24740 + Interview Questions in Mathematics Page 216 InterviewSolution

10751.	If x2+1x2=66, find the value of x-1x
Answer» If $x^{2} + \frac{1}{x^{2}} = 66$ , find the value of $x - \frac{1}{x}$

Discussion

10752.	If Y=¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯AB+¯¯¯¯BC+A¯¯¯¯C+CD, then dual of Y is
Answer» If $Y = ¯ ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ ¯ ¯ ¯¯ ¯ A B + ¯ ¯¯ ¯ B C + A ¯ ¯¯ ¯ C + C D$ , then dual of Y is

Discussion

10753.	If x = 1 and y = 6 is a solution of the equation 8x − ay + a2 = 0, find the value of a.
Answer» If x = 1 and y = 6 is a solution of the equation 8x − ay + a² = 0, find the value of a.

Discussion

10754.	The zeros of the polynomial p(x) = 2x2 + 5x – 3 are(a) 12, 3(b) 12, -3(c) -12, 3(d) 1,-12
Answer» The zeros of the polynomial p(x) = 2x² + 5x – 3 are (a) $\frac{1}{2}, 3$ (b) $\frac{1}{2}, - 3$ (c) $\frac{- 1}{2}, 3$ (d) $1, \frac{- 1}{2}$

Discussion

10755.	The mean of a data set with 12 observations is calculated as 19.25. If one more value is included in the data, then for the new data with 13 observations, mean becomes 20. The value of this 13th observation is
Answer» The mean of a data set with 12 observations is calculated as 19.25. If one more value is included in the data, then for the new data with 13 observations, mean becomes 20. The value of this 13^th observation is

Discussion

10756.	The tangent to a circle is a line which touches the circle at exactly ________.
Answer» The tangent to a circle is a line which touches the circle at exactly ________.

Discussion

10757.	Question 3A gulab jamun contains sugar syrup up to about 30% of its volume. Find approximately how much syrup would be found in 45 gulab jamuns, each shaped like a cylinder with two hemispherical ends with length 5 cm and diameter 2.8 cm.
Answer» Question 3 A gulab jamun contains sugar syrup up to about 30% of its volume. Find approximately how much syrup would be found in 45 gulab jamuns, each shaped like a cylinder with two hemispherical ends with length 5 cm and diameter 2.8 cm.

Discussion

10758.	In the given figure, AOB is a straight line. The value of x is(a) 12(b) 15(c) 20(d) 25
Answer» In the given figure, AOB is a straight line. The value of x is (a) 12 (b) 15 (c) 20 (d) 25

Discussion

10759.	13. F(x)={kcosx/-2x ,x2; 3 when x=/2; 3tan2x/2x- when x>/2
Answer» 13. F(x)={kcosx/-2x ,x2; 3 when x=/2; 3tan2x/2x- when x>/2

Discussion

10760.	If the area of an equilateral triangle is 81√3 cm2, find its height.
Answer» If the area of an equilateral triangle is 81 $\sqrt{3} c m^{2}$ , find its height.

Discussion

10761.	Question 5 (iii) D, E and F are respectively the mid-points of the sides BC, CA and AB of triangle ABC Show that: (iii)area(BDEF)=12area(ABC)
Answer» Question 5 (iii) D, E and F are respectively the mid-points of the sides BC, CA and AB of triangle ABC Show that: $(i i i) a r e a (B D E F) = \frac{1}{2} a r e a (A B C)$

Discussion

10762.	40.IN BOUNDARY SURACE DIAGRAM WHAT DOES + AND -SIGN INDICATES
Answer» 40.IN BOUNDARY SURACE DIAGRAM WHAT DOES + AND -SIGN INDICATES

Discussion

10763.	If a solid sphere of radius 10 cm is moulded into 8 spherical solid balls of equal radius, then the surface area of each ball (in sq.cm) is(a) 100 π(b) 75 π(c) 60 π(d) 50 π
Answer» If a solid sphere of radius 10 cm is moulded into 8 spherical solid balls of equal radius, then the surface area of each ball (in sq.cm) is (a) 100 π (b) 75 π (c) 60 π (d) 50 π

Discussion

10764.	If an angle of a parallelogram is two thirds of its adjacent angle, the smallest angle of the parallelogram is (a) 108∘ (b) 54∘ (c) 72∘ (d) 81∘
Answer» If an angle of a parallelogram is two thirds of its adjacent angle, the smallest angle of the parallelogram is (a) $108^{\circ}$ (b) $54^{\circ}$ (c) $72^{\circ}$ (d) $81^{\circ}$

10764.

