3694 + Interview Questions in Maths in Class 10 Page 19 InterviewSolution

901.	Find the roots of the following equations by factorisation. (i) x^(2)+x-12=0
Answer» ANSWER :`:.X= -4` or `x= -3` are the ROOTS.

Discussion

902.	Use a graph paper for this question. (Take 2 cm = 1 unit on both x and y axes) where A (0, 4), B (2, 3), C (1, 1) and D (2, 0) and reflect points B', C', D' on y-axis Join the points A, B, C, D, D', C', B' and A in order, so as to form a closed figure. Write down the equation of the line about which if this closed figure obtained is folded, the two parts of the figure exactly coincide.
Answer» ANSWER :X = 0

Discussion

903.	In a certain code ''il be pee'' means ''rose are blue'' ''sik hee'' means ''red flowers'' and ''pee mit hee'' means ''flowers are vegetables''. How is 'rose' written in that code?
Answer» il pee be can not be determined Answer :D

Discussion

904.	Prove that:(sintheta-costheta+1)/(sintheta+costheta-1)=(1)/(sectheta-tantheta)
Answer»

Discussion

905.	In a certain code ''il be pee'' means ''rose are blue'' ''sik hee'' means ''red flowers'' and ''pee mit hee'' means ''flowers are vegetables''. How is 'red' written in that code?
Answer» hee sik be can not be determined Answer :D

Discussion

906.	Prove that : (1+cotA)/(cosA)+(1+tanA)/(sinA)=2(secA+"cosec"A)
Answer» ANSWER :`15^@`

Discussion

907.	Two brothers A and B invest 16000rs each in buying shares of two companies. A buys 3% hundread-rupee shares at 80 and B buys ten-rupee shares at par. If they both receive equal dividend at the end of the year, find the rate percent of the dividend received by B.
Answer» ANSWER :`3.75%`

Discussion

908.	In what ratio does the point P (a, 2) divide the line segment joining the points A(5,-3) and B(-9, 4) ? Also, find the value of 'a'.
Answer» ANSWER :`5:2 and a = -5`

Discussion

909.	In the given figure O is the centre of the circle and AB is a tangent at B. If AB=15 cm and AC=7.5 cm, find the rdius of the circle.
Answer» ANSWER :11.25cm

Discussion

910.	If P varies directly as QR and the values of P, Q. R be 6, 9, 10 repectively, then the value of P when Q = 5 and R= 3 is
Answer» `1/2` `3` `1/3` `1` ANSWER :D

Discussion

911.	Solve (x)/(b) + (y)/(b) = 1 and a(x - a)- b(y + b) = 2a^(2) + b^(2).
Answer» ANSWER :X = 3A, y = -2B

Discussion

912.	State whether each of the following statements is true or false. Justify your answers. (i) {2,3,4,5} and {3,6} are disjoint sets. (ii) {a,e,I,o,u} and {a,b,c,d} are disjoint sets. (iii) {2,6,10,14} and {3,7,11,15} are disjoint sets. (iv) {2,6,10} and {3,7,11} are disjoint sets.
Answer» Answer :(i) False, because they have common element '3' (ii) False, because the two SETS have a common element 'a' (iii) TRUE, because no common elements for the sets. (IV) True, because no common elements for the sets.

Discussion

913.	M/s, Beauty Products paid 18% GST on cosmetics worth 6000 and sold to a customer for 10,000. What are the amounts of CGST and SGST shown in the tax invoice issued?
Answer» Answer :`therefore` Amount of CGST and SGST shown in the tax INVOICE ISSUED is 900 each.

Discussion

914.	Deepak is the brother of Anil. Deepak is the son of Prem. Bimal is Prem's father. How is Anil related to Bimal?
Answer» SON GRAND son BROTHER Grand father Solution :Anil is the brother of DEEPAK and Deepak is the son of Prem. So Anil is the son of prem. Now Bimal is the father of Prem. Thus, Anil is the grand son of Primal.

