24740 + Interview Questions in Mathematics Page 23 InterviewSolution

1101.	If sin[90 - (A+B)] = cosx = cosy, then find the value of x and y; if y is the angle C of triangle ABC.(In triangle ABC, A + B = 90∘)
Answer» If sin[90 - (A+B)] = cosx = cosy, then find the value of x and y; if y is the angle C of triangle ABC. (In triangle ABC, A + B = $90^{\circ}$ )

Discussion

1102.	In which of the following cases construction of a triangle is possible?
Answer» In which of the following cases construction of a triangle is possible?

Discussion

1103.	A line passes through A(-3,0) and B (0,-4) A variable line perpendicular to AB is drawn to cut x and y axis at M and N. Find the locus of the point of intersection of lines AN and BM.
Answer» A line passes through A(-3,0) and B (0,-4) A variable line perpendicular to AB is drawn to cut x and y axis at M and N. Find the locus of the point of intersection of lines AN and BM.

Discussion

1104.

The daily earnings of 30 workers are given below: Daily earning (in ₹) No. of workers 1-50 3 50-100 7 100-150 4 150-200 5 200-250 4 250-300 3 300-350 2 350-400 2 Draw a histogram and a frequency polygon to represent the above data.

Answer» The daily earnings of 30 workers are given below:

Daily earning (in ₹)	No. of workers
1-50	3
50-100	7
100-150	4
150-200	5
200-250	4
250-300	3
300-350	2
350-400	2

Draw a histogram and a frequency polygon to represent the above data.

Discussion

1105.	Given below are the heights of 20 students in centimetres. Find the number of students whose height is less than or equal to 169 cm 150178153156162184170176186173153186162159180183165180150156
Answer» Given below are the heights of 20 students in centimetres. Find the number of students whose height is less than or equal to 169 cm $\begin{matrix} 150 & 178 153 & 156 162 & 184 170 & 176 186 & 173 153 & 186 162 & 159 180 & 183 165 & 180 150 & 156 \end{matrix}$

1105.

Given below are the heights of 20 students in centimetres. Find the number of students whose height is less than or equal to 169 cm 150178153156162184170176186173153186162159180183165180150156

Answer»

Given below are the heights of 20 students in centimetres.

Find the number of students whose height is less than or equal to 169 cm

$\begin{matrix} 150 & 178 153 & 156 162 & 184 170 & 176 186 & 173 153 & 186 162 & 159 180 & 183 165 & 180 150 & 156 \end{matrix}$

Discussion

1106.	Simplify 30×42×5−2
Answer» Simplify $3^{0} \times 4^{2} \times 5^{- 2}$

Discussion

1107.	Non terminating and repeating rational number from among the following is .
Answer» Non terminating and repeating rational number from among the following is .

Discussion

1108.

Three coins are tossed simultaneously 200 times with the following frequencies of different outcomes: Outcome 3 heads 2 heads 1 head No head Frequency 23 72 77 28 Find the probability of getting at most two heads.

Answer» Three coins are tossed simultaneously 200 times with the following frequencies of different outcomes:

Outcome	3 heads	2 heads	1 head	No head
Frequency	23	72	77	28

Find the probability of getting at most two heads.

Discussion

1109.	If ABCD is a rhombus, then the value of x is
Answer» If ABCD is a rhombus, then the value of x is

Discussion

1110.	Define the incircle of a triangle? How can you locate the incenter of a triangle?
Answer» Define the incircle of a triangle? How can you locate the incenter of a triangle?

Discussion

1111.	A vector →a=x^i+y^j−2^k,(x,y∈R) lies in the plane of vectors, →b=2^i+^j−2^k and →c=3^i−4^j. If →a bisect the angle between →b and →c, then which of the following stetement(s) can be correct
Answer» A vector $\to a = x^i + y^j - 2^k, (x, y \in R)$ lies in the plane of vectors, $\to b = 2^i +^j - 2^k$ and $\to c = 3^i - 4^j .$ If $\to a$ bisect the angle between $\to b$ and $\to c,$ then which of the following stetement(s) can be correct

Discussion

1112.	From an aeroplane vertically above a straight horizontal road, the angles of depression of two stones on opposite sides of the aeroplane are observed to be α and β. The distance between the stones is 1m.Then the height in meters of the aeroplane above the road is
Answer» From an aeroplane vertically above a straight horizontal road, the angles of depression of two stones on opposite sides of the aeroplane are observed to be $α$ and $β$ . The distance between the stones is 1m.Then the height in meters of the aeroplane above the road is

Discussion

1113.	Question 42Rational numbers can be added or multiplied in any ____.
Answer» Question 42 Rational numbers can be added or multiplied in any ____.