If an angle of a parallelogram is two thirds of its adjacent angle, the smallest angle of the parallelogram is (a) 108∘ (b) 54∘ (c) 72∘ (d) 81∘

Answer»

If an angle of a parallelogram is two thirds of its adjacent angle, the smallest angle of the parallelogram is

(a) $108^{\circ}$

(b) $54^{\circ}$

(c) $72^{\circ}$

(d) $81^{\circ}$

Discussion

10765.	In the six cornered figure,AC, AD and AE are joined. Find ∠FAB+∠ABC+∠BCD+∠CDE+∠DEF+∠EFA
Answer» In the six cornered figure,AC, AD and AE are joined. Find $∠ F A B + ∠ A B C + ∠ B C D + ∠ C D E + ∠ D E F + ∠ E F A$

Discussion

10766.	The length of a chord of a circle of 16.8 cm, radius is 9.1 cm. Find its distance from the centre.
Answer» The length of a chord of a circle of 16.8 cm, radius is 9.1 cm. Find its distance from the centre.

Discussion

10767.	What are primary data and secondary data? which of the two is more reliable and why?
Answer» What are primary data and secondary data? which of the two is more reliable and why?

Discussion

10768.	How to verify that the roots obtained for a polynomial are correct or not?
Answer» How to verify that the roots obtained for a polynomial are correct or not?

Discussion

10769.	what is centre and plane of symmetry? explain their types and how to find i
Answer» what is centre and plane of symmetry? explain their types and how to find i

Discussion

10770.	Which of these numbers is not a natural number?
Answer» Which of these numbers is not a natural number?

Discussion

10771.	Find the area of an equilateral triangle whose area is equal to the triangle of sides 12 cm, 8 cm and 16 cm.
Answer» Find the area of an equilateral triangle whose area is equal to the triangle of sides 12 cm, 8 cm and 16 cm.

Discussion

10772.	△ABC is an isosceles triangle in which AB = AC. Side BA is produced to D such that AD = AB. ∠BCD is equal to
Answer» $△ A B C$ is an isosceles triangle in which AB = AC. Side BA is produced to D such that AD = AB. $∠ B C D$ is equal to

Discussion

10773.	There is a thin metal plate having length, breadth and thickness as 2M mm, 2K mm and 1 mm respectively. If ‘N’ plates are placed one on top of the other, what is the object formed and what is its volume in mm3?
Answer» There is a thin metal plate having length, breadth and thickness as 2M mm, 2K mm and 1 mm respectively. If ‘N’ plates are placed one on top of the other, what is the object formed and what is its volume in $m m^{3}$ ?

Discussion

10774.	If x =2, y = -1, then the value of x2+4xy+4y2 is
Answer» If x =2, y = -1, then the value of $x^{2} + 4 x y + 4 y^{2}$ is

Discussion

10775.	Question 4In the following figure, ABCD is a parallelogram and BC is produced to a point Q such that AD =CQ. If AQ intersects DC at P,Show that ar (BPC) = ar (DPQ).
Answer» Question 4 In the following figure, ABCD is a parallelogram and BC is produced to a point Q such that AD =CQ. If AQ intersects DC at P, Show that ar (BPC) = ar (DPQ).

Discussion

10776.	The number x is 2 more than the number y. If the sum of the squares of x and y is 34; find the product of x and y.
Answer» The number x is 2 more than the number y. If the sum of the squares of x and y is 34; find the product of x and y.

Discussion

10777.	In fig. BD \|\| CA, E is mid-point of CA and BD=12AC.Then
Answer» In fig. BD \|\| CA, E is mid-point of CA and $B D = \frac{1}{2}$ AC.Then

Discussion

10778.	Is distance formula of coordinate geometry similar to pythagoras theorem?
Answer» Is distance formula of coordinate geometry similar to pythagoras theorem?

Discussion

10779.	What is the area of △ABC (in square cm) if AD is the median and area △ADB= 18 square cm?__
Answer» What is the area of $△ A B C$ (in square cm) if AD is the median and area $△ A D B$ = 18 square cm? __

10779.

What is the area of △ABC (in square cm) if AD is the median and area △ADB= 18 square cm?__

Answer»

What is the area of $△ A B C$ (in square cm) if AD is the median and area $△ A D B$ = 18 square cm?

