32581 + Interview Questions in Mathematics Page 73 InterviewSolution

3601.	Find the HCF and LCM of 6, 72 and 120 using the prime factorisation method.
Answer» Find the HCF and LCM of 6, 72 and 120 using the prime factorisation method.

Discussion

3602.	A solid is in the form of a cylinder with hemispherical ends. Total height of the solid is 19 cm and the diameter of the cylinder is 7 cm. Find the volume and total surface area of the solid.
Answer» A solid is in the form of a cylinder with hemispherical ends. Total height of the solid is 19 cm and the diameter of the cylinder is 7 cm. Find the volume and total surface area of the solid.

Discussion

3603.	a) Solve the inequation and represent the solution set on the number line. −3+x≤8x3+2≤143+2x,where xϵI b) Solve the given inequation and graph the solution on the number line 2y−3<y+1≤4y+7;yϵR [6 MARKS]
Answer» a) Solve the inequation and represent the solution set on the number line. $- 3 + x \leq \frac{8 x}{3} + 2 \leq \frac{14}{3} + 2 x, w h e r e x ϵ I$ b) Solve the given inequation and graph the solution on the number line $2 y - 3 < y + 1 \leq 4 y + 7; y ϵ R$ [6 MARKS]

Discussion

3604.	Question 2The polynomial p(x)=x4–2x3+3x2–ax+3a–7 when divided by x + 1 leaves the remainder 19. Find the value of a. Also , find the remainder when p(x) is divided by x + 2.
Answer» Question 2 The polynomial $p (x) = x^{4} - 2 x^{3} + 3 x^{2} - a x + 3 a - 7$ when divided by x + 1 leaves the remainder 19. Find the value of a. Also , find the remainder when p(x) is divided by x + 2.

Discussion

3605.	x2n– y2n is divisible by x+ y.
Answer» x²ⁿ – y²ⁿ is divisible by x + y.

Discussion

3606.	76.Prove that. Tan(b+c)+ tan(c+a)+ tan (a+b)/tan(-a)+ tan (2-b)+ tan (3-c)=1
Answer» 76.Prove that. Tan(b+c)+ tan(c+a)+ tan (a+b)/tan(-a)+ tan (2-b)+ tan (3-c)=1

Discussion

3607.	If sin θ=13, then find the value of 2cot2 θ + 2.
Answer» If $\sin θ = \frac{1}{3}$ , then find the value of 2cot² θ + 2.

Discussion

3608.	A ladder 15 m long just reaches the top of a vertical wall. If the ladder makes an angle of 60° with the wall, then the height of the wall is(a) 153m (b) 1532m (c) 152 m (d) 15 m [CBSE 2013]
Answer» A ladder 15 m long just reaches the top of a vertical wall. If the ladder makes an angle of 60° with the wall, then the height of the wall is (a) $15 \sqrt{3} m$ (b) $\frac{15 \sqrt{3}}{2} m$ (c) $\frac{15}{2}$ m (d) 15 m [CBSE 2013]

Discussion

3609.	Pass entries in the firm's journal for the following on admission of a partner:(i) Machinery be reduced by ₹ 16,000 and Building be appreciated by ₹ 40,000.(ii) A provision be created for Doubtful Debts 5% of Debtors amounting to ₹ 80,000.(iii) Provision for warranty claims be increased by ₹ 12,000.
Answer» Pass entries in the firm's journal for the following on admission of a partner: (i) Machinery be reduced by ₹ 16,000 and Building be appreciated by ₹ 40,000. (ii) A provision be created for Doubtful Debts 5% of Debtors amounting to ₹ 80,000. (iii) Provision for warranty claims be increased by ₹ 12,000.

