25365 + Interview Questions in Mathematics Page 213 InterviewSolution

10601.	The twoadjacent sides of a parallelogram areand.Find theunit vector parallel to its diagonal. Also, find its area.
Answer» The two adjacent sides of a parallelogram areand . Find the unit vector parallel to its diagonal. Also, find its area.

10601.

The twoadjacent sides of a parallelogram areand.Find theunit vector parallel to its diagonal. Also, find its area.

Answer»

The two
adjacent sides of a parallelogram areand
.

Find the
unit vector parallel to its diagonal. Also, find its area.

Discussion

10602.	Question 19Rohan and Shalu are playing with 5 cards as shown in the given figure. What is the probability of Rohan picking a card without seeing, that has the number 2 on it?(a) 25(b) 15(c) 35(d) 45
Answer» Question 19 Rohan and Shalu are playing with 5 cards as shown in the given figure. What is the probability of Rohan picking a card without seeing, that has the number 2 on it? (a) $\frac{2}{5}$ (b) $\frac{1}{5}$ (c) $\frac{3}{5}$ (d) $\frac{4}{5}$

10602.

Question 19Rohan and Shalu are playing with 5 cards as shown in the given figure. What is the probability of Rohan picking a card without seeing, that has the number 2 on it?(a) 25(b) 15(c) 35(d) 45

Answer»

Question 19

Rohan and Shalu are playing with 5 cards as shown in the given figure. What is the probability of Rohan picking a card without seeing, that has the number 2 on it?

(a) $\frac{2}{5}$

(b) $\frac{1}{5}$

(c) $\frac{3}{5}$

(d) $\frac{4}{5}$

Discussion

10603.	Find the square of 1468 by writing this as 1465 + 3.
Answer» Find the square of 1468 by writing this as 1465 + 3.

Discussion

10604.	Which among the following options contains a point lying on the line: y=3x+8?
Answer» Which among the following options contains a point lying on the line: $y = 3 x + 8$ ?

Discussion

10605.	FIND TWO CONSECUTIVE POSITIVE INTEGERS, SUM OF WHOSE SQAURES IS 365
Answer» FIND TWO CONSECUTIVE POSITIVE INTEGERS, SUM OF WHOSE SQAURES IS 365

Discussion

10606.	What is the value of 1.52?
Answer» What is the value of ${1.5}^{2} ?$

Discussion

10607.	Cost of 20 Pencils is 100 Rupees. Cost of a pen is 40 more than 8 times the cost of a Pencil. Find the cost of 5 Pencils and 6 Pens.
Answer» Cost of 20 Pencils is 100 Rupees. Cost of a pen is 40 more than 8 times the cost of a Pencil. Find the cost of 5 Pencils and 6 Pens.

Discussion

10608.

Question 1(iv) Use a suitable identity to get each of the following products:(3a−12)(3a−12)

Answer»

Question 1(iv)

Use a suitable identity to get each of the following products:

$(3 a - \frac{1}{2}) (3 a - \frac{1}{2})$

Discussion

10609.	In the construction of a square inside a circle, the angle between the two diameters should be _____ degrees.90
Answer» In the construction of a square inside a circle, the angle between the two diameters should be _____ degrees. 90

Discussion

10610.	Lines AB and CD interesct at O. If ∠AOC = 135∘, then ∠BOC3 = .
Answer» Lines AB and CD interesct at O. If $∠$ AOC = $135^{\circ}$ , then $\frac{∠ B O C}{3}$ = .

Discussion

10611.	In how many years will a sum of money becomes three times at the rate of interest 10% per annum?
Answer» In how many years will a sum of money becomes three times at the rate of interest 10% per annum?

Discussion

10612.	Find the median of the following data set.70 50 90 120 110 100 80 60
Answer» Find the median of the following data set. 70 50 90 120 110 100 80 60

Discussion

10613.	If y=xsin^2x find dy/dx
Answer» If y=xsin^2x find dy/dx

Discussion

10614.	Question 10(a)In a college, out of 4320 students, 2300 are girls. Find the ratio of:Number of girls to the total number of students.
Answer» Question 10(a) In a college, out of 4320 students, 2300 are girls. Find the ratio of: Number of girls to the total number of students.

10614.

Question 10(a)In a college, out of 4320 students, 2300 are girls. Find the ratio of:Number of girls to the total number of students.

Answer»

Question 10(a)

In a college, out of 4320 students, 2300 are girls. Find the ratio of:

Number of girls to the total number of students.