__

Discussion

10780.	17. Factorise it: 1/(2x-3) + 1/(x-5)=10/9
Answer» 17. Factorise it: 1/(2x-3) + 1/(x-5)=10/9

Discussion

10781.	Is the decimal form of 139/(2^3×7^2×5^7) non terminating and non repeating??
Answer» Is the decimal form of 139/(2^3×7^2×5^7) non terminating and non repeating??

Discussion

10782.	The point (3, - 5) lies in the ....... quadrant.
Answer» The point (3, - 5) lies in the ....... quadrant.

Discussion

10783.	Question 14If (x + 1) is a factor of f(x) = 2x3+ax2+2bx+1, then find the value of a and b is given that 2a – 3b = 4.
Answer» Question 14 If (x + 1) is a factor of f(x) = $2 x^{3} + a x^{2} + 2 b x + 1$ , then find the value of a and b is given that 2a – 3b = 4.

Discussion

10784.	In parallelogram ABCD, two points P and Q are taken on diagonal BD such that DP=BQ (see the given figure) Show that:ΔAQB≅ΔCPD
Answer» In parallelogram ABCD, two points P and Q are taken on diagonal BD such that DP=BQ (see the given figure) Show that: $Δ A Q B ≅ Δ C P D$

Discussion

10785.	Locate √3 on the number line.
Answer» Locate $\sqrt{3}$ on the number line.

Discussion

10786.	At an intersection the weaving ratio for N - E, E - S, S - W, and W - N direction are 0.70, 0.75, 0.71 and 0.69 respectively. The width of weaving section is 11.5 m, the length of weaving section is 46 m and average entry width is 8 m. The practical capacity (in PCU/hr) will be .3276
Answer» At an intersection the weaving ratio for N - E, E - S, S - W, and W - N direction are 0.70, 0.75, 0.71 and 0.69 respectively. The width of weaving section is 11.5 m, the length of weaving section is 46 m and average entry width is 8 m. The practical capacity (in PCU/hr) will be . 3276

Discussion

10787.	A person rows downstream 20 km in 2 hours and upstream 4 km in 2 hours. Find man's speed of rowing in still water and the speed of the current.
Answer» A person rows downstream 20 km in 2 hours and upstream 4 km in 2 hours. Find man's speed of rowing in still water and the speed of the current.

Discussion

10788.	24. An equilateral triangle is inserted inside a triangle having sides of length 4,5 and 6 cm.find the side of equilateral triangle.
Answer» 24. An equilateral triangle is inserted inside a triangle having sides of length 4,5 and 6 cm.find the side of equilateral triangle.

Discussion

10789.	On a number line, points A, B, and C are such that d(A, B) = 5 units, d(B, C) = 11 units, and d(A, C) = 6 units. Which of the points is between the other two?
Answer» On a number line, points A, B, and C are such that d(A, B) = 5 units, d(B, C) = 11 units, and d(A, C) = 6 units. Which of the points is between the other two?

Discussion

10790.	Draw an isosceles triangle ABC in which AB=AC = 6 cm and BC=5 cm Construct a triangle PQR similar to ΔABC in which PQ = 8 cm, Also justify the construction.
Answer» Draw an isosceles triangle ABC in which AB=AC = 6 cm and BC=5 cm Construct a triangle PQR similar to $Δ A B C$ in which PQ = 8 cm, Also justify the construction.

Discussion

10791.	The front compound wall of a house is decorated by wooden spheres of diameter 21 cm, placed on small supports as shown in the given figure. Eight such spheres are used for this purpose, and are to be painted silver. Each support is a cylinder of radius 1.5 cm and height 7 cm and is to be painted black. Find the cost of paint required if silver paint costs 25 paise per cm2 and black paint costs 5 paise per cm2.
Answer» The front compound wall of a house is decorated by wooden spheres of diameter 21 cm, placed on small supports as shown in the given figure. Eight such spheres are used for this purpose, and are to be painted silver. Each support is a cylinder of radius 1.5 cm and height 7 cm and is to be painted black. Find the cost of paint required if silver paint costs 25 paise per cm² and black paint costs 5 paise per cm².

Discussion

10792.	An oil tin in the shape of a cuboid having dimensions, 26 cm × 26 cm × 45 cm . If 1 sq. m sheet costs ₹10 , then find the total cost for making 20 such tins.
Answer» An oil tin in the shape of a cuboid having dimensions, 26 cm $\times$ 26 cm $\times$ 45 cm . If 1 sq. m sheet costs ₹10 , then find the total cost for making 20 such tins.

Discussion

10793.	Assertion: ABCD is a quadrilateral in which P, Q, R and S are the mid - points of AB, BC, CD and DA respectively. Then, PQRS is a parallelogram.Reason: The line segment joining the mid - points of any two sides of a triangle is parallel to the third side and equal to half of it.Which of the following is correct?
Answer» Assertion: ABCD is a quadrilateral in which P, Q, R and S are the mid - points of AB, BC, CD and DA respectively. Then, PQRS is a parallelogram. Reason: The line segment joining the mid - points of any two sides of a triangle is parallel to the third side and equal to half of it. Which of the following is correct?

Discussion

10794.	Question 8 (iv) In right triangle ABC, right angled at C, M is the mid-point of hypotenuse AB. C is joined to M and produced to a point D such that DM = CM. Point D is joined to point B (see the given figure). Show that: CM=12 AB
Answer» Question 8 (iv) In right triangle ABC, right angled at C, M is the mid-point of hypotenuse AB. C is joined to M and produced to a point D such that DM = CM. Point D is joined to point B (see the given figure). Show that: $C M = \frac{1}{2} A B$

Discussion

10795.	82. Prove that tan -1(1/4) = 1/3 cot-1(52/47)
Answer» 82. Prove that tan -1(1/4) = 1/3 cot-1(52/47)

Discussion

10796.	A jeep was moving with v km/h while going from one city to another. The distance between these two cities is 10 Km. If this distance can be expressed as two kilometers more than half of the speed of the jeep, calculate the speed of the jeep.
Answer» A jeep was moving with v km/h while going from one city to another. The distance between these two cities is 10 Km. If this distance can be expressed as two kilometers more than half of the speed of the jeep, calculate the speed of the jeep.

Discussion

10797.	If the perpendicular distance of a point A, which lies on the x-axis, from the origin is 8 units, then the coordinates of A can be
Answer» If the perpendicular distance of a point A, which lies on the x-axis, from the origin is 8 units, then the coordinates of A can be

Discussion

10798.	Question 5For which of the following, diagonals are equal?a) Trapeziumb) Rhombusc) Parallelogramd) Rectangle
Answer» Question 5 For which of the following, diagonals are equal? a) Trapezium b) Rhombus c) Parallelogram d) Rectangle

Discussion

10799.	Anshul drew a figure that looked like the one shown in the figure given below
Answer» Anshul drew a figure that looked like the one shown in the figure given below

Discussion

10800.	one of the zero of the polynomial f(x)=(k+4)x+13x+4k is reciprocal of the other then find the value of k.
Answer» one of the zero of the polynomial f(x)=(k+4)x+13x+4k is reciprocal of the other then find the value of k.

Discussion

Explore topic-wise InterviewSolutions in .

If x2+1x2=66, find the value of x-1x

If Y=¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯AB+¯¯¯¯BC+A¯¯¯¯C+CD, then dual of Y is

If x = 1 and y = 6 is a solution of the equation 8x − ay + a2 = 0, find the value of a.

The zeros of the polynomial p(x) = 2x2 + 5x – 3 are(a) 12, 3(b) 12, -3(c) -12, 3(d) 1,-12

The mean of a data set with 12 observations is calculated as 19.25. If one more value is included in the data, then for the new data with 13 observations, mean becomes 20. The value of this 13th observation is

The tangent to a circle is a line which touches the circle at exactly ________.

Question 3A gulab jamun contains sugar syrup up to about 30% of its volume. Find approximately how much syrup would be found in 45 gulab jamuns, each shaped like a cylinder with two hemispherical ends with length 5 cm and diameter 2.8 cm.

In the given figure, AOB is a straight line. The value of x is(a) 12(b) 15(c) 20(d) 25

13. F(x)={kcosx/-2x ,x2; 3 when x=/2; 3tan2x/2x- when x>/2

If the area of an equilateral triangle is 81√3 cm2, find its height.

Question 5 (iii) D, E and F are respectively the mid-points of the sides BC, CA and AB of triangle ABC Show that: (iii)area(BDEF)=12area(ABC)

40.IN BOUNDARY SURACE DIAGRAM WHAT DOES + AND -SIGN INDICATES

If a solid sphere of radius 10 cm is moulded into 8 spherical solid balls of equal radius, then the surface area of each ball (in sq.cm) is(a) 100 π(b) 75 π(c) 60 π(d) 50 π

If an angle of a parallelogram is two thirds of its adjacent angle, the smallest angle of the parallelogram is (a) 108∘ (b) 54∘ (c) 72∘ (d) 81∘

In the six cornered figure,AC, AD and AE are joined. Find ∠FAB+∠ABC+∠BCD+∠CDE+∠DEF+∠EFA

The length of a chord of a circle of 16.8 cm, radius is 9.1 cm. Find its distance from the centre.

What are primary data and secondary data? which of the two is more reliable and why?

How to verify that the roots obtained for a polynomial are correct or not?

what is centre and plane of symmetry? explain their types and how to find i

Which of these numbers is not a natural number?

Find the area of an equilateral triangle whose area is equal to the triangle of sides 12 cm, 8 cm and 16 cm.

△ABC is an isosceles triangle in which AB = AC. Side BA is produced to D such that AD = AB. ∠BCD is equal to

There is a thin metal plate having length, breadth and thickness as 2M mm, 2K mm and 1 mm respectively. If ‘N’ plates are placed one on top of the other, what is the object formed and what is its volume in mm3?

If x =2, y = -1, then the value of x2+4xy+4y2 is

Question 4In the following figure, ABCD is a parallelogram and BC is produced to a point Q such that AD =CQ. If AQ intersects DC at P,Show that ar (BPC) = ar (DPQ).

The number x is 2 more than the number y. If the sum of the squares of x and y is 34; find the product of x and y.

In fig. BD || CA, E is mid-point of CA and BD=12AC.Then

Is distance formula of coordinate geometry similar to pythagoras theorem?

What is the area of △ABC (in square cm) if AD is the median and area △ADB= 18 square cm?__

17. Factorise it: 1/(2x-3) + 1/(x-5)=10/9

Is the decimal form of 139/(2^3×7^2×5^7) non terminating and non repeating??

The point (3, - 5) lies in the ....... quadrant.

Question 14If (x + 1) is a factor of f(x) = 2x3+ax2+2bx+1, then find the value of a and b is given that 2a – 3b = 4.

In parallelogram ABCD, two points P and Q are taken on diagonal BD such that DP=BQ (see the given figure) Show that:ΔAQB≅ΔCPD

Locate √3 on the number line.

At an intersection the weaving ratio for N - E, E - S, S - W, and W - N direction are 0.70, 0.75, 0.71 and 0.69 respectively. The width of weaving section is 11.5 m, the length of weaving section is 46 m and average entry width is 8 m. The practical capacity (in PCU/hr) will be .3276

A person rows downstream 20 km in 2 hours and upstream 4 km in 2 hours. Find man's speed of rowing in still water and the speed of the current.

24. An equilateral triangle is inserted inside a triangle having sides of length 4,5 and 6 cm.find the side of equilateral triangle.

On a number line, points A, B, and C are such that d(A, B) = 5 units, d(B, C) = 11 units, and d(A, C) = 6 units. Which of the points is between the other two?

Draw an isosceles triangle ABC in which AB=AC = 6 cm and BC=5 cm Construct a triangle PQR similar to ΔABC in which PQ = 8 cm, Also justify the construction.

An oil tin in the shape of a cuboid having dimensions, 26 cm × 26 cm × 45 cm . If 1 sq. m sheet costs ₹10 , then find the total cost for making 20 such tins.

Question 8 (iv) In right triangle ABC, right angled at C, M is the mid-point of hypotenuse AB. C is joined to M and produced to a point D such that DM = CM. Point D is joined to point B (see the given figure). Show that: CM=12 AB

82. Prove that tan -1(1/4) = 1/3 cot-1(52/47)

A jeep was moving with v km/h while going from one city to another. The distance between these two cities is 10 Km. If this distance can be expressed as two kilometers more than half of the speed of the jeep, calculate the speed of the jeep.

If the perpendicular distance of a point A, which lies on the x-axis, from the origin is 8 units, then the coordinates of A can be

Question 5For which of the following, diagonals are equal?a) Trapeziumb) Rhombusc) Parallelogramd) Rectangle

Anshul drew a figure that looked like the one shown in the figure given below

one of the zero of the polynomial f(x)=(k+4)x+13x+4k is reciprocal of the other then find the value of k.