3694 + Interview Questions in Maths in Class 10 Page 55 InterviewSolution

2701.	If x = (sqrt(3) + 1)/(sqrt(3) -1) and y = (sqrt(3) -1)/(sqrt(3) + 1), find the value of x^(2) + xy + y^(2).
Answer» 18 16 21 15 Answer :D

Discussion

2702.	If r, h and l are the radius, height and slant height respectively of a comen, than which of the following relations is correct ?
Answer» `R^(2)=H^(2)+L^(2)` `h^(2)=l^(2)=r^(2)` `l^(2)=h^(2)+r^(2)` `l^(2)=h^(2)-r^(2)` Answer :C

Discussion

2703.	The value of x and y in the equation 0.2x+0.3y=1.3 and 0.4x+0.5y=2.3 are :
Answer» `x=2, y=3` `x=3, y=2` `x=-2,y=-3` `x=-3, y=-2` ANSWER :A

Discussion

2704.	A man invested 45000rs in 15% 100rs shares quoted at 125rs. When the M.V. of these shares rose to 140rs, he sold some shares, just enough to raise 8400rs Calculate (i) the number of shares he still holds (ii) the dividend due to him on these remaining shares.
Answer» ANSWER :`(i) 300` `(II) 4500RS`

Discussion

2705.	A monkey climbs five metres at the beginning of each minute and then slips back two metres in the next minute before he again starts climbing. If he starts his ascent at 8:00 am, at what time will he first touch a flag 17 metres from the ground?
Answer» 8:10 am 8:06 am 8:09 am 8:15 am Solution : Clearly, the monkey ascends 3 metres in every two MINUTES and 12 metres in 8 minutes. Now the remaining 5 metres he will ascend in one minute. Thus it takes 9 minutes to touch the flag and so he TOUCHES the flag at 8.09 am.

Discussion

2706.	Construct a quadrilateral ABCD with AB=3 cm, AB=3cm, AD=2.7 cm, DB=3.6 cm, angleB=110^(@) and BC=4.2 cm. Construct another quadrilateral A'BC'D' similar to quadrilateral ABCD so that diagonal BD'=4.8 cm.
Answer» Solution :Steps of construction: 1. Draw a line segment BC=4.2 2. At B, construct angle YBC`=110^(@)`. 3. With centre B and RADIUS equalt to 3cm draw ab arc cutting BY at A. 4. With centre A and radius equals to 2.7 cm, draw an arc . 5. With centre B and radius equals to 3.6 cm, draw another arc cutting the previous arc at D. 6. JOIN AD, CD and BD. Then, ABCD is the required quadrilateral . 7. Produce BD to D' such that BD'=4.8 cm. 8. From D', draw a line parallel to DAwhich cuts BY at A' 9. From D', draw a line parallel to DC when cuts BC produced atD'. Then `squareA'BC'D'` is the required quadrilateral similar to `squareABCD`.

Discussion

2707.	ABC is a right triangle right angled at C.Let BC = a, CA = b, AB = c and let p be the length of perpendicular from C on AB.Prove that (i) pc = ab(ii) (1)/(p^(2)) = (1)/(a^(2)) + (1)/(b^(2)) .
Answer» ANSWER :` (1)/(a^(2)) + (1)/(B^(2))` .

Discussion

2708.	Among the following, Arithmetic Progression is:
Answer» 1,4,6…….. 10,12,14,………. 35,30,25,……. 8,13,19,…….. ANSWER :B

Discussion

2709.	Write the following rationals in decimal form using fundamental theorem of arithmetic. 7218/(3^(2).5^2)
Answer» ANSWER :32.08

Discussion

2710.	The weight of a bucket is 15kg, when it is filled with water upto 3/5 of its capacity and the weight is 19kg, if it is filled with water upto 4/5 of its capacity. Find the weight of bucket, if it is completely filled with water.
Answer» ANSWER :X = 3

Discussion

2711.	In the question, if angleABC=45^(@), then the area of segment BXC is 27.93cm^(2) and not 3.72cm^(2) as given in the textbook nut if we consider angleBAC=45^(@) instead of angleABC=45^(@) then area of segment BXC will be 3.92cm^(2) which is near to 3.72cm^(2) as given in th textbook, if angleBAC = 45^(@) then solution be as follows.
Answer» ANSWER :A (SEGMENT BXC) `=3.92cm^(2)`.