Discussion

3610.	The angles of elevation of the top of a tower from the bottom and top of a building of height 'd' are beta and Alfa respectively.Find the height of the tower
Answer» The angles of elevation of the top of a tower from the bottom and top of a building of height 'd' are beta and Alfa respectively.Find the height of the tower

Discussion

3611.	Solve the following systems of equations:2x+3y=24x-9y=-1
Answer» Solve the following systems of equations: $\frac{2}{\sqrt{x}} + \frac{3}{\sqrt{y}} = 2 \frac{4}{\sqrt{x}} - \frac{9}{\sqrt{y}} = - 1$

Discussion

3612.	Question 15 In Fig. 12.33, ABC is a quadrant of a circle of radius 14 cm and a semicircle is drawn with BC as diameter. Find the area of the shaded region.
Answer» Question 15 In Fig. 12.33, ABC is a quadrant of a circle of radius 14 cm and a semicircle is drawn with BC as diameter. Find the area of the shaded region.

3612.

Question 15 In Fig. 12.33, ABC is a quadrant of a circle of radius 14 cm and a semicircle is drawn with BC as diameter. Find the area of the shaded region.

Answer»

Question 15
In Fig. 12.33, ABC is a quadrant of a circle of radius 14 cm and a semicircle is drawn with BC as diameter. Find the area of the shaded region.

Discussion

3613.	The perimeter of a certain sector of a circle of radius 5.6 m is 27.2 m. Find the area of the sector.
Answer» The perimeter of a certain sector of a circle of radius 5.6 m is 27.2 m. Find the area of the sector.

Discussion

3614.	The sum of the areas of two squares is 640 m2. If the difference of their perimeters is 64 m, find the sides of the squares.
Answer» The sum of the areas of two squares is 640 m². If the difference of their perimeters is 64 m, find the sides of the squares.

Discussion

3615.	Sum of the digit of a two digit number is 9 when we interchange the digit, it is found that the resulting new number is greater than the original number by 27.what is the two digit number?
Answer» Sum of the digit of a two digit number is 9 when we interchange the digit, it is found that the resulting new number is greater than the original number by 27.what is the two digit number?

Discussion

3616.	351 means "students like maths”; 197 means "we are students”; 748 means "they are parents”. The digit for We is:
Answer» 351 means "students like maths”; 197 means "we are students”; 748 means "they are parents”. The digit for We is:

Discussion

3617.	Find the curved surface area of a cone with base radius 5.25 cm and slant height 10 cm.
Answer» Find the curved surface area of a cone with base radius $5.25 c m$ and slant height $10 c m .$

Discussion

3618.	Question 162 Neha needs to stretch some sticks to 252 times of their original lengths, but her (×25) machine is broken. find a hook-up of two repeater machines that will do the same work as a (×252) machine. To get started, think about the hook-up you could use to replace the (×25) machine.
Answer» Question 162 Neha needs to stretch some sticks to $25^{2}$ times of their original lengths, but her $(\times 25)$ machine is broken. find a hook-up of two repeater machines that will do the same work as a $(\times 25^{2})$ machine. To get started, think about the hook-up you could use to replace the $(\times 25)$ machine.

3618.

Question 162 Neha needs to stretch some sticks to 252 times of their original lengths, but her (×25) machine is broken. find a hook-up of two repeater machines that will do the same work as a (×252) machine. To get started, think about the hook-up you could use to replace the (×25) machine.

Answer»

Question 162

Neha needs to stretch some sticks to $25^{2}$ times of their original lengths, but her $(\times 25)$ machine is broken. find a hook-up of two repeater machines that will do the same work as a $(\times 25^{2})$ machine. To get started, think about the hook-up you could use to replace the $(\times 25)$ machine.

Discussion

3619.	In a cricket match, Humpty scored a century and Dumpty scored a half-century. The average or the arithmetic mean of the scores of Humpty and Dumpty is 100.
Answer» In a cricket match, Humpty scored a century and Dumpty scored a half-century. The average or the arithmetic mean of the scores of Humpty and Dumpty is 100.

Discussion

3620.	Match the following events with corresponding probability on tossing two coins simultaneously.
Answer» Match the following events with corresponding probability on tossing two coins simultaneously.