Discussion

915.	A sphere and a cube have the same surface area. Show that the ratio of the volume of the sphere to that of cube is sqrt(6):sqrt(pi).
Answer» ANSWER :`therefore` Ratioof voume of sphere and cube is `SQRT(6):sqrt(PI).`

Discussion

916.	If 32^(x- 2) = 64 + 8^x, the value of x is
Answer» `1//2` `1//4` `1//8` 2 Answer :D

Discussion

917.	Two cubes each of volume 64 cm^3 are joined end to end together. Find the surface area of the resulting cuboid.
Answer» ANSWER :`96 cm^2`

Discussion

918.	Name the type of quadrilateral formed, if any by the following points, and give reasons for your answer : (-3, 5), (3, 1), (0, 3), (-1,-4)
Answer» ANSWER :TREPEZIUM

Discussion

919.	The points (1, 1), (13, 1) and (13, 6) are the vertices of a right triangle.
Answer» ANSWER :TRUE

Discussion

920.	Find the roots of the following quadraticequations by factorisation : 2x^(2)+x-6=0
Answer» ANSWER :`-2; (3)/(2)`

Discussion

921.	The surface areas of two spheres are in the ratio 1:2. Then, the ratio of their volumes is ..........
Answer» `SQRT(2):1` `1:2:sqrt(2)` `1:8` `1:4` ANSWER :A::B

Discussion

922.	Two metallic spheres of radii 9 cm and 10 cm are melted and recast to make two new spheres. If the radius of one of the new spheres is 12 cm, the radius of the other new sphere is ......... cm.
Answer» 7 5 3 1 Answer :A

Discussion

923.	If REASON is coded as 5 and BELIEVED as 7, then what is the code for GOVERNMENT?
Answer» 6 8 9 10 Solution :LOGIC: Number of Letters in the word LESS 1

Discussion

924.	To conduct Sports Day activities,in your rectangular shaped school ground ABCD, lines have been drawn withchalk powder at a distance of 1m each. 100 flower pots have been placed at a distance of 1 m from each otheralong AD,as shown in the given figure. Niharika runs (1)/(4) th the distance AD on the 2ndline and posts a green flag. Preet runs (1)/(5) ththe distance ADon the eighthline and posts a red flag. What isthe distance between boththe flags ? IfRashmi has to post a blue flag exactly halfway between the line segmentjoiningthe two flags, where should she post her flag ?
Answer» Answer :`SQRT(61)` m and Rashmi should post the BLUE flag on the5th LINE at DISTANCE 22.5 m from AB.

Discussion

925.	Find the common ratio of the GP 25, -5, 1, -1/5,………
Answer» ANSWER :`-1/5`

Discussion

926.	Write the following sets in roster form (i) A={ x : x is a natural number greater than 50 but smaller than 100} B={x : x is an integer, x^(2)=4} (iii) D={x : x is a letter in the word "LOYAL"}
Answer» ANSWER :(i) A={51,52,53.....,98,99} (II) B={+2,-2} (iii) D={L,O,Y,A}

Discussion

927.	Find diagonal of square with side 8 cm.
Answer» ANSWER :`8sqrt2` CM

Discussion

928.	Village R is in which direction with respect to village D? I. Village R is to the north of village T which is to the west of village F. II. Village D is to the west of village T.
Answer» if 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, if 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, if the data either in statement I alone or in statement II alone are sufficient to answer the question, if the data in both statements I and II together are necessary to answer the question. Solution :From both I and II, we GET the following ARRANGEMENT: CLEARLY, village R is to the north-east of village D.

Discussion

929.	Draw a DeltaABC, right angled at B such that AB=3cm and BC=4 cm. Now, construct a triangle similar to DeltaABC,each of whose sides is (2)/(5) times the corresponding sides of DeltaABC.
Answer» ANSWER :`DeltaPBR` is the REQUIRED SIMILAR to the GIVEN `DELTAABC.

Discussion

930.	Write the GP if the first term a=3, and the common ratio r=2.
Answer» ANSWER :3,6,12,24,…….

Discussion

931.	Prove that: (i) sin (70^@+theta) -cos (20^@-theta) =0 (ii) tan (55^@-theta) -cot (35^@-theta)=0 (iii) cosec(67^@+theta) -sec (23^@-theta)=0 (iv) cosec (65^@+theta) -sec (25^@-theta )-tan (55^@-theta) +cot (35^@+theta) =0 (v) sin (50^@+theta) -cos (40^@-theta) +tan 1^@ tan 10 ^@ tan 80^@ tan 89^@=1
Answer» Solution :`(i) LHS =SIN {90^@-(20^@-theta)}-cos (20^@-theta)=cos (20^@-theta) -cos (20^@-theta) =0`. `(v) LHS =sin {90^@-(40^@-theta )}-cos (40^@-theta)+(tan 1^@tan 89^@)(tan 10^@tan 80^@)=cos (40^@-theta) -cos (40^@-theta) +(1xx1)=1`.