Discussion

2712.	If (x + 1) and (x - 2) are factors of x^(3)+ (a + 1)x^2 -(b - 2) x-6, find the values of a and b. And then, factorise the given expression completely.
Answer» ANSWER :a-1 and b=7; (x+1) (x-2) (x+3)

Discussion

2713.	Consider the following sets and fill up the blanks with =or ne so as to make the statement true. A={1,2,3{} B={The first three natural numbers} C={a,b,c,d} D={d,c,a,b} E={a,e,I,o,u} F={sets of vowels in English Alphabet} (i) A....B (ii) A...E (iii) C....D (iv) D....F (v) F....A (vi) D.....E (vii) F.....B
Answer» ANSWER :(i) EQUAL(=) (ii) Not equal `(ne)` (III) Equal(=) (IV) Not equal `(ne)` (v) Not equal `(ne)` (VI) Not equal `(ne)` (vii)

Discussion

2714.	A cylinder and a cone are of same base radius and of same height. Find the ratio of the volume of the cylinder to the volume of the cone.
Answer» ANSWER :`3:1`

Discussion

2715.	Find the roots of the following quadratic equations by factorisation: (i) x^(2)-3x-10=0 (ii) 2x^(2)+x-6=0 (iii) sqrt(2)x^(2)+7x-5sqrt(2)=0 (iv)2x^(2)-x+1/8=0 (v)100x^(2)-20x+1=0
Answer» Answer :(i) 5 and -2 (II) 2 and 3/2 (III) `-sqrt(2)` (IV)`+1/4` (v) `1/10`

Discussion

2716.	Find how many terms of G.P. (2)/(9)-(1)/(3)+(1)/(2) . . . . .. . . . . .must be added to get the sum equal to (55)/(72) ?
Answer» ANSWER :5

Discussion

2717.	How many terms of the AP 24,21,18,…. Must be taken so that their sum is 78?
Answer» ANSWER :n=4 or 13

Discussion

2718.	Find the area of sector of a circle with radius 6cm, if angle of the sector is 60^(@)
Answer» ANSWER :`( 132)/( 7) CM^(2)`

Discussion

2719.	Findthe sum of first 14 terms of the sequence -3,3,9,15,…….
Answer» ANSWER :504

Discussion

2720.	Find the root of the quadratic equation (x+4)(2x-3).
Answer»

Discussion

2721.	Find the roots of the equation 5x^(2)-6x-2=0 by the method of completing squares.
Answer» ANSWER :`(3 + SQRT(19))/(5), (3-sqrt(19))/(5)`

Discussion

2722.	If AB:BC=3:5, then into how many equal parts seg AC is divided to get point B?
Answer» ANSWER :C

Discussion

2723.	Write the following rationals in decimal form using 23/(2^(3).5^2)
Answer» ANSWER :0.115

Discussion

2724.	Evaluate the following (sin 30^(@) +tan 45^(@) -cosec 60^(@) )/( cot 45^(@)+cos 60^(@) -sec 30^(@))
Answer» ANSWER :` 1`

Discussion

2725.	Check whether the following are quadratic equations : (2x-1) (x-3) =(x+5)(x-1)
Answer» ANSWER :YES

Discussion

2726.	costheta xx sec theta is equal to :
Answer» `-1` 1 0 `2COS THETA.` Answer :B

Discussion

2727.	A man holds 800 shares of rupes 100 each of a companypaying 7.5%divided semi - annually. If he had bought these shares at 40%premium. What percentage return does he get on his investment?
Answer» ANSWER :` 10 (5)/(7) %`

Discussion

2728.	Coordinates (3, 3),(-4, 1) and (3, -5) are the vertices of an….
Answer» RIGHT ANGLE triangle Isosceles triangle Equilateral triangle Scalene triangle Answer :D

Discussion

2729.	Name the figure PQR.
Answer» ANSWER :RIGHT ANGLED TRIANGLE

Discussion

2730.	Ravi is not wearing white and Ajay is not wearing blue.Ravi and Sohan wear different colours.Sachin alone wears red .What is Sohan's colour ,if all four of them are wearing different colours?
Answer» Red Blue White Can't say Solution :The FOURTH COLOUR and some more INFORMATION are REQUIRED.

