. Given that: (i) 20% of the canvas is used in folds and stitchings. (il) canvas used in folds and stitchings is 20% of the curved surface area of the tent.

Rajat invested Rs 24,000 in 7% hundred rupee shares at 20% discount. After one year, he sold these shares at Rs 75 each and invested the proceeds (including dividend of first year) in 18% twenty five rupee shares at 64% premium. Find : his gain or loss after one year.

find the equation of cicle in each of the following cases ) (c)touches both the coordinate axes inthrid quadrant and having rasius

Given [{:(,x,y+2),(,3,z-1):}] =[{:(,3,1),(,3,2):}] find x,y and z.

If the number of zeroes between the decimal point and the first non-zero digit of a number is 2, then the characteristic of logarithm of that number is ______.

In the format of GSTIN there are ......alpha-numberals.

ABCD is a cyclic quadrilateral , Sides AB and DC produced meet at point E ,whereas sides BC and AD produced meet at point F.Ifangle DCF : angle F : angle E =3 : 5 : 4find the angles of the cyclic quadrilateral ABCD.

P and Q have co-ordinates (0, 5) and (-2, 4). Write the co-ordinates of the image of Q, obtained by reflecting it in the origin followed by reflection in x-axis.

A cone of height 24 cm and radius of base 6 cm is made up of modelling clay. A child moulds it in the form of a sphere. Find the radius of the shape.

A woodern article was made by scooping out a hemisphere from each end of a soid cylinder is 12 cm and its base is of radius 4.2 cm find the total suface area of the article. Also find the volume of the wood left in the article.

Find the sum of G.P. : sqrt(3)+(1)/(sqrt(3))+(1)/(3sqrt(3))+ . . . . . . . . to n terms.

Construct a triangle similar to a given triangle ABC with its sides equal to (3)/(4)th of the corresponding sides of the Delta ABC For this construction, which of the following statements are true?

In what ratio is the line segment joining the point (-2,-3) and (3,7) divided by y-axis ?

The outer radius and the inner radius of a 30 cm long cylindrical gold pipe are 14 cm and 7 cm respectively. It is filled with bronze. The densitiesof gold and bronze are 20gm/cm^(3) and 30gm/cm^(3) respectively. Find the weight of the cylinder formed. (in gm)

The mean of x_(1),x_(2)....... x_(50) is M, if every x_ị, i = 1, 2 ..... 50is replaced by x_(i)//50then the mean is

If sec theta +tan theta =p,then what is the value ofsec theta -tan theta ?

Mr. Tiwari invested 29040rs in 15% 100rs shares quoted at a premium of 20%. Calculate (i) the number of shares bought by Mr. Tiwari (ii) Mr. Tiwari income from the investment (iii) the percentage return on his investment

A copper wire of diameter 6 mm is evenly wrapped on a cylinder of length 18 cm and diameter 49 cm to vover its whole surface. Find the length and the volume of the wire. If the density of copper be 8.8 g per cu-cm, find the weight of the wire.

Find the common difference of an AP in which a_(25) - a_(12) = -52.

Can (x - 2) be the remainder on division of a polynomial p(x) by (x + 3)?

If a parallelogram circumscribes a circle then prove that it must be a rhombus.

Find the area of that triangle whose vertices are(1,1),(-1,4)and(3,2).

Ratio of two supplementary angles is 7:2. Find measure of each angle.

Do the line segments joining the points (-6, 2), (-2, -2) and (1,1) form a triangle ? If so name the type of triangle so formed

Describe the locus of points at distances greater than 4 cm from a given point.

Name the type of quadrilateral formed, if any, by the points, and give reasons for your answer. (-1, -2), (1, 0), (-1, 2), (-3, 0)

The volumes of two spheres are in the ratio 27:8. Find the ratio of their diameters.

x^(3)-2x+5 find coefficient of x^2,x^1,x^0.

Draw a line segment of length 7cm. Find a point P on it which divides it in the ratio 3:5.

If the roots of the equation q^(2)x^(2)+p^(2)x+r^(2)=0 are the squares of the roots of the equation qx^(2)+px+r=0 then q, p, r are in___.