Discussion

1114.	Question 5 In the figure, if AOB is a diameter of the circle and AC = BC, then ∠CAB is equal to (A) 30∘ (B) 60∘ (C) 90∘ (D) 45∘
Answer» Question 5 In the figure, if AOB is a diameter of the circle and AC = BC, then $∠ C A B$ is equal to (A) $30^{\circ}$ (B) $60^{\circ}$ (C) $90^{\circ}$ (D) $45^{\circ}$

Discussion

1115.	Factorise:x2-3x-6
Answer» Factorise: $x^{2} - \sqrt{3} x - 6$

Discussion

1116.	If Q is the set of all Rational Numbers, P is the set of all Irrational Numbers, R is the set of all Real Numbers, then
Answer» If $Q$ is the set of all Rational Numbers, $P$ is the set of all Irrational Numbers, $R$ is the set of all Real Numbers, then

Discussion

1117.	The capacity of a closed cylindrical vessel of height 1 m is 15.4 litres. How many square metres of metal sheet would be needed to make it?
Answer» The capacity of a closed cylindrical vessel of height 1 m is 15.4 litres. How many square metres of metal sheet would be needed to make it?

Discussion

1118.	The least number of non-collinear points required to draw a unique circle passing through them is:
Answer» The least number of non-collinear points required to draw a unique circle passing through them is:

Discussion

1119.	33. If the area and perimeter of a right angled triangle are numerically equal than what will be the possible area possible hint is that there are more than one area possible
Answer» 33. If the area and perimeter of a right angled triangle are numerically equal than what will be the possible area possible hint is that there are more than one area possible

Discussion

1120.	Construct a circle of radius 7 cm. In that circle, draw two congruent angles of any degree.
Answer» Construct a circle of radius 7 cm. In that circle, draw two congruent angles of any degree.

Discussion

1121.	In an isoceles triangle abc where ab =ac then a median drawn on bc could be its altitude
Answer» In an isoceles triangle abc where ab =ac then a median drawn on bc could be its altitude

Discussion

1122.	Jayanti takes shortest route to her home by walking diagonally across a rectangular park. The park measures 60 m×80 m. How much shorter is the route across park than the route around its edges?
Answer» Jayanti takes shortest route to her home by walking diagonally across a rectangular park. The park measures $60 m \times 80 m$ . How much shorter is the route across park than the route around its edges?

Discussion

1123.	Find the values of x and y using the information shown in figure .Find the measure of ∠ABD and m∠ACD.
Answer» Find the values of x and y using the information shown in figure . Find the measure of $∠$ ABD and m $∠$ ACD.

Discussion

1124.	Check whether 85125 is terminating or non terminating?
Answer» Check whether $\frac{85}{125}$ is terminating or non terminating?

Discussion

1125.	The pillars on the veranda of a school are square prisms of base length 20 centimetres and height 2.25 metres. There are 60 such pillars. What is the total cost of painting them all, at 250 rupees per square metre?
Answer» The pillars on the veranda of a school are square prisms of base length 20 centimetres and height 2.25 metres. There are 60 such pillars. What is the total cost of painting them all, at 250 rupees per square metre?

1125.

The pillars on the veranda of a school are square prisms of base length 20 centimetres and height 2.25 metres. There are 60 such pillars. What is the total cost of painting them all, at 250 rupees per square metre?

Answer»

The pillars on the veranda of a school are square prisms of base length 20 centimetres and height 2.25 metres. There are 60 such pillars. What is the total cost of painting them all, at 250 rupees per square metre?

Discussion

1126.	Question 6 (iii)The volume of a right circular cone is 9856cm3. If the diameter of the base is 28cm, find:(iii) curved surface area of the cone.[Assume π=227]
Answer» Question 6 (iii) The volume of a right circular cone is $9856 c m^{3}$ . If the diameter of the base is 28cm, find: (iii) curved surface area of the cone. $[A s s u m e π = \frac{22}{7}]$

Discussion

1127.	In the construction given, what is the ratio in which the point C divides the line segment AB?
Answer» In the construction given, what is the ratio in which the point C divides the line segment AB?

1127.

In the construction given, what is the ratio in which the point C divides the line segment AB?

Answer»

In the construction given, what is the ratio in which the point C divides the line segment AB?

Discussion

1128.	If Q (0, 1) is equidistant from P (5, − 3) and R (x, 6), find the values of x. Also find the distance QR and PR.
Answer» If Q (0, 1) is equidistant from P (5, − 3) and R (x, 6), find the values of x. Also find the distance QR and PR.