Discussion

2731.	Find the point on the X-axis which is equidistant from (2, -5) and (-2, 9).
Answer» ANSWER :(,7, 0)

Discussion

2732.	Draw a circle of radius 6 cm. From a point 10 cm away from its centre, construct the pair of tangents to the circle and measure their lengths.
Answer» ANSWER :`OA bot AP and OA`is the RADIUS; so, AP is the tangent to the GIVEN circle.

Discussion

2733.	A company pays a dividend of 15% on itsten -rupee shares from which it deducts income tax at the rate of 22%. Find the annual income of a man who owns one thousand shares of this company ?
Answer» ANSWER :`1170rs`

Discussion

2734.	Which term of the AP 5, 15, 25 is 150 more than its 12th term?
Answer» ANSWER :It is the 27TH TERM.

Discussion

2735.	The surface area of a sphere is 2464 cm^(2), find its volume.
Answer» ANSWER :`11498.67 CM ^(3)`

Discussion

2736.	If Thursday was the day after the day before yesterday five days ago, what is the least number of days ago when Sunday was three days before the day after tomorrow?
Answer» Two THREE Four FIVE Solution : DAY after the day before yesterday is yesterday. Now, five days ago, yesterday was Thursday. So five days ago it was Friday. ` therefore`Today is Wednesday. Now three days before the day after tomorrow is yesterday. Now it is on Monday that we say yesterday was SUNDAY.

Discussion

2737.	Find the ratio of the area of the semicircle formed on the diagonal of a square of side 14 cm to that of the semicircle forned on the side of the square.
Answer» ANSWER :`2:1`

Discussion

2738.	Check whether the following equations are consistent or inconsistent. Solve them graphically. 5x-3y = 11, -10x+6y = -22
Answer» ANSWER :They have INFINITELY MANY SOLUTIONS.

Discussion

2739.	Twocircles intersect each other such that each circle passes through the centre of the other. If the distance between theircentres is 12, what is the radius of each circle ?
Answer» 6 CM 12 cm 24 cm can't SAY Answer :A::B::C

Discussion

2740.	Find the the indicated term of each Geometric, Progression (i) a_(1) = 9, r=1/3, find a_(7), (ii) a_(1) =-12, r=1/3, find a_(6)
Answer» ANSWER :(i) `1/3^(4)`, (II) `-4/3^(4)`

Discussion

2741.	The product of Yusuf's age 5 years ago and his age 5 years ago and his age 9 years hence is 176. find Yusuf's present age.
Answer» ANSWER :13 YEARS

Discussion

2742.	If 2 is a root of the equation x^2+ kx + 12 =0 and the equation x^2 + kx + q = 0 has equal roots, find the value of q.
Answer» ANSWER :q=16

Discussion

2743.	Fill in the blanks Calculate the length of tangent from a point 15cm away from the centre of a circle of radius 9cm.
Answer» ANSWER :`12CM`

Discussion

2744.	The pointP(2,-4) is reflected about the line y = 0 to get the image R. Find the co-ordinates of R.
Answer» ANSWER :R = (-2,4)

Discussion

2745.	Two solid right circular cones have the same height and radii r_(1)cm and r_(2) cm. They are melted and recast into a right circular cylinder of the same height. Then, the radius of the cylinder is ......... cm.
Answer» `(r_(1)^(2)+r_(2)^(2))/(3)` ` SQRT((r_(1)^(2)+r_(2)^(2))/(3))` `sqrt(r_(1)^(2)+r_(2)^(2))` `sqrt(r_(1)r_(2))` Answer :A::B::C