Discussion

3621.	Simplify (3x - 11y)- (17x + 13y) and choose the right answer. (i) 7x -12y (ii) - 14x -54y (iii) -3 (5x + 4y ) (iv) -2 (7x + 12y )
Answer» Simplify (3x $-$ 11y) $-$ (17x + 13y) and choose the right answer. (i) 7x $-$ 12y (ii) $-$ 14x $-$ 54y (iii) $-$ 3 (5x + 4y ) (iv) $-$ 2 (7x + 12y )

Discussion

3622.	Solve x + √2x+9=13
Answer» Solve x + $\sqrt{2 x + 9}$ =13

Discussion

3623.	Fill In The Blanks Two chords AB and AC of a circle are on the opposite sides of the centre. If AB and AC subtend angles equal to 90∘ and 150∘ respectively at the centre, then ∠BAC = _________.
Answer» Fill In The Blanks Two chords AB and AC of a circle are on the opposite sides of the centre. If AB and AC subtend angles equal to 90^∘ and 150^∘ respectively at the centre, then ∠BAC = _________.

Discussion

3624.	Solve each of the following equations by using the method of completing the square: 8x2−14x−15=0
Answer» Solve each of the following equations by using the method of completing the square: $8 x^{2} - 14 x - 15 = 0$

Discussion

3625.	In the given figure, O is the centre of the circle such that ∠AOC = 130°, then ∠ABC =(a) 130°(b) 115°(c) 65°(d) 165°
Answer» In the given figure, O is the centre of the circle such that ∠AOC = 130°, then ∠ABC = (a) 130° (b) 115° (c) 65° (d) 165°

Discussion

3626.	Ram has a semicircular disc. He rotates it about its diameter by 360 degrees. When he rotates the disc, a volume of air in his room gets swept. What is the name of the object/shape that exactly occupies this volume?
Answer» Ram has a semicircular disc. He rotates it about its diameter by 360 degrees. When he rotates the disc, a volume of air in his room gets swept. What is the name of the object/shape that exactly occupies this volume?

Discussion

3627.	As shown in the figure, Avinash is standing near his house. He can choose from two roads to go to school. Which way isshorter? Explain why.
Answer» As shown in the figure, Avinash is standing near his house. He can choose from two roads to go to school. Which way is shorter? Explain why.

Discussion

3628.	173 saplings are to be planted equally in 12 rows. How many trees are there in each row? How many will be left out?
Answer» 173 saplings are to be planted equally in 12 rows. How many trees are there in each row? How many will be left out?

Discussion

3629.	A carpenter was hired to build 192 window frames. The first day he made five frames and each day thereafter he made two more frames than he made the day before. How many days did it take him to finish the job? [NCERT EXEMPLAR]
Answer» A carpenter was hired to build 192 window frames. The first day he made five frames and each day thereafter he made two more frames than he made the day before. How many days did it take him to finish the job? [NCERT EXEMPLAR]

Discussion

3630.	In Fig. 14.36, a right triangle BOA is given C is the mid-point of the hypotenuse AB. Show that it is equidistant from the vertices O, A and B.
Answer» In Fig. 14.36, a right triangle BOA is given C is the mid-point of the hypotenuse AB. Show that it is equidistant from the vertices O, A and B.

Discussion

3631.	If Ram walks 15 KM uphill and cycles straight to Pochinki, at what time will he get chicken dinner. (dummy)0
Answer» If Ram walks 15 KM uphill and cycles straight to Pochinki, at what time will he get chicken dinner. (dummy) 0

Discussion

3632.	The average marks of the students in Mathematics of class 8th is 45. But most of the students were given 60 out of 100. The median of the class would be ___ .
Answer» The average marks of the students in Mathematics of class $8^{t h}$ is 45. But most of the students were given 60 out of 100. The median of the class would be ___ .