Discussion

10615.	Raj bought 10 chocolates, each for ₹ 40. He sold 6 of them at ₹50 each, and the rest of it at ₹ 55 each. Find the percentage of profit he made.
Answer» Raj bought 10 chocolates, each for ₹ 40. He sold 6 of them at ₹50 each, and the rest of it at ₹ 55 each. Find the percentage of profit he made.

Discussion

10616.	The large pizza is cut into 8 equal slices. Find the central angle of each slice.
Answer» The large pizza is cut into 8 equal slices. Find the central angle of each slice.

10616.

The large pizza is cut into 8 equal slices. Find the central angle of each slice.

Answer»

The large pizza is cut into 8 equal slices. Find the central angle of each slice.

Discussion

10617.	Draw a rhombus whose side is 7.2 cm and one angle is 60∘.
Answer» Draw a rhombus whose side is 7.2 cm and one angle is $60^{\circ}$ .

Discussion

10618.	While doing an experiment on plotting the temperature-time graph of hot water as it cools, we can get a good graph :(1) only by noting the temperature of hot water every 30 seconds throughout(2) only by noting the temperature of hot water every 1 minute throughout(3) by noting the temperature of hot water every 1 minute to start with and every 2 minutes later on(4) by noting the temperature of hot water every 2 minutes to start with and every 1 minutes later on
Answer» While doing an experiment on plotting the temperature-time graph of hot water as it cools, we can get a good graph : (1) only by noting the temperature of hot water every 30 seconds throughout (2) only by noting the temperature of hot water every 1 minute throughout (3) by noting the temperature of hot water every 1 minute to start with and every 2 minutes later on (4) by noting the temperature of hot water every 2 minutes to start with and every 1 minutes later on

Discussion

10619.	How many first odd natural numbers do we need to add together to get the number 81?
Answer» How many first odd natural numbers do we need to add together to get the number $81 ?$

Discussion

10620.	Solve √5x2+x+√5=0
Answer» Solve $\sqrt{5} x^{2} + x + \sqrt{5} = 0$

Discussion

10621.	Construct a square in which each diagonal is 5 cm long.
Answer» Construct a square in which each diagonal is 5 cm long.

Discussion

10622.	State whether the following statements are true or false. Also, justify your answer in each case. All rectangles are Squares All Squares are trapeziums All rhombuses are parallelograms
Answer» State whether the following statements are true or false. Also, justify your answer in each case. All rectangles are Squares All Squares are trapeziums All rhombuses are parallelograms

Discussion

10623.	43. if Ax+31x-Bx-10 is exactly divisible by 2x+9x-5,find the values of A and B.
Answer» 43. if Ax+31x-Bx-10 is exactly divisible by 2x+9x-5,find the values of A and B.

Discussion

10624.	12×base×height is the formula of area for which type of triangles?
Answer» $\frac{1}{2} \times base \times height$ is the formula of area for which type of triangles?

Discussion

10625.	If three concurrent straight lines AD,BE and CF are drawn from the angular points of a △ABC such that AFFB=12,BDDC=23, then EAEC is equal to
Answer» If three concurrent straight lines $A D, B E$ and $C F$ are drawn from the angular points of a $△ A B C$ such that $\frac{A F}{F B} = \frac{1}{2}, \frac{B D}{D C} = \frac{2}{3},$ then $\frac{E A}{E C}$ is equal to

Discussion

10626.	Question 97The side of a square board is 50 cm. A student has to draw its image in her notebook. If the drawing of the square board in the notebook has perimeter of 40 cm, then by which scale the figure has been drawn?
Answer» Question 97 The side of a square board is 50 cm. A student has to draw its image in her notebook. If the drawing of the square board in the notebook has perimeter of 40 cm, then by which scale the figure has been drawn?

Discussion

10627.	Draw a histogram representing the following data:Class interval600−640640−680680−720720−760760−800800−840Frequency184515328817163
Answer» Draw a histogram representing the following data: $\begin{matrix} Class interval & 600 - 640 & 640 - 680 & 680 - 720 & 720 - 760 & 760 - 800 & 800 - 840 Frequency & 18 & 45 & 153 & 288 & 171 & 63 \end{matrix}$

10627.

Draw a histogram representing the following data:Class interval600−640640−680680−720720−760760−800800−840Frequency184515328817163

Answer»

Draw a histogram representing the following data:

$\begin{matrix} Class interval & 600 - 640 & 640 - 680 & 680 - 720 & 720 - 760 & 760 - 800 & 800 - 840 Frequency & 18 & 45 & 153 & 288 & 171 & 63 \end{matrix}$

Discussion

10628.	50 labourers can dig a pond in 16 days how many labourers will be required to dig another pond double in size in 20 days?
Answer» 50 labourers can dig a pond in 16 days how many labourers will be required to dig another pond double in size in 20 days?