Discussion

932.	Find four numbers in A.P. whose sum is 20 and the sum of whose squares is 120.
Answer» ANSWER :2,4,6 and 8 or 8,6,4 and 2

Discussion

933.	A right triangle, whose sides are 3 cm and 4 cm(other than hypotenuse) is made to revolve about its hypotenuse. Find thevolume and surface area of the double cone so formed.
Answer» ANSWER :`52.75 CM^(2)`

Discussion

934.	A pen stand is made of wood in the shape of cuboid with three conical depressions to hold the pens. The dimensions of the cuboid are 15 cm by 10 cm by 3.5 cm. The radius of each of the depression is 0.5 cm and the depth is 1.4 cm n the entire stand.
Answer» ANSWER :523.9 `cm^3`

Discussion

935.	Riya has a field with a flowerbed and grass land. The grass land is in the shape of rectangle while flowerbed is in the shape of square. The length of the grassland is found to be 3 m more than twice the length of the flowerbed. Total area of the whole land is 1260 m^(2). What will be the perimeter of the whole field?
Answer» `(8X + 6) m` `(6x + 8) m` `(4x + 3) m` `(4x + 3) m` Solution :Perimeter `=2(3x+3+x)` `=2(4x+3)=(8x+6)` Thus (a) is correct option.

Discussion

936.	Riya has a field with a flowerbed and grass land. The grass land is in the shape of rectangle while flowerbed is in the shape of square. The length of the grassland is found to be 3 m more than twice the length of the flowerbed. Total area of the whole land is 1260 m^(2). If the length of the flowerbed is x m then what is the total length of the field ?
Answer» `(2x+3)m` `(3x+3)m` `6xm` `(2x+5)m` SOLUTION :The length of the grassland is 3 m more than twice the length of the flowerbed. THUS it will be 2x + 3 . Now the total length of field is 2x + 3 + x = 3x + 3 . Thus (b) is correct OPTION.

Discussion

937.	Riya has a field with a flowerbed and grass land. The grass land is in the shape of rectangle while flowerbed is in the shape of square. The length of the grassland is found to be 3 m more than twice the length of the flowerbed. Total area of the whole land is 1260 m^(2). What is the area of grassland ?
Answer» `180 m^(2) ` `360 m^(2) ` `400 m^(2) ` `860 m^(2)` Solution :Area of GRASSLAND, `A_(g) = (2x+3)X` `=(2xx 20+3)20` `=860 m^(2)` Thus (c) is CORRECT option.

Discussion

938.	A circular tank of diameter 2 m is dug and the earth removed is spread uniformly all around the tank to form an embankment 2 m in width and 1.6 m in height. Find the depth of the circular tank.
Answer» ANSWER :`12.8 m`

Discussion

939.	Riya has a field with a flowerbed and grass land. The grass land is in the shape of rectangle while flowerbed is in the shape of square. The length of the grassland is found to be 3 m more than twice the length of the flowerbed. Total area of the whole land is 1260 m^(2). What is the value of x if the area of total field is 1260 m^(2).
Answer» 21 m 10 m 20 m 15 m Solution :We have `A=(3x+3)x` `1260 =3x^(2) +3x` `420=x^(2) +x` `x^(2) +x -420=0` `(x+21) (x-20) =0` THUS, x = 20 is only POSSIBLE value. Thus (c) is CORRECT option.

Discussion

940.	Draw two concentric circles of radii 3 cm and 5 cm. Taking a point on outer circle, construct the pair of tangents to the other. Measure the length of a tangent and verify is by actual calculation.
Answer» Solution :Steps of Consstruction : 1. Draw two concentric CIRCLES `C_(1),C_(2)` of radil 3 cm and 5 cm respectively taking 'O' as centre. 2. DREW CIRCLE `C_(3)` taking radius TM = OM and M as centre. 4. Circle `C_(3)` intersect the circle `C_(1)` at P and Q. Join TP and TQ. These are the required tangents. TP = TQ = 4.1 cm by measuring. Mathematically Length of Tangent : Join OP. OP and TP are radius and tangent respectively at contact point P. So, `angleTPO =90^(@).` By Pythagoras THEOREM in `DeltaTPO,` `""PT^(2)=OT^(2)-OP^(2)=5^(2)-3^(2)=25-9=16` `implies""PT=4cm` Difference in measurment and by mathematical calculation `""PT=4.1cm-4cm=0.1cm`

Discussion

941.	Riya has a field with a flowerbed and grass land. The grass land is in the shape of rectangle while flowerbed is in the shape of square. The length of the grassland is found to be 3 m more than twice the length of the flowerbed. Total area of the whole land is 1260 m^(2). What is the ratio of area of flowerbed to area of grassland ?
Answer» `(20)/(43)` `(23)/(40)` `(26)/(43)` `(23)/(46)` Solution :Area of flowerved, `A_(f) = X^(2) =20^(2)= 400 m^(2)` Ratio `=(400)/(860)=(20)/(43)` Thus (a) is CORRECT option.

Discussion

942.	How much money will be required to buy 400, 12.50rs shares at a premium of 1rs ?
Answer» ANSWER :`5400rs`

Discussion

943.	Points are A(-2,0), B(0,2), C(2,0) which point lies to the right of the origin on x-axis
Answer» ANSWER :C(2, 0)

Discussion

944.	A person buys 120 shares at a nominal value of 40rs each, which he sells at 42.50rs each. Find his profit and profit percent.
Answer» ANSWER :`300RS` and `6.25%`

Discussion

945.	IfA(-5, 7), B (4, 5), C(-1,-6) and D (4,5) are the vertices of a quadrilateral. Find the area of quadrilateral.
Answer» ANSWER :52 SQ. UNITS.

Discussion

946.	angleA=70^@,angleB=40^@. Find angleACB.
Answer» ANSWER :`110^@`

Discussion

947.	M is midpoint of seg PQ. Find PM, if PQ=13 cm.
Answer» ANSWER :PM=6.5cm

Discussion

948.	By division algorithm for polynomials P(x)= \|g(x)q(x)\|+r(x) P(X)-r(x)= g(x)q(x) P(x)+ {-r(x)}= g(x)q(x)
Answer» <P> ANSWER : ADD {-R(X)} to p(x)

Discussion

949.	If a ox_(m) b = 1, then b is called the reciprocal of under modulo m. Find the reciprocal of 8 under modulo 17.
Answer» ANSWER :3

Discussion

950.	Is it possible to divide a line segment in the ratio sqrt5 : (1)/(sqrt 5) by geometrical construction?
Answer» ANSWER :YES, as `SQRT5: (1)/(sqrt5)= 5:1`

Discussion

Explore topic-wise InterviewSolutions in .

Find the roots of the following equations by factorisation. (i) x^(2)+x-12=0

In a certain code ''il be pee'' means ''rose are blue'' ''sik hee'' means ''red flowers'' and ''pee mit hee'' means ''flowers are vegetables''. How is 'rose' written in that code?

Prove that:(sintheta-costheta+1)/(sintheta+costheta-1)=(1)/(sectheta-tantheta)

In a certain code ''il be pee'' means ''rose are blue'' ''sik hee'' means ''red flowers'' and ''pee mit hee'' means ''flowers are vegetables''. How is 'red' written in that code?

Prove that : (1+cotA)/(cosA)+(1+tanA)/(sinA)=2(secA+"cosec"A)

Two brothers A and B invest 16000rs each in buying shares of two companies. A buys 3% hundread-rupee shares at 80 and B buys ten-rupee shares at par. If they both receive equal dividend at the end of the year, find the rate percent of the dividend received by B.

In what ratio does the point P (a, 2) divide the line segment joining the points A(5,-3) and B(-9, 4) ? Also, find the value of 'a'.

In the given figure O is the centre of the circle and AB is a tangent at B. If AB=15 cm and AC=7.5 cm, find the rdius of the circle.

If P varies directly as QR and the values of P, Q. R be 6, 9, 10 repectively, then the value of P when Q = 5 and R= 3 is

Solve (x)/(b) + (y)/(b) = 1 and a(x - a)- b(y + b) = 2a^(2) + b^(2).

State whether each of the following statements is true or false. Justify your answers. (i) {2,3,4,5} and {3,6} are disjoint sets. (ii) {a,e,I,o,u} and {a,b,c,d} are disjoint sets. (iii) {2,6,10,14} and {3,7,11,15} are disjoint sets. (iv) {2,6,10} and {3,7,11} are disjoint sets.

M/s, Beauty Products paid 18% GST on cosmetics worth 6000 and sold to a customer for 10,000. What are the amounts of CGST and SGST shown in the tax invoice issued?

Deepak is the brother of Anil. Deepak is the son of Prem. Bimal is Prem's father. How is Anil related to Bimal?

A sphere and a cube have the same surface area. Show that the ratio of the volume of the sphere to that of cube is sqrt(6):sqrt(pi).

If 32^(x- 2) = 64 + 8^x, the value of x is

Two cubes each of volume 64 cm^3 are joined end to end together. Find the surface area of the resulting cuboid.

Name the type of quadrilateral formed, if any by the following points, and give reasons for your answer : (-3, 5), (3, 1), (0, 3), (-1,-4)

The points (1, 1), (13, 1) and (13, 6) are the vertices of a right triangle.

Find the roots of the following quadraticequations by factorisation : 2x^(2)+x-6=0

The surface areas of two spheres are in the ratio 1:2. Then, the ratio of their volumes is ..........

Two metallic spheres of radii 9 cm and 10 cm are melted and recast to make two new spheres. If the radius of one of the new spheres is 12 cm, the radius of the other new sphere is ......... cm.

If REASON is coded as 5 and BELIEVED as 7, then what is the code for GOVERNMENT?

Find the common ratio of the GP 25, -5, 1, -1/5,………

Write the following sets in roster form (i) A={ x : x is a natural number greater than 50 but smaller than 100} B={x : x is an integer, x^(2)=4} (iii) D={x : x is a letter in the word "LOYAL"}

Find diagonal of square with side 8 cm.

Village R is in which direction with respect to village D? I. Village R is to the north of village T which is to the west of village F. II. Village D is to the west of village T.

Draw a DeltaABC, right angled at B such that AB=3cm and BC=4 cm. Now, construct a triangle similar to DeltaABC,each of whose sides is (2)/(5) times the corresponding sides of DeltaABC.

Write the GP if the first term a=3, and the common ratio r=2.

Prove that: (i) sin (70^@+theta) -cos (20^@-theta) =0 (ii) tan (55^@-theta) -cot (35^@-theta)=0 (iii) cosec(67^@+theta) -sec (23^@-theta)=0 (iv) cosec (65^@+theta) -sec (25^@-theta )-tan (55^@-theta) +cot (35^@+theta) =0 (v) sin (50^@+theta) -cos (40^@-theta) +tan 1^@ tan 10 ^@ tan 80^@ tan 89^@=1

Find four numbers in A.P. whose sum is 20 and the sum of whose squares is 120.

A right triangle, whose sides are 3 cm and 4 cm(other than hypotenuse) is made to revolve about its hypotenuse. Find thevolume and surface area of the double cone so formed.

A pen stand is made of wood in the shape of cuboid with three conical depressions to hold the pens. The dimensions of the cuboid are 15 cm by 10 cm by 3.5 cm. The radius of each of the depression is 0.5 cm and the depth is 1.4 cm n the entire stand.

A circular tank of diameter 2 m is dug and the earth removed is spread uniformly all around the tank to form an embankment 2 m in width and 1.6 m in height. Find the depth of the circular tank.

Draw two concentric circles of radii 3 cm and 5 cm. Taking a point on outer circle, construct the pair of tangents to the other. Measure the length of a tangent and verify is by actual calculation.

How much money will be required to buy 400, 12.50rs shares at a premium of 1rs ?

Points are A(-2,0), B(0,2), C(2,0) which point lies to the right of the origin on x-axis

A person buys 120 shares at a nominal value of 40rs each, which he sells at 42.50rs each. Find his profit and profit percent.

IfA(-5, 7), B (4, 5), C(-1,-6) and D (4,5) are the vertices of a quadrilateral. Find the area of quadrilateral.

angleA=70^@,angleB=40^@. Find angleACB.

M is midpoint of seg PQ. Find PM, if PQ=13 cm.

By division algorithm for polynomials P(x)= |g(x)q(x)|+r(x) P(X)-r(x)= g(x)q(x) P(x)+ {-r(x)}= g(x)q(x)

If a ox_(m) b = 1, then b is called the reciprocal of under modulo m. Find the reciprocal of 8 under modulo 17.

Is it possible to divide a line segment in the ratio sqrt5 : (1)/(sqrt 5) by geometrical construction?