32581 + Interview Questions in Mathematics Page 148 InterviewSolution

7351.	Sonam and radha drive around a circular sports field.sonam takes 16 min to complete 1round while radha takes 20 min. If both started at same point and at same point, then after how much time they meet at the starting point.
Answer» Sonam and radha drive around a circular sports field.sonam takes 16 min to complete 1round while radha takes 20 min. If both started at same point and at same point, then after how much time they meet at the starting point.

Discussion

7352.	In the given figure, PA and PB are two tangents to the circle with centre O. If ∠ APB = 60o then find the measure of ∠ OAB.
Answer» In the given figure, PA and PB are two tangents to the circle with centre O. If $∠$ APB = $60^{o}$ then find the measure of $∠$ OAB.

7352.

In the given figure, PA and PB are two tangents to the circle with centre O. If ∠ APB = 60o then find the measure of ∠ OAB.

Answer»

In the given figure, PA and PB are two tangents to the circle with centre O. If $∠$ APB = $60^{o}$ then find the measure of $∠$ OAB.

Discussion

7353.	In a △ABC, right angled at B, AB + AC = 25 units, and BC = 5 units.What is sinC?
Answer» In a $△$ ABC, right angled at B, AB + AC = 25 units, and BC = 5 units. What is $sin C$ ?

Discussion

7354.	Question 1For some integer m, every even integer is of the formA) mB) m + 1C) 2mD) 2m + 1
Answer» Question 1 For some integer m, every even integer is of the form A) m B) m + 1 C) 2m D) 2m + 1

Discussion

7355.	if the coordinates of the midpoints of the side of the triangle are (4,-3),(-3,1),(3,-2) then the coordinates of the side of the triangle are
Answer» if the coordinates of the midpoints of the side of the triangle are (4,-3),(-3,1),(3,-2) then the coordinates of the side of the triangle are

Discussion

7356.	Fond the HCF of 65 and 117 and express it in the form 65n + 117n.
Answer» Fond the HCF of 65 and 117 and express it in the form 65n + 117n.

Discussion

7357.	In ABC ,Given that DE//BC , D is the midpoint of AB and E is a midpoint of AC. The ratio AE : EC is ____.
Answer» In ABC ,Given that DE//BC , D is the midpoint of AB and E is a midpoint of AC. The ratio AE : EC is ____.

7357.

In ABC ,Given that DE//BC , D is the midpoint of AB and E is a midpoint of AC. The ratio AE : EC is ____.

Answer»

In ABC ,Given that DE//BC , D is the midpoint of AB and E is a midpoint of AC. The ratio AE : EC is ____.

Discussion

7358.	If 2x^3 + ax^2 + bx - 6 has (x-1) as a factor and leaves a remainder 2 when divided by (x-2),find the relations between 'a' and 'b'.
Answer» If 2x^3 + ax^2 + bx - 6 has (x-1) as a factor and leaves a remainder 2 when divided by (x-2),find the relations between 'a' and 'b'.

Discussion

7359.	Show that for any set A and B, A=(A∩B)∪(A−B) and A∪(B−A)=(A∪B)
Answer» Show that for any set $A$ and $B, A = (A \cap B) \cup (A - B)$ and $A \cup (B - A) = (A \cup B)$

Discussion

7360.	2361 = ( 784 × Q ) + RFind the value of Q and R.
Answer» 2361 = ( 784 $\times$ Q ) + R Find the value of Q and R.

Discussion

7361.	A person eats a 100 g of rice and 100 g of flour in a day. He eats pulses equal to 13rd of the total quantity of rice and flour. What is the quantity of pulses eaten by him in 6 days?
Answer» A person eats a 100 g of rice and 100 g of flour in a day. He eats pulses equal to ${\frac{1}{3}}^{r d}$ of the total quantity of rice and flour. What is the quantity of pulses eaten by him in 6 days?

Discussion

7362.	In fig., PQ is parallel to MN. If KPPM=413 and KN = 20.4 cm. Find KQ [2 MARKS]
Answer» In fig., PQ is parallel to MN. If $\frac{K P}{P M} = \frac{4}{13}$ and KN = 20.4 cm. Find KQ [2 MARKS]

7362.

In fig., PQ is parallel to MN. If KPPM=413 and KN = 20.4 cm. Find KQ [2 MARKS]

Answer»

In fig., PQ is parallel to MN. If $\frac{K P}{P M} = \frac{4}{13}$ and KN = 20.4 cm. Find KQ [2 MARKS]

Discussion

7363.	The radii of the internal and external surfaces of a metallic spherical shell are 3 cm and 5 cm respectively. It is melted and recast into a solid right circular cylinder of height 1023 cm. Find the diameter of the base of the cylinder.
Answer» The radii of the internal and external surfaces of a metallic spherical shell are 3 cm and 5 cm respectively. It is melted and recast into a solid right circular cylinder of height $10 \frac{2}{3} c m$ . Find the diameter of the base of the cylinder.

Discussion

7364.	Question 1There are two cuboidal boxes as shown in the adjoining figure. Which box requires the lesser amount of material to make?
Answer» Question 1 There are two cuboidal boxes as shown in the adjoining figure. Which box requires the lesser amount of material to make?

Discussion

7365.	Question 8A vertical tower stands on a horizontal plane and is surmounted by a vertical flagstaff of height "h" units. At a point on the plane, the angles of elevation of the bottom and the top of the flagstaff are α and β respectively. Prove that the height of the tower is (h tan αtan β−tan α).
Answer» Question 8 A vertical tower stands on a horizontal plane and is surmounted by a vertical flagstaff of height "h" units. At a point on the plane, the angles of elevation of the bottom and the top of the flagstaff are $α$ and $β$ respectively. Prove that the height of the tower is $(\frac{h t a n α}{t a n β - t a n α})$ .

Discussion

7366.	If 2x – 3y + 1, x + y – 1 and 3x – y – 9 denote the three sides of an equilateral triangle. Find its perimeter.
Answer» If 2x – 3y + 1, x + y – 1 and 3x – y – 9 denote the three sides of an equilateral triangle. Find its perimeter.

7366.

If 2x – 3y + 1, x + y – 1 and 3x – y – 9 denote the three sides of an equilateral triangle. Find its perimeter.

Answer»

If 2x – 3y + 1, x + y – 1 and 3x – y – 9 denote the three sides of an equilateral triangle.

Find its perimeter.

Discussion

7367.	Which measure of central tendency will a shoe manufacturer make use of to determine the size(s) which he should manufacture in maximum quantity?
Answer» Which measure of central tendency will a shoe manufacturer make use of to determine the size(s) which he should manufacture in maximum quantity?

Discussion

7368.	P and Q are two points observed from the top of a building 10√3m high. If the angles of depression of the points are complementary, find the distance of two points from the building if PQ = 20m.
Answer» P and Q are two points observed from the top of a building 10√3m high. If the angles of depression of the points are complementary, find the distance of two points from the building if PQ = 20m.

Discussion

7369.	Solve the solution 14/x+3-1=3/x+1,x not equal -3,-1,for x.
Answer» Solve the solution 14/x+3-1=3/x+1,x not equal -3,-1,for x.

Discussion

7370.	Question 1 (iv)Find the roots of the quadratic equations by using the quadratic formula in the following question.−x2+7x−10=0
Answer» Question 1 (iv) Find the roots of the quadratic equations by using the quadratic formula in the following question. $- x^{2} + 7 x - 10 = 0$

7370.

Question 1 (iv)Find the roots of the quadratic equations by using the quadratic formula in the following question.−x2+7x−10=0

Answer»

Question 1 (iv)

Find the roots of the quadratic equations by using the quadratic formula in the following question.

$- x^{2} + 7 x - 10 = 0$

Discussion

7371.	Use Euclid’s division lemma to show that the cube of any positive integer is of the form9m, 9m + 1 or 9m + 8.
Answer» Use Euclid’s division lemma to show that the cube of any positive integer is of the form9m, 9m + 1 or 9m + 8.

Discussion

7372.	A circular field has a circumference 360 km. three cyclists start together and can cycle 48 , 60 and 72 km a day round the field when will they meet again.
Answer» A circular field has a circumference 360 km. three cyclists start together and can cycle 48 , 60 and 72 km a day round the field when will they meet again.

Discussion

7373.	In a Fig., D is a point on hypotenuse AC of triangle ABC , such that BD is perpendicular to AC, DM is perpendicular to BC and DN is perpendicular to AB. Prove that: (1). DM^2=DN\ast MC (2). DN^2=DM\ast AN
Answer» In a Fig., D is a point on hypotenuse AC of triangle ABC , such that BD is perpendicular to AC, DM is perpendicular to BC and DN is perpendicular to AB. Prove that: (1). DM^2=DN\ast MC (2). DN^2=DM\ast AN

Discussion

7374.	Adding 6 to numerator of a fraction , the numerator becomes twice the denominator. Write the equation(s) that represent the given statement.
Answer» Adding 6 to numerator of a fraction , the numerator becomes twice the denominator. Write the equation(s) