3694 + Interview Questions in Maths in Class 10 Page 25 InterviewSolution

1201.	Students of a class are made to stand in row. If one student is extra in each row, there would be 2 rows less. If one student is less in each row, there would be 3 rows more. Find the number of students in the calss.
Answer» ANSWER :`=5 XX 12 =60`

Discussion

1202.	If a+b+c=0, then (1)/( b^(2) + c^(2) - a^(2) ) +(1)/( c^(2) + a^(2) - b^(2) ) + (1)/( a^(2) + b^(2) -c^(2) ) is equal to
Answer» 3 6 1 0 Answer :D

Discussion

1203.	Find the 12th term of a G.P. whose 8th term is 192, and the common ratio is 2.
Answer» ANSWER :`3 XX 2^(10) = 3072`

Discussion

1204.	If triangleABC is similar totriangleDFE such that BC=3cm, EF=4cm and area of triangleABC=54cm^(2). Find thearea of triangle DFE.
Answer» ANSWER :`96CM^(@)`

Discussion

1205.	Find the coordinates of a point A, where AB is the diameter of a circle whose centre is (2, -3) and B is (1, 4).
Answer» ANSWER :(3,-10)

Discussion

1206.	Goods/services are sold from Kota (Rajasthan) to Mumbai for Rs. 20,000 and then from Mumbai to Pune. If the rate of GST is 12% and the profit made at Mumbai is Rs. 5,000, find the net GST paid at Pune, if the dealer at Pune is the end - user.
Answer» ANSWER :RS. 3,000

Discussion

1207.	Find the nature of the roots of the following quadratic equations. If the real roots exists, find them: (i) 2x^(2)-2x+5=0 (ii)3x^(2)-4sqrt(3x)+4=0 (iii)2x^(2)-6x+3=0
Answer» Answer :(i) no REAL ROOTS exist. (ii)`2//sqrt(3)` (iii)`(3-sqrt(3))/2`

Discussion

1208.	Ratio of two complementary angles is 5:4. Find the measure of each angle.
Answer» ANSWER :`40^@`

Discussion

1209.	The diagonal of a rectangular field is 60 metres more than the shorter side. If the longer side is 30 metres more than the shorter side, find the sides of the field. ORSum of the areas of two squares is 468m^(2). If the difference of their perimeters is 24m, find the sides of two squares.
Answer» ANSWER :18M; 12M

Discussion

1210.	The sum of the inner and the outer curved surfaces of a hollow metallic cylinder is 1056 cm ^(2) and the volume of material in it is 1056 cm^(3). Find its internal and external radii. Given that the height of the cylinder is 21 cm.
Answer» ANSWER :`5 CM and 3 cm`

Discussion

1211.	Is the following situation possible? If so, determine their present ages. The sum of the ages of two friends is 20 years. Four years ago, the product of their ages in years was 48.
Answer» ANSWER :No

Discussion

1212.	In the given figure ,O is the centre of the circle AB=2cm,AC=3cm,CE=6cm.Find DE.
Answer» ANSWER :4 CM

Discussion

1213.	The range of first 10 prime numbers is…….
Answer» ANSWER :27

Discussion

1214.	A solid cylinder and a cone have the same radius and height . If the volume of cylinder is 27 cc, then the volume of cone is :
Answer» 9 c.c 27 c.c 81 c.c 3 c.c Answer :a

Discussion

1215.	If the fourth and nineth terms of a G.P. are 54 and 13122 respectively, find the G.P. Also find its general term.
Answer» ANSWER :2,6,18,54,162 . . . . . . . and `2XX3^(n-1)`

Discussion

1216.	Show that the points (a,a),(-a,-a)and(-sqrt3a,sqrt3a) are the vertices of an equilateral triangle. Find its area.
Answer» ANSWER :`2sqrt3a^(2)` SQUARE UNITS

Discussion

1217.	IF B={1,2,3,4,5,6} and C={3,5,6} thenfind B-C.
Answer» ANSWER :So A-B `NE` B-A

Discussion

1218.	Find the values of x,y,a and b, if : [{:(,x-2,y),(,a//2,b+1):}]=[{:(,0,3),(,1,5):}]
Answer» ANSWER :a=2, b=4

Discussion

1219.	Study the following fgures and find out in each case whether the triangles are similar. Give reason. (a) (b)
Answer» ANSWER :`DELTA XUV ~ Delta XYZ`

Discussion

1220.	It is true to say that the mean, mode and median of grouped data always be different? Justify your answer.
Answer» SOLUTION :No, the VALUE of these THREE MEASURES can be the same, it depends on the type of DATA.

Discussion

1221.	If P(E ) = 0.05 , then find the probability of not E.
Answer» ANSWER :`1/2`

Discussion

1222.	The sum of first 7 terms of an AP is 63 and the sum of next 7 terms is 161. Find a_(28).
Answer» ANSWER :`a_(25) = 3+ (28 -1) 2=3 + (27 XX 2) 3 + 54 = 57`

Discussion

1223.	True or False : A pair of tangents to a circle can be constructed which are inclined at an angle of 170^(@).
Answer» ANSWER :TRUE

Discussion

1224.	Is (3x-2)(2x-3)=(2x+5)(2x-1) a quadratic equation ?
Answer» ANSWER :GIVEN EQUATION is a QUADRATIC equation.

Discussion

1225.	Find the ratio in which (-4, 6) divides the line segment joining A (6, 10) and B (3,-8).
Answer» ANSWER :`2: 7`

Discussion

1226.	A solid is in the form of a right circular cone mounted on a hemisphere. The radius of the hemisphere is 2.1 cm and the height of the cone is 4 cm. The solid is placed in a cylindrical tub full of water
Answer» ANSWER :`732.116 CM^(2)`

Discussion

1227.	Construct a DeltaABC with BC = 6.5 cm, AB = 5.5 cm, AC = 5 cm. Construct the incircle of the triangle. Measure and record the radius of the incircle.
Answer» ANSWER :1.6CM

Discussion

1228.	If in a certain language, POPULAR is coded as QPQVMBS, which word would be coded as GBNPVT?
Answer» FAMOSU FAMOUS FASOUM FOSAUM Solution :Each LETTER of the word in ONE STEP behind the CORRESPONDING letter of the code

Discussion

1229.	Solve : (x)/(x-1)+(x-1)/(x)=2(1)/(2).
Answer» ANSWER :`x=2`, or `x=-1`

Discussion

1230.	If 453945 stands for DECIDE, then how 8978 is written?
Answer» BHEF CDEH GHEF HIGH SOLUTION :NUMBER are replaced by the FACE values of English alphabets. `8 to H , 9 to I , 7 to G` . Thus `8978 to HIGH`

Discussion

1231.	A rectangular park is to be designed whose breadth is 3 m less than its length. Its area is to be 4 square metres more than area of a park that has already been made in the shape of an isosceles triangle with its base as the breadth of the reatangular park and of altitude 12m. Find its length and breadth.
Answer» ANSWER :breath=4m and LENGTH 7M

Discussion

1232.	Naresh invested a certain amount of money in Rs. 100 shares at a discount of Rs. 20 paying a dividend of 7%, while Sahil invested an equal amount in Rs. 90 shares at a discount of Rs. 10 paying a dividend of 8%. Who earns more ?
Answer» ANSWER :SAHIL

Discussion

1233.	Evaluate the(cos 60^(@) - cot 45^(@) + "cosec" 30^(@))/(sec 60^(@) + tan 45^(@) - sin 30^(@)).
Answer» ANSWER :`(3)/(5)`

Discussion

1234.	Which of the alternatives will come next in the series. CZX, DYW, EXV, FWU, ?
Answer» GWT GUT GTV GVT Answer :D

Discussion

1235.	If A=[{:(,1,3),(,3,4):}], B=[{:(,-2,1),(,-3,2):}] and A^2-5B^2=5C. find matrix C where C is a 2 by 2 matrix.
Answer» ANSWER :`[{:(,1,3),(,3,4):}]`

Discussion

1236.	The radii of two cylinders are in the ratio 2:3 and their heights are in the ratio 5:3. Then, the ratio of their volumes is
Answer» `27:20` `20:27` `9:4` `1:4` ANSWER :B

Discussion

1237.	Find the roots of the following quadraticequations by factorisation :2x^(2)-x+1/8=0
Answer» ANSWER :`(1)/(4); (1)/(4)`

Discussion

1238.	From the top of a light house, angles of depression of two ships are 45^(@) and 60^(@). The ships are on opposite sides of the ight house and in line with its foot. If the distance between the ships is 400 m, find the height of the light house.
Answer» ANSWER :`(400sqrt(3))/(SQRT(3)+1)`.

Discussion

1239.	How many squares are contained in the following figure ?
Answer» 6 7 8 9 Answer :D

Discussion

1240.	Solve the following simultaneous equations : 4x + 3y = 4 , 6x + 5y = 8
Answer» ANSWER :`(-2,4)`

Discussion

1241.	Prove that opposites of a quadrilaterial circumscribing a circle subtend supplementary angles at the centre of the circle.
Answer» ANSWER :`180^(@)`

Discussion

1242.	Two line segments AB and AC include an angle of 60°, where AB = 5 cm and AC = 7 cm. Locate points P and Q on AB and AC respectively such that AP = (3)/(4) AB and AQ = (1)/(4) AC. Join P and Q and measure PQ.
Answer» ANSWER :`(AQ)/(AC ) = (1)/(4)`

Discussion

1243.	Express the relation of a and b if sin theta =(2ab)/(a^2+b^2) , where a gt 0 , b gt 0.
Answer» ANSWER :` a GT0 , B GT 0`

Discussion

1244.	The sum of three consecutive terms of an A.P. is 21 and the sum of their squares is 165. Find these terms.
Answer» ANSWER :4,7 and 10 or 10,7 and 4

Discussion

1245.	Mr. Rohit is a retailer. He paid GST of 6500 at the time of purchase. He collected of GST of 8000 at the time of sale. (i) Find has input tax and output tax. (ii) What is his Input tax credit? (iii) Find his payable GST. (iv). Hence find the payable CGST and payable SGST.
Answer» ANSWER :Output tax=8000 Input tax=6500 (II) 6500 (iii) 1500 iv CGST=SGST=750

Discussion

1246.	Using the Factor theorem, show that (i) (x-2) is a factor of x^(3)-2x^(2)-9x+18. Hence factorise the expression x^2-2x^2-9x+18 completely. (ii) (x+5) is a factor of 2x^3+5x^2-28x-15. Hence factorise the expression 2x^3+5x^2-28x-15 completely. (iii) (3x+2) is a factor of 3x^(3)+2x^(2)-3x-2. Hence factorise the expression 3x^3+2x^2-3x-2 completely.
Answer» ANSWER :(i) (x-2) (x+3) (x-3) (II) (x+5) (2x+1) (x-3) (III) (3x+2) (x+1) (x-1)

Discussion

1247.	A bucket when filled (5)/(7) with water weights 12 kg and filled (3)/(4) of itwith water weight 12.5 kg. What is the weight of the empty bucket?
Answer» ANSWER :2 KG

Discussion

1248.	A chord of a circle of radius 6cm is making an angle60 ^(@)at the centre.Find the length of the chord.
Answer» ANSWER :`THEREFORE ` Therefore LENGTH of the CHORD =6CM

Discussion

1249.	Metallic spheres of radii 6cm, 8cm and 10cm , respectively are melted to form a single solid sphere. Find the radius of the resulting sphere.
Answer» ANSWER :12 CM

Discussion

1250.	The maturity value of a cumulative deposit account is Rs 1,20,400. If each monthly instalment for this account isRs 1,600 and the rate of interest is 10% per year, find the time for which the account was held.
Answer» ANSWER :5 YEARS

Discussion

Explore topic-wise InterviewSolutions in .

Students of a class are made to stand in row. If one student is extra in each row, there would be 2 rows less. If one student is less in each row, there would be 3 rows more. Find the number of students in the calss.

If a+b+c=0, then (1)/( b^(2) + c^(2) - a^(2) ) +(1)/( c^(2) + a^(2) - b^(2) ) + (1)/( a^(2) + b^(2) -c^(2) ) is equal to

Find the 12th term of a G.P. whose 8th term is 192, and the common ratio is 2.

If triangleABC is similar totriangleDFE such that BC=3cm, EF=4cm and area of triangleABC=54cm^(2). Find thearea of triangle DFE.

Find the coordinates of a point A, where AB is the diameter of a circle whose centre is (2, -3) and B is (1, 4).

Goods/services are sold from Kota (Rajasthan) to Mumbai for Rs. 20,000 and then from Mumbai to Pune. If the rate of GST is 12% and the profit made at Mumbai is Rs. 5,000, find the net GST paid at Pune, if the dealer at Pune is the end - user.

Find the nature of the roots of the following quadratic equations. If the real roots exists, find them: (i) 2x^(2)-2x+5=0 (ii)3x^(2)-4sqrt(3x)+4=0 (iii)2x^(2)-6x+3=0

Ratio of two complementary angles is 5:4. Find the measure of each angle.

The diagonal of a rectangular field is 60 metres more than the shorter side. If the longer side is 30 metres more than the shorter side, find the sides of the field. ORSum of the areas of two squares is 468m^(2). If the difference of their perimeters is 24m, find the sides of two squares.

The sum of the inner and the outer curved surfaces of a hollow metallic cylinder is 1056 cm ^(2) and the volume of material in it is 1056 cm^(3). Find its internal and external radii. Given that the height of the cylinder is 21 cm.