Discussion

3633.	In ∆PQR, right-angled at Q, PQ = 3 cm and PR = 6 cm. Determine ∠P and ∠R.
Answer» In ∆PQR, right-angled at Q, PQ = 3 cm and PR = 6 cm. Determine ∠P and ∠R.

Discussion

3634.	Find the polynomial whose sum of zeroes is −85 and the products of zeroes is 75.
Answer» Find the polynomial whose sum of zeroes is $- \frac{8}{5}$ and the products of zeroes is $\frac{7}{5}$ .

Discussion

3635.	a train travels at a certain average speed for a distance of 54 km and then travels a distance of 63 km at an average speed of 6 km/h more than the first speed. if it takes 3 hours to complete the total journey, what is its speed?
Answer» a train travels at a certain average speed for a distance of 54 km and then travels a distance of 63 km at an average speed of 6 km/h more than the first speed. if it takes 3 hours to complete the total journey, what is its speed?

Discussion

3636.	If cos θ+sin θ=√cos θ, then what is the value of cos θ−sin θ? [3 MARKS]
Answer» If $c o s θ + s i n θ = \sqrt{c o s θ}$ , then what is the value of $c o s θ - s i n θ$ ? [3 MARKS]

Discussion

3637.

If the mean of the following distribution is 54, find the value of p: Class : 0−20 20−40 40−60 60−80 80−100 Frequency : 7 p 10 9 13

Answer» If the mean of the following distribution is 54, find the value of p:

Class :	0−20	20−40	40−60	60−80	80−100
Frequency :	7	p	10	9	13

Discussion

3638.	Question 26Size of the class 150 - 175 is:(a) 150(b) 175(c) 25(d) –25
Answer» Question 26 Size of the class 150 - 175 is: (a) 150 (b) 175 (c) 25 (d) –25

3638.

Question 26Size of the class 150 - 175 is:(a) 150(b) 175(c) 25(d) –25

Answer»

Question 26

Size of the class 150 - 175 is:

(a) 150

(b) 175

(c) 25

(d) –25

Discussion

3639.	Question 12If the height of a tower and the distance of the point of observation from its foot, both are increased by 10%, then the angle of elevation of its top remains unchanged.
Answer» Question 12 If the height of a tower and the distance of the point of observation from its foot, both are increased by $10 %$ , then the angle of elevation of its top remains unchanged.

Discussion

3640.	A diver descends 20 feet in the water from the boat at the surface of the lake. He then rose 12 feet and descends another 18 feet. At this point, what is his depth in water?
Answer» A diver descends 20 feet in the water from the boat at the surface of the lake. He then rose 12 feet and descends another 18 feet. At this point, what is his depth in water?

Discussion

3641.	What is cotA in terms of sinA?
Answer» What is $cot A$ in terms of $sin A$ ?

Discussion

3642.	The figure shows the graph of y=x2. This graph is shifted downward by 9 units. Find the new roots of the equation.
Answer» The figure shows the graph of $y = x^{2}$ . This graph is shifted downward by 9 units. Find the new roots of the equation.

Discussion

3643.	A solid cone of a base radius 10cm is cut into two parts through the mid-point of it's height, by a plane parallel to it's base. Find the ratio in the volumes of two parts of the cone.
Answer» A solid cone of a base radius 10cm is cut into two parts through the mid-point of it's height, by a plane parallel to it's base. Find the ratio in the volumes of two parts of the cone.

Discussion

3644.	The probability of winning a race of an athlete is 1/5 less than the thrice the probability of losing the race. Find the probability of winning the race.
Answer» The probability of winning a race of an athlete is 1/5 less than the thrice the probability of losing the race. Find the probability of winning the race.

Discussion

3645.	If y = 12 (3x+7) is rewritten in the form ax+by+c=0, what are the values of a, b and c?
Answer» If y = $\frac{1}{2}$ (3x+7) is rewritten in the form $a x + b y + c = 0$ , what are the values of a, b and c?

Discussion

3646.	Very-Short and Short-Answer QuestionsThe first three terms of an AP are respectively (3y − 1), (3y + 5) and (5y + 1), find the value of y. [CBSE 2014]
Answer» Very-Short and Short-Answer Questions The first three terms of an AP are respectively (3y − 1), (3y + 5) and (5y + 1), find the value of y. [CBSE 2014]

Discussion

3647.	If the replacement set is the set of natural numbers, find the solution set for the given inequation, 1+9x≥x+81.
Answer» If the replacement set is the set of natural numbers, find the solution set for the given inequation, $1 + 9 x \geq x + 81$ .

Discussion

3648.	6 bells commence tolling together and toll at intervals 2, 4 ,6,8,10,12 respectively. After how many minutes they will toll together?
Answer» 6 bells commence tolling together and toll at intervals 2, 4 ,6,8,10,12 respectively. After how many minutes they will toll together?

Discussion

3649.	If one of the zeros of the polynomial 5x² + 13x + a is reciprocal of the other.Find the value of a.
Answer» If one of the zeros of the polynomial 5x² + 13x + a is reciprocal of the other.Find the value of a.

Discussion

3650.	Integrate tan x
Answer» Integrate tan x

Discussion

Explore topic-wise InterviewSolutions in .

Find the HCF and LCM of 6, 72 and 120 using the prime factorisation method.

A solid is in the form of a cylinder with hemispherical ends. Total height of the solid is 19 cm and the diameter of the cylinder is 7 cm. Find the volume and total surface area of the solid.

a) Solve the inequation and represent the solution set on the number line. −3+x≤8x3+2≤143+2x,where xϵI b) Solve the given inequation and graph the solution on the number line 2y−3&lt;y+1≤4y+7;yϵR [6 MARKS]

Question 2The polynomial p(x)=x4–2x3+3x2–ax+3a–7 when divided by x + 1 leaves the remainder 19. Find the value of a. Also , find the remainder when p(x) is divided by x + 2.

x2n– y2n is divisible by x+ y.

76.Prove that. Tan(b+c)+ tan(c+a)+ tan (a+b)/tan(-a)+ tan (2-b)+ tan (3-c)=1

If sin θ=13, then find the value of 2cot2 θ + 2.

A ladder 15 m long just reaches the top of a vertical wall. If the ladder makes an angle of 60° with the wall, then the height of the wall is(a) 153m (b) 1532m (c) 152 m (d) 15 m [CBSE 2013]

The angles of elevation of the top of a tower from the bottom and top of a building of height 'd' are beta and Alfa respectively.Find the height of the tower

Solve the following systems of equations:2x+3y=24x-9y=-1

Question 15 In Fig. 12.33, ABC is a quadrant of a circle of radius 14 cm and a semicircle is drawn with BC as diameter. Find the area of the shaded region.

The perimeter of a certain sector of a circle of radius 5.6 m is 27.2 m. Find the area of the sector.

The sum of the areas of two squares is 640 m2. If the difference of their perimeters is 64 m, find the sides of the squares.

Sum of the digit of a two digit number is 9 when we interchange the digit, it is found that the resulting new number is greater than the original number by 27.what is the two digit number?

351 means "students like maths”; 197 means "we are students”; 748 means "they are parents”. The digit for We is:

Find the curved surface area of a cone with base radius 5.25 cm and slant height 10 cm.

Question 162 Neha needs to stretch some sticks to 252 times of their original lengths, but her (×25) machine is broken. find a hook-up of two repeater machines that will do the same work as a (×252) machine. To get started, think about the hook-up you could use to replace the (×25) machine.

In a cricket match, Humpty scored a century and Dumpty scored a half-century. The average or the arithmetic mean of the scores of Humpty and Dumpty is 100.

Match the following events with corresponding probability on tossing two coins simultaneously.

Simplify (3x - 11y)- (17x + 13y) and choose the right answer. (i) 7x -12y (ii) - 14x -54y (iii) -3 (5x + 4y ) (iv) -2 (7x + 12y )

Solve x + √2x+9=13

Fill In The Blanks Two chords AB and AC of a circle are on the opposite sides of the centre. If AB and AC subtend angles equal to 90∘ and 150∘ respectively at the centre, then ∠BAC = _________.

Solve each of the following equations by using the method of completing the square: 8x2−14x−15=0

In the given figure, O is the centre of the circle such that ∠AOC = 130°, then ∠ABC =(a) 130°(b) 115°(c) 65°(d) 165°

Ram has a semicircular disc. He rotates it about its diameter by 360 degrees. When he rotates the disc, a volume of air in his room gets swept. What is the name of the object/shape that exactly occupies this volume?

As shown in the figure, Avinash is standing near his house. He can choose from two roads to go to school. Which way isshorter? Explain why.

173 saplings are to be planted equally in 12 rows. How many trees are there in each row? How many will be left out?

A carpenter was hired to build 192 window frames. The first day he made five frames and each day thereafter he made two more frames than he made the day before. How many days did it take him to finish the job? [NCERT EXEMPLAR]

In Fig. 14.36, a right triangle BOA is given C is the mid-point of the hypotenuse AB. Show that it is equidistant from the vertices O, A and B.

If Ram walks 15 KM uphill and cycles straight to Pochinki, at what time will he get chicken dinner. (dummy)0

The average marks of the students in Mathematics of class 8th is 45. But most of the students were given 60 out of 100. The median of the class would be ___ .

In ∆PQR, right-angled at Q, PQ = 3 cm and PR = 6 cm. Determine ∠P and ∠R.

Find the polynomial whose sum of zeroes is −85 and the products of zeroes is 75.

a train travels at a certain average speed for a distance of 54 km and then travels a distance of 63 km at an average speed of 6 km/h more than the first speed. if it takes 3 hours to complete the total journey, what is its speed?

If cos θ+sin θ=√cos θ, then what is the value of cos θ−sin θ? [3 MARKS]

If the mean of the following distribution is 54, find the value of p: Class : 0−20 20−40 40−60 60−80 80−100 Frequency : 7 p 10 9 13

Question 26Size of the class 150 - 175 is:(a) 150(b) 175(c) 25(d) –25

Question 12If the height of a tower and the distance of the point of observation from its foot, both are increased by 10%, then the angle of elevation of its top remains unchanged.

A diver descends 20 feet in the water from the boat at the surface of the lake. He then rose 12 feet and descends another 18 feet. At this point, what is his depth in water?

What is cotA in terms of sinA?

The figure shows the graph of y=x2. This graph is shifted downward by 9 units. Find the new roots of the equation.

A solid cone of a base radius 10cm is cut into two parts through the mid-point of it's height, by a plane parallel to it's base. Find the ratio in the volumes of two parts of the cone.

The probability of winning a race of an athlete is 1/5 less than the thrice the probability of losing the race. Find the probability of winning the race.

If y = 12 (3x+7) is rewritten in the form ax+by+c=0, what are the values of a, b and c?

Very-Short and Short-Answer QuestionsThe first three terms of an AP are respectively (3y − 1), (3y + 5) and (5y + 1), find the value of y. [CBSE 2014]

If the replacement set is the set of natural numbers, find the solution set for the given inequation, 1+9x≥x+81.

6 bells commence tolling together and toll at intervals 2, 4 ,6,8,10,12 respectively. After how many minutes they will toll together?

If one of the zeros of the polynomial 5x² + 13x + a is reciprocal of the other.Find the value of a.

Integrate tan x

a) Solve the inequation and represent the solution set on the number line. −3+x≤8x3+2≤143+2x,where xϵI b) Solve the given inequation and graph the solution on the number line 2y−3<y+1≤4y+7;yϵR [6 MARKS]