Discussion

2746.	Find the value of 'a', if (x - a) is a factor of x^(3)-ax^2+x+2.
Answer» ANSWER :`-2`

Discussion

2747.	The total surface area of a right circular cone of slant height 13 cm is 90pi cm^(2). Calculate its volume in cm^(3). (Take pi = 3.14).
Answer» ANSWER :`314 CM ^(3)`

Discussion

2748.	How is M related to N? I. P, who has only two kids, M and N, is the mother-in-law of Q, who is sister-in-law of N. II. R, the sister-in-law of M, is the daughter in-law of S, who has only two kids, M and N.
Answer» <P>the data in STATEMENT I alone are sufficient to answer the question, while the data in statement II alone are not sufficient to answer the question, the data in statement II alone are sufficient to answer the question, while the data in statement I alone are not sufficient to answer the question, the data either in statement I alone or in statement II alone are sufficient to answer the question, the data given in both STATEMENTS I and II together are not sufficient to answer the question, Solution :From I, we conclude that P is the mother of M and N, while Q is the daughter-in-law of P and sister-in-law of N. Thus, Q is M.s WIFE and hence, M is N.s brother. From II, we conclude that M and N are the CHILDREN of S. Also, R is the daughter-in-law of S and sister-in-law of M. So, R is N.s wife and thus, N is M.s brother. Hence, M is either brother or sister of N.

Discussion

2749.	Find the slope of the line passing through the given two point (a, 0) and (0, b)
Answer» ANSWER :`(-B)/(a)`

Discussion

2750.	The tow adjacentsides of the rightangleof a rigledtriangleare 3 cmand4 cm . Cosntructthe triangle and then bydrawingits incricle , determine the inradiusof thistriangle . (Givenconstruction signs only).
Answer» ANSWER :1 CM

Discussion

Explore topic-wise InterviewSolutions in .

If x = (sqrt(3) + 1)/(sqrt(3) -1) and y = (sqrt(3) -1)/(sqrt(3) + 1), find the value of x^(2) + xy + y^(2).

If r, h and l are the radius, height and slant height respectively of a comen, than which of the following relations is correct ?

The value of x and y in the equation 0.2x+0.3y=1.3 and 0.4x+0.5y=2.3 are :

A man invested 45000rs in 15% 100rs shares quoted at 125rs. When the M.V. of these shares rose to 140rs, he sold some shares, just enough to raise 8400rs Calculate (i) the number of shares he still holds (ii) the dividend due to him on these remaining shares.

A monkey climbs five metres at the beginning of each minute and then slips back two metres in the next minute before he again starts climbing. If he starts his ascent at 8:00 am, at what time will he first touch a flag 17 metres from the ground?

Construct a quadrilateral ABCD with AB=3 cm, AB=3cm, AD=2.7 cm, DB=3.6 cm, angleB=110^(@) and BC=4.2 cm. Construct another quadrilateral A'BC'D' similar to quadrilateral ABCD so that diagonal BD'=4.8 cm.

ABC is a right triangle right angled at C.Let BC = a, CA = b, AB = c and let p be the length of perpendicular from C on AB.Prove that (i) pc = ab(ii) (1)/(p^(2)) = (1)/(a^(2)) + (1)/(b^(2)) .

Among the following, Arithmetic Progression is:

Write the following rationals in decimal form using fundamental theorem of arithmetic. 7218/(3^(2).5^2)

The weight of a bucket is 15kg, when it is filled with water upto 3/5 of its capacity and the weight is 19kg, if it is filled with water upto 4/5 of its capacity. Find the weight of bucket, if it is completely filled with water.

If (x + 1) and (x - 2) are factors of x^(3)+ (a + 1)x^2 -(b - 2) x-6, find the values of a and b. And then, factorise the given expression completely.

A cylinder and a cone are of same base radius and of same height. Find the ratio of the volume of the cylinder to the volume of the cone.