Discussion

10629.	Find the amount which Ram will get on Rs. 4,096, he gave it for 18 months at 1212% per annum, interest being compounded half yearly.
Answer» Find the amount which Ram will get on $R s . 4, 096$ , he gave it for $18$ months at $12 \frac{1}{2} %$ per annum, interest being compounded half yearly.

Discussion

10630.	Question 8In countries like USA and Canada, the temperature is measured in Fahrenheit, whereas in countries like India, it is measured in Celsius. Here is a linear equation that converts Fahrenheit to Celsius: F=95C+32(i) Draw the graph of the linear equation above using Celsius for x-axis and Fahrenheit for the y-axis.(ii) If the temperature is 30∘C, what is the temperature in Fahrenheit?(iii) If the temperature is 95∘F, what is the temperature in Celsius?(iv) If the temperature is 0∘C, what is the temperature in Fahrenheit and if the temperature is 0∘F, what is the temperature in Celsius?(v) Is there a temperature which is numerically the same in both Fahrenheit and Celsius? If yes, find it.
Answer» Question 8 In countries like USA and Canada, the temperature is measured in Fahrenheit, whereas in countries like India, it is measured in Celsius. Here is a linear equation that converts Fahrenheit to Celsius: $F = \frac{9}{5} C + 32$ (i) Draw the graph of the linear equation above using Celsius for x-axis and Fahrenheit for the y-axis. (ii) If the temperature is $30^{\circ} C$ , what is the temperature in Fahrenheit? (iii) If the temperature is $95^{\circ} F$ , what is the temperature in Celsius? (iv) If the temperature is $0^{\circ} C$ , what is the temperature in Fahrenheit and if the temperature is $0^{\circ} F$ , what is the temperature in Celsius? (v) Is there a temperature which is numerically the same in both Fahrenheit and Celsius? If yes, find it.

Discussion

10631.	8. A washing machine is available for Rs. 13,500 cash or Rs. 6,500 as cash down payment followed by three monthly instalments of Rs. 2,500 each . Find the rate of interest charged under instalment plan .
Answer» 8. A washing machine is available for Rs. 13,500 cash or Rs. 6,500 as cash down payment followed by three monthly instalments of Rs. 2,500 each . Find the rate of interest charged under instalment plan .

Discussion

10632.	Convert the following Income Statement into Common Size Statement and interpret the changes in 2011 in the light of the conditions in 2010. Particulars2010 (Rs)2011 (Rs)Gross Sales30,60036,720(-) Return(600)(700)Net Sales¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯30,000¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯36,020(-) Cost of Goods Sold(18,200)––––––––––(20,250)––––––––––Gross Profit 11,800–––––––––– 15,770––––––––––(-) Operating ExpensesAdministration Expenses(3,000)(3,400)Sales Expenses(6,000)(6,600)Total Expenses¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ 9,000––––––––¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ 10,000–––––––––Income from operations2,8005,770(+)Non -operating Income300400Total Income¯¯¯¯¯¯¯¯¯¯¯¯¯3,100¯¯¯¯¯¯¯¯¯¯¯¯¯6,170(-) Non -opearating Expenses(400)(600)Net Profit2,700––––––––––––5,570––––––––––––
Answer» Convert the following Income Statement into Common Size Statement and interpret the changes in 2011 in the light of the conditions in 2010. $\begin{matrix} Particulars & 2010 (Rs) & 2011 (Rs) Gross Sales & 30, 600 & 36, 720 (-) Return & (600) & (700) Net Sales & ¯ ¯¯¯¯¯¯¯¯¯¯¯¯¯¯ ¯ 30, 000 & ¯ ¯¯¯¯¯¯¯¯¯¯¯¯¯¯ ¯ 36, 020 (-) Cost of Goods Sold & (18, 200) - -------- - & (20, 250) - -------- - Gross Profit & 11, 800 - -------- - & 15, 770 - -------- - (-) Operating Expenses Administration Expenses & (3, 000) & (3, 400) Sales Expenses & (6, 000) & (6, 600) Total Expenses & ¯ ¯¯¯¯¯¯¯¯¯¯¯¯¯¯ ¯ 9, 000 - ------ - & ¯ ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ ¯ 10, 000 - ------- - Income from operations & 2, 800 & 5, 770 (+)Non -operating Income & 300 & 400 Total Income & ¯ ¯¯¯¯¯¯¯¯¯¯¯ ¯ 3, 100 & ¯ ¯¯¯¯¯¯¯¯¯¯¯ ¯ 6, 170 (-) Non -opearating Expenses & (400) & (600) Net Profit & 2, 700 - ---- - - ---- - & 5, 570 - ---- - - ---- - \end{matrix}$

Discussion

10633.	Rohit scored 92, 85, and 78 in three Maths tests. How much should he score in the 4th test so as to get an average of 87 in four Maths test?
Answer» Rohit scored 92, 85, and 78 in three Maths tests. How much should he score in the 4th test so as to get an average of 87 in four Maths test?

Discussion

10634.	An almirah is sold at Rs. 5225 after allowing a discount of 5%. Find its marked price.
Answer» An almirah is sold at $R s . 5225$ after allowing a discount of $5 % .$ Find its marked price.

Discussion

10635.	The square of 4014 is
Answer» The square of $40 \frac{1}{4}$ is

Discussion

10636.	The angle subtended by blue portion at the center of following pie-chart is _____(in degrees).234
Answer» The angle subtended by blue portion at the center of following pie-chart is _____(in degrees). 234

Discussion

10637.	Question 159ABCDE is a regular pentagon. The bisector of angle A meets the sides CD at M. Find ∠AMC
Answer» Question 159 ABCDE is a regular pentagon. The bisector of angle A meets the sides CD at M. Find $∠ A M C$

Discussion

10638.	What is the last step in constructing quadrilateral with 3 sides and 2 included angles given?
Answer» What is the last step in constructing quadrilateral with 3 sides and 2 included angles given?

Discussion

10639.	Find the values of x for which \|x−2\|+\|x−8\|=10.
Answer» Find the values of x for which $\| x - 2 \| + \| x - 8 \| = 10$ .

Discussion

10640.	Which of the following regular polygons has sum of all the interior angles as 720°?
Answer» Which of the following regular polygons has sum of all the interior angles as 720°?

Discussion

10641.	In the given figure, ABCD is a kite with AC and BD as diagonals and ∠ABC = 30∘. Find x.
Answer» In the given figure, ABCD is a kite with AC and BD as diagonals and $∠ A B C$ = $30^{\circ}$ . Find $x$ .

10641.

In the given figure, ABCD is a kite with AC and BD as diagonals and ∠ABC = 30∘. Find x.

Answer»

In the given figure, ABCD is a kite with AC and BD as diagonals and $∠ A B C$ = $30^{\circ}$ . Find $x$ .

Discussion

10642.	What is the coefficient of z in (z−5)3?
Answer» What is the coefficient of z in $(z - 5)^{3}$ ?

Discussion

10643.	Question 3(v) Find the smallest number by which each of the following numbers must be divided to obtain a perfect cube: 704
Answer» Question 3(v) Find the smallest number by which each of the following numbers must be divided to obtain a perfect cube: 704

Discussion

10644.	The difference between A's and B's salary is ₹ 540.60. If B's salary is greater and A's salary is ₹ 27030, Find the percentage by which B's salary is higher.
Answer» The difference between A's and B's salary is ₹ 540.60. If B's salary is greater and A's salary is ₹ 27030, Find the percentage by which B's salary is higher.

Discussion

10645.	If x+1x=2, then x3+1x3 =(a) 64(b) 14(c) 8(d) 2
Answer» If $x + \frac{1}{x} = 2$ , then $x^{3} + \frac{1}{x^{3}} =$ (a) 64 (b) 14 (c) 8 (d) 2

Discussion

10646.	Find the cube root of 175616 by prime factorisation method.
Answer» Find the cube root of 175616 by prime factorisation method.

Discussion

10647.	Question 4(v)Find the multiplicative inverse of the following:−1×−25
Answer» Question 4(v) Find the multiplicative inverse of the following: $- 1 \times \frac{- 2}{5}$

Discussion

10648.	If the two right triangles in the diagram above are congruent. choose the pairs of equal sides and angles.
Answer» If the two right triangles in the diagram above are congruent. choose the pairs of equal sides and angles.

Discussion

10649.	Question 34There are 1000 sealed envelopes in a box, 10 of them contain a cash prize of Rs 100 each, 100 of them contain a cash prize of Rs 50 each and 200 of them contain a cash prize of Rs 10 each and rest do not contain any cash prize. If they are well shuffled and an envelope is picked up out, what is the probability that it contains no cash prize?
Answer» Question 34 There are 1000 sealed envelopes in a box, 10 of them contain a cash prize of Rs 100 each, 100 of them contain a cash prize of Rs 50 each and 200 of them contain a cash prize of Rs 10 each and rest do not contain any cash prize. If they are well shuffled and an envelope is picked up out, what is the probability that it contains no cash prize?

Discussion

10650.	Evaluate :1012
Answer» Evaluate : $101^{2}$

Discussion

Explore topic-wise InterviewSolutions in .

The twoadjacent sides of a parallelogram areand.Find theunit vector parallel to its diagonal. Also, find its area.

Question 19Rohan and Shalu are playing with 5 cards as shown in the given figure. What is the probability of Rohan picking a card without seeing, that has the number 2 on it?(a) 25(b) 15(c) 35(d) 45

Find the square of 1468 by writing this as 1465 + 3.

Which among the following options contains a point lying on the line: y=3x+8?

FIND TWO CONSECUTIVE POSITIVE INTEGERS, SUM OF WHOSE SQAURES IS 365

What is the value of 1.52?

Cost of 20 Pencils is 100 Rupees. Cost of a pen is 40 more than 8 times the cost of a Pencil. Find the cost of 5 Pencils and 6 Pens.

Question 1(iv) Use a suitable identity to get each of the following products:(3a−12)(3a−12)

In the construction of a square inside a circle, the angle between the two diameters should be _____ degrees.90

Lines AB and CD interesct at O. If ∠AOC = 135∘, then ∠BOC3 = .

In how many years will a sum of money becomes three times at the rate of interest 10% per annum?

Find the median of the following data set.70 50 90 120 110 100 80 60

If y=xsin^2x find dy/dx

Question 10(a)In a college, out of 4320 students, 2300 are girls. Find the ratio of:Number of girls to the total number of students.

Raj bought 10 chocolates, each for ₹ 40. He sold 6 of them at ₹50 each, and the rest of it at ₹ 55 each. Find the percentage of profit he made.

The large pizza is cut into 8 equal slices. Find the central angle of each slice.

Draw a rhombus whose side is 7.2 cm and one angle is 60∘.

How many first odd natural numbers do we need to add together to get the number 81?

Solve √5x2+x+√5=0

Construct a square in which each diagonal is 5 cm long.

State whether the following statements are true or false. Also, justify your answer in each case. All rectangles are Squares All Squares are trapeziums All rhombuses are parallelograms

43. if Ax+31x-Bx-10 is exactly divisible by 2x+9x-5,find the values of A and B.

12×base×height is the formula of area for which type of triangles?

If three concurrent straight lines AD,BE and CF are drawn from the angular points of a △ABC such that AFFB=12,BDDC=23, then EAEC is equal to

Question 97The side of a square board is 50 cm. A student has to draw its image in her notebook. If the drawing of the square board in the notebook has perimeter of 40 cm, then by which scale the figure has been drawn?

Draw a histogram representing the following data:Class interval600−640640−680680−720720−760760−800800−840Frequency184515328817163

50 labourers can dig a pond in 16 days how many labourers will be required to dig another pond double in size in 20 days?

Find the amount which Ram will get on Rs. 4,096, he gave it for 18 months at 1212% per annum, interest being compounded half yearly.

8. A washing machine is available for Rs. 13,500 cash or Rs. 6,500 as cash down payment followed by three monthly instalments of Rs. 2,500 each . Find the rate of interest charged under instalment plan .

Rohit scored 92, 85, and 78 in three Maths tests. How much should he score in the 4th test so as to get an average of 87 in four Maths test?

An almirah is sold at Rs. 5225 after allowing a discount of 5%. Find its marked price.

The square of 4014 is

The angle subtended by blue portion at the center of following pie-chart is _____(in degrees).234

Question 159ABCDE is a regular pentagon. The bisector of angle A meets the sides CD at M. Find ∠AMC

What is the last step in constructing quadrilateral with 3 sides and 2 included angles given?

Find the values of x for which |x−2|+|x−8|=10.

Which of the following regular polygons has sum of all the interior angles as 720°?

In the given figure, ABCD is a kite with AC and BD as diagonals and ∠ABC = 30∘. Find x.

What is the coefficient of z in (z−5)3?

Question 3(v) Find the smallest number by which each of the following numbers must be divided to obtain a perfect cube: 704

The difference between A's and B's salary is ₹ 540.60. If B's salary is greater and A's salary is ₹ 27030, Find the percentage by which B's salary is higher.

If x+1x=2, then x3+1x3 =(a) 64(b) 14(c) 8(d) 2

Find the cube root of 175616 by prime factorisation method.

Question 4(v)Find the multiplicative inverse of the following:−1×−25

If the two right triangles in the diagram above are congruent. choose the pairs of equal sides and angles.

Evaluate :1012