Is the following situation possible? If so, determine their present ages. The sum of the ages of two friends is 20 years. Four years ago, the product of their ages in years was 48.

In the given figure ,O is the centre of the circle AB=2cm,AC=3cm,CE=6cm.Find DE.

The range of first 10 prime numbers is…….

A solid cylinder and a cone have the same radius and height . If the volume of cylinder is 27 cc, then the volume of cone is :

If the fourth and nineth terms of a G.P. are 54 and 13122 respectively, find the G.P. Also find its general term.

Show that the points (a,a),(-a,-a)and(-sqrt3a,sqrt3a) are the vertices of an equilateral triangle. Find its area.

IF B={1,2,3,4,5,6} and C={3,5,6} thenfind B-C.

Find the values of x,y,a and b, if : [{:(,x-2,y),(,a//2,b+1):}]=[{:(,0,3),(,1,5):}]

Study the following fgures and find out in each case whether the triangles are similar. Give reason. (a) (b)

It is true to say that the mean, mode and median of grouped data always be different? Justify your answer.

If P(E ) = 0.05 , then find the probability of not E.

The sum of first 7 terms of an AP is 63 and the sum of next 7 terms is 161. Find a_(28).

True or False : A pair of tangents to a circle can be constructed which are inclined at an angle of 170^(@).

Is (3x-2)(2x-3)=(2x+5)(2x-1) a quadratic equation ?

Find the ratio in which (-4, 6) divides the line segment joining A (6, 10) and B (3,-8).

A solid is in the form of a right circular cone mounted on a hemisphere. The radius of the hemisphere is 2.1 cm and the height of the cone is 4 cm. The solid is placed in a cylindrical tub full of water

Construct a DeltaABC with BC = 6.5 cm, AB = 5.5 cm, AC = 5 cm. Construct the incircle of the triangle. Measure and record the radius of the incircle.

If in a certain language, POPULAR is coded as QPQVMBS, which word would be coded as GBNPVT?

Solve : (x)/(x-1)+(x-1)/(x)=2(1)/(2).

If 453945 stands for DECIDE, then how 8978 is written?

Naresh invested a certain amount of money in Rs. 100 shares at a discount of Rs. 20 paying a dividend of 7%, while Sahil invested an equal amount in Rs. 90 shares at a discount of Rs. 10 paying a dividend of 8%. Who earns more ?

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

Which of the alternatives will come next in the series. CZX, DYW, EXV, FWU, ?

If A=[{:(,1,3),(,3,4):}], B=[{:(,-2,1),(,-3,2):}] and A^2-5B^2=5C. find matrix C where C is a 2 by 2 matrix.

The radii of two cylinders are in the ratio 2:3 and their heights are in the ratio 5:3. Then, the ratio of their volumes is

Find the roots of the following quadraticequations by factorisation :2x^(2)-x+1/8=0

From the top of a light house, angles of depression of two ships are 45^(@) and 60^(@). The ships are on opposite sides of the ight house and in line with its foot. If the distance between the ships is 400 m, find the height of the light house.

How many squares are contained in the following figure ?

Solve the following simultaneous equations : 4x + 3y = 4 , 6x + 5y = 8

Prove that opposites of a quadrilaterial circumscribing a circle subtend supplementary angles at the centre of the circle.

Two line segments AB and AC include an angle of 60°, where AB = 5 cm and AC = 7 cm. Locate points P and Q on AB and AC respectively such that AP = (3)/(4) AB and AQ = (1)/(4) AC. Join P and Q and measure PQ.

Express the relation of a and b if sin theta =(2ab)/(a^2+b^2) , where a gt 0 , b gt 0.

The sum of three consecutive terms of an A.P. is 21 and the sum of their squares is 165. Find these terms.

Mr. Rohit is a retailer. He paid GST of 6500 at the time of purchase. He collected of GST of 8000 at the time of sale. (i) Find has input tax and output tax. (ii) What is his Input tax credit? (iii) Find his payable GST. (iv). Hence find the payable CGST and payable SGST.

A bucket when filled (5)/(7) with water weights 12 kg and filled (3)/(4) of itwith water weight 12.5 kg. What is the weight of the empty bucket?

A chord of a circle of radius 6cm is making an angle60 ^(@)at the centre.Find the length of the chord.

Metallic spheres of radii 6cm, 8cm and 10cm , respectively are melted to form a single solid sphere. Find the radius of the resulting sphere.

The maturity value of a cumulative deposit account is Rs 1,20,400. If each monthly instalment for this account isRs 1,600 and the rate of interest is 10% per year, find the time for which the account was held.