Find the roots of the following quadratic equations by factorisation: (i) x^(2)-3x-10=0 (ii) 2x^(2)+x-6=0 (iii) sqrt(2)x^(2)+7x-5sqrt(2)=0 (iv)2x^(2)-x+1/8=0 (v)100x^(2)-20x+1=0

Find how many terms of G.P. (2)/(9)-(1)/(3)+(1)/(2) . . . . .. . . . . .must be added to get the sum equal to (55)/(72) ?

How many terms of the AP 24,21,18,…. Must be taken so that their sum is 78?

Find the area of sector of a circle with radius 6cm, if angle of the sector is 60^(@)

Findthe sum of first 14 terms of the sequence -3,3,9,15,…….

Find the root of the quadratic equation (x+4)(2x-3).

Find the roots of the equation 5x^(2)-6x-2=0 by the method of completing squares.

If AB:BC=3:5, then into how many equal parts seg AC is divided to get point B?

Write the following rationals in decimal form using 23/(2^(3).5^2)

Evaluate the following (sin 30^(@) +tan 45^(@) -cosec 60^(@) )/( cot 45^(@)+cos 60^(@) -sec 30^(@))

Check whether the following are quadratic equations : (2x-1) (x-3) =(x+5)(x-1)

costheta xx sec theta is equal to :

A man holds 800 shares of rupes 100 each of a companypaying 7.5%divided semi - annually. If he had bought these shares at 40%premium. What percentage return does he get on his investment?

Coordinates (3, 3),(-4, 1) and (3, -5) are the vertices of an….

Name the figure PQR.

Ravi is not wearing white and Ajay is not wearing blue.Ravi and Sohan wear different colours.Sachin alone wears red .What is Sohan's colour ,if all four of them are wearing different colours?

Find the point on the X-axis which is equidistant from (2, -5) and (-2, 9).

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

A company pays a dividend of 15% on itsten -rupee shares from which it deducts income tax at the rate of 22%. Find the annual income of a man who owns one thousand shares of this company ?

Which term of the AP 5, 15, 25 is 150 more than its 12th term?

The surface area of a sphere is 2464 cm^(2), find its volume.

If Thursday was the day after the day before yesterday five days ago, what is the least number of days ago when Sunday was three days before the day after tomorrow?

Find the ratio of the area of the semicircle formed on the diagonal of a square of side 14 cm to that of the semicircle forned on the side of the square.

Check whether the following equations are consistent or inconsistent. Solve them graphically. 5x-3y = 11, -10x+6y = -22

Twocircles intersect each other such that each circle passes through the centre of the other. If the distance between theircentres is 12, what is the radius of each circle ?

Find the the indicated term of each Geometric, Progression (i) a_(1) = 9, r=1/3, find a_(7), (ii) a_(1) =-12, r=1/3, find a_(6)

The product of Yusuf's age 5 years ago and his age 5 years ago and his age 9 years hence is 176. find Yusuf's present age.

If 2 is a root of the equation x^2+ kx + 12 =0 and the equation x^2 + kx + q = 0 has equal roots, find the value of q.

Fill in the blanks Calculate the length of tangent from a point 15cm away from the centre of a circle of radius 9cm.

The pointP(2,-4) is reflected about the line y = 0 to get the image R. Find the co-ordinates of R.

Two solid right circular cones have the same height and radii r_(1)cm and r_(2) cm. They are melted and recast into a right circular cylinder of the same height. Then, the radius of the cylinder is ......... cm.

Find the value of 'a', if (x - a) is a factor of x^(3)-ax^2+x+2.

The total surface area of a right circular cone of slant height 13 cm is 90pi cm^(2). Calculate its volume in cm^(3). (Take pi = 3.14).

How is M related to N? I. P, who has only two kids, M and N, is the mother-in-law of Q, who is sister-in-law of N. II. R, the sister-in-law of M, is the daughter in-law of S, who has only two kids, M and N.

Find the slope of the line passing through the given two point (a, 0) and (0, b)

The tow adjacentsides of the rightangleof a rigledtriangleare 3 cmand4 cm . Cosntructthe triangle and then bydrawingits incricle , determine the inradiusof thistriangle . (Givenconstruction signs only).