Discussion

1129.	What is the least rationalising factor of √72?
Answer» What is the least rationalising factor of $\sqrt{72}$ ?

Discussion

1130.	TWO CIRCLES ARE PLACED ONE SMALL AND OTHER BIG IN EQUILATERAL TRIANGLE CALCULATE THE RATIO OF THEIR RADII
Answer» TWO CIRCLES ARE PLACED ONE SMALL AND OTHER BIG IN EQUILATERAL TRIANGLE CALCULATE THE RATIO OF THEIR RADII

Discussion

1131.	In triangle ABC, angle B = 35o, angle C = 65o and the bisector of angle BAC meets BC in P. Choose the correct descending order of AP, BP and CP
Answer» In triangle ABC, angle B = 35^o, angle C = 65^o and the bisector of angle BAC meets BC in P. Choose the correct descending order of AP, BP and CP

1131.

In triangle ABC, angle B = 35o, angle C = 65o and the bisector of angle BAC meets BC in P. Choose the correct descending order of AP, BP and CP

Answer»

In triangle ABC, angle B = 35^o, angle C = 65^o and the bisector of angle BAC meets BC in P. Choose the correct descending order of AP, BP and CP

Discussion

1132.	Which of these lines pass through the point (2,-2)?
Answer» Which of these lines pass through the point (2,-2)?

Discussion

1133.	The coordinates of the image of the point (–4, 5) in y-axis are _________.
Answer» The coordinates of the image of the point (–4, 5) in y-axis are _________.

Discussion

1134.	Question 129(i)Astronomy The table shows the mass of the planets, the Sun and the Moon in our solar system.Write the mass of each planet and the Moon in scientific notation.
Answer» Question 129(i) Astronomy The table shows the mass of the planets, the Sun and the Moon in our solar system. Write the mass of each planet and the Moon in scientific notation.

1134.

Question 129(i)Astronomy The table shows the mass of the planets, the Sun and the Moon in our solar system.Write the mass of each planet and the Moon in scientific notation.

Answer»

Question 129(i)

Astronomy The table shows the mass of the planets, the Sun and the Moon in our solar system.

Write the mass of each planet and the Moon in scientific notation.

Discussion

1135.

Question 2 (iv) Find 33.1 ÷ 10

Answer»

Question 2 (iv)

Find
33.1

\div

10

Discussion

1136.	The table below shows the sale of shirts of various sizes in a week.Shirt size3839404142Number sold6073899023The size which is demanded the most is ___.
Answer» The table below shows the sale of shirts of various sizes in a week. $\begin{matrix} Shirt size & 38 & 39 & 40 & 41 & 42 Number sold & 60 & 73 & 89 & 90 & 23 \end{matrix}$ The size which is demanded the most is ___.

1136.

The table below shows the sale of shirts of various sizes in a week.Shirt size3839404142Number sold6073899023The size which is demanded the most is ___.

Answer»

The table below shows the sale of shirts of various sizes in a week.

$\begin{matrix} Shirt size & 38 & 39 & 40 & 41 & 42 Number sold & 60 & 73 & 89 & 90 & 23 \end{matrix}$

The size which is demanded the most is

___.

Discussion

1137.	Draw the graph of the equation y=3x. Does the point (3,1) lie on this? [3 MARKS]
Answer» Draw the graph of the equation y=3x. Does the point (3,1) lie on this? [3 MARKS]

Discussion

1138.	The locus of the centre of the circle for which one end of diameter is (3,3) while the other end lies on the line (x+y=4) is- (a) x+y=3 (b)x+y=5 (c)x+y=7 (d)x+y=9.
Answer» The locus of the centre of the circle for which one end of diameter is (3,3) while the other end lies on the line (x+y=4) is- (a) x+y=3 (b)x+y=5 (c)x+y=7 (d)x+y=9.

Discussion

1139.	The part of the number line between the points denoted by the numbers 13 and 12 is divided into four equal parts as shown below. Find the numbers denoted by A,B and C.
Answer» The part of the number line between the points denoted by the numbers $\frac{1}{3}$ and $\frac{1}{2}$ is divided into four equal parts as shown below. Find the numbers denoted by A,B and C.

1139.

The part of the number line between the points denoted by the numbers 13 and 12 is divided into four equal parts as shown below. Find the numbers denoted by A,B and C.

Answer»

The part of the number line between the points denoted by the numbers $\frac{1}{3}$ and $\frac{1}{2}$ is divided into four equal parts as shown below. Find the numbers denoted by A,B and C.

Discussion

1140.	Solve: 3x + 4y = 10, 2x − 2y = 2 by the method of elimination.
Answer» Solve: 3x + 4y = 10, 2x − 2y = 2 by the method of elimination.

Discussion

1141.	Find the fvolume of a sphere whose radius is (i) 2 cm (ii) 3.5 cm (iii) 10.5 cm
Answer» Find the fvolume of a sphere whose radius is (i) 2 cm (ii) 3.5 cm (iii) 10.5 cm

Discussion

1142.	If x2 + x + 1 is a factor of the polynomial 3x3 + 8x2 + 8x + 3 + 5k, then the value of k is(a) 0(b) 2/5(c) 5/2(d) −1
Answer» If x² + x + 1 is a factor of the polynomial 3x³ + 8x²+ 8x + 3 + 5k, then the value of k is (a) 0 (b) 2/5 (c) 5/2 (d) −1

Discussion

1143.	The present age of Pratik and Arjun are in the ratio 2 : 3. After 4 years, the ratio of their ages will be 4 : 5. The present age of Pratik would be_____years. ___
Answer» The present age of Pratik and Arjun are in the ratio 2 : 3. After 4 years, the ratio of their ages will be 4 : 5. The present age of Pratik would be_____years. ___

Discussion

1144.	A group of people prepares 512 L oflemonade for the sports day. How many L of lemonade was prepared by 7 similar groups?
Answer» $A group of people prepares 5 \frac{1}{2} L of$ $lemonade for the sports day. How many L$ $of lemonade was prepared by 7 similar groups?$

Discussion

1145.	Will the measure of ∠ ABC and of ∠ CBD make the measure of ∠ ABD in the given figure? Name all the rays in the figure. Which of the two angles share a common ray?[4 MARKS]
Answer» Will the measure of $∠$ ABC and of $∠$ CBD make the measure of $∠$ ABD in the given figure? Name all the rays in the figure. Which of the two angles share a common ray? [4 MARKS]

Discussion

1146.	represent \sqrt{2 } on a number line.
Answer» represent \sqrt{2 } on a number line.

Discussion

1147.	Find the value of a and b so that the polynomial x³-13x+b is exactly divisible by (x-1) and (x+3).
Answer» Find the value of a and b so that the polynomial x³-13x+b is exactly divisible by (x-1) and (x+3).

Discussion

1148.

In the given figure, if ∠ACB = 30∘, then what is the value of ∠ACD?

Answer»

In the given figure, if $∠$ ACB = $30^{\circ}$ , then what is the value of $∠$ ACD?

Discussion

1149.	Draw a line l. Take a point T outside the line. Through point T draw a line parallel to line l.
Answer» Draw a line l. Take a point T outside the line. Through point T draw a line parallel to line l.

Discussion

1150.	Insert a rational and an irrational number between 2 and 2.5.
Answer» Insert a rational and an irrational number between 2 and 2.5.

Discussion

Explore topic-wise InterviewSolutions in .

If sin[90 - (A+B)] = cosx = cosy, then find the value of x and y; if y is the angle C of triangle ABC.(In triangle ABC, A + B = 90∘)

In which of the following cases construction of a triangle is possible?

A line passes through A(-3,0) and B (0,-4) A variable line perpendicular to AB is drawn to cut x and y axis at M and N. Find the locus of the point of intersection of lines AN and BM.

The daily earnings of 30 workers are given below: Daily earning (in ₹) No. of workers 1-50 3 50-100 7 100-150 4 150-200 5 200-250 4 250-300 3 300-350 2 350-400 2 Draw a histogram and a frequency polygon to represent the above data.

Given below are the heights of 20 students in centimetres. Find the number of students whose height is less than or equal to 169 cm 150178153156162184170176186173153186162159180183165180150156

Simplify 30×42×5−2

Non terminating and repeating rational number from among the following is .

Three coins are tossed simultaneously 200 times with the following frequencies of different outcomes: Outcome 3 heads 2 heads 1 head No head Frequency 23 72 77 28 Find the probability of getting at most two heads.

If ABCD is a rhombus, then the value of x is

Define the incircle of a triangle? How can you locate the incenter of a triangle?

A vector →a=x^i+y^j−2^k,(x,y∈R) lies in the plane of vectors, →b=2^i+^j−2^k and →c=3^i−4^j. If →a bisect the angle between →b and →c, then which of the following stetement(s) can be correct

From an aeroplane vertically above a straight horizontal road, the angles of depression of two stones on opposite sides of the aeroplane are observed to be α and β. The distance between the stones is 1m.Then the height in meters of the aeroplane above the road is

Question 42Rational numbers can be added or multiplied in any ____.

Question 5 In the figure, if AOB is a diameter of the circle and AC = BC, then ∠CAB is equal to (A) 30∘ (B) 60∘ (C) 90∘ (D) 45∘

Factorise:x2-3x-6

If Q is the set of all Rational Numbers, P is the set of all Irrational Numbers, R is the set of all Real Numbers, then

The capacity of a closed cylindrical vessel of height 1 m is 15.4 litres. How many square metres of metal sheet would be needed to make it?

The least number of non-collinear points required to draw a unique circle passing through them is:

33. If the area and perimeter of a right angled triangle are numerically equal than what will be the possible area possible hint is that there are more than one area possible

Construct a circle of radius 7 cm. In that circle, draw two congruent angles of any degree.

In an isoceles triangle abc where ab =ac then a median drawn on bc could be its altitude

Jayanti takes shortest route to her home by walking diagonally across a rectangular park. The park measures 60 m×80 m. How much shorter is the route across park than the route around its edges?

Find the values of x and y using the information shown in figure .Find the measure of ∠ABD and m∠ACD.

Check whether 85125 is terminating or non terminating?

The pillars on the veranda of a school are square prisms of base length 20 centimetres and height 2.25 metres. There are 60 such pillars. What is the total cost of painting them all, at 250 rupees per square metre?

Question 6 (iii)The volume of a right circular cone is 9856cm3. If the diameter of the base is 28cm, find:(iii) curved surface area of the cone.[Assume π=227]

In the construction given, what is the ratio in which the point C divides the line segment AB?

If Q (0, 1) is equidistant from P (5, − 3) and R (x, 6), find the values of x. Also find the distance QR and PR.

What is the least rationalising factor of √72?

TWO CIRCLES ARE PLACED ONE SMALL AND OTHER BIG IN EQUILATERAL TRIANGLE CALCULATE THE RATIO OF THEIR RADII

In triangle ABC, angle B = 35o, angle C = 65o and the bisector of angle BAC meets BC in P. Choose the correct descending order of AP, BP and CP

Which of these lines pass through the point (2,-2)?

The coordinates of the image of the point (–4, 5) in y-axis are _________.

Question 129(i)Astronomy The table shows the mass of the planets, the Sun and the Moon in our solar system.Write the mass of each planet and the Moon in scientific notation.

Question 2 (iv) Find 33.1 ÷ 10

The table below shows the sale of shirts of various sizes in a week.Shirt size3839404142Number sold6073899023The size which is demanded the most is ___.

Draw the graph of the equation y=3x. Does the point (3,1) lie on this? [3 MARKS]

The locus of the centre of the circle for which one end of diameter is (3,3) while the other end lies on the line (x+y=4) is- (a) x+y=3 (b)x+y=5 (c)x+y=7 (d)x+y=9.

The part of the number line between the points denoted by the numbers 13 and 12 is divided into four equal parts as shown below. Find the numbers denoted by A,B and C.

Solve: 3x + 4y = 10, 2x − 2y = 2 by the method of elimination.

Find the fvolume of a sphere whose radius is (i) 2 cm (ii) 3.5 cm (iii) 10.5 cm

If x2 + x + 1 is a factor of the polynomial 3x3 + 8x2 + 8x + 3 + 5k, then the value of k is(a) 0(b) 2/5(c) 5/2(d) −1

The present age of Pratik and Arjun are in the ratio 2 : 3. After 4 years, the ratio of their ages will be 4 : 5. The present age of Pratik would be_____years. ___

A group of people prepares 512 L oflemonade for the sports day. How many L of lemonade was prepared by 7 similar groups?

Will the measure of ∠ ABC and of ∠ CBD make the measure of ∠ ABD in the given figure? Name all the rays in the figure. Which of the two angles share a common ray?[4 MARKS]

represent \sqrt{2 } on a number line.

Find the value of a and b so that the polynomial x³-13x+b is exactly divisible by (x-1) and (x+3). ​​​​​

In the given figure, if ∠ACB = 30∘, then what is the value of ∠ACD?

Draw a line l. Take a point T outside the line. Through point T draw a line parallel to line l.

Insert a rational and an irrational number between 2 and 2.5.

The present age of Pratik and Arjun are in the ratio 2 : 3. After 4 years, the ratio of their ages will be 4 : 5. The present age of Pratik would be___years. _

Find the value of a and b so that the polynomial x³-13x+b is exactly divisible by (x-1) and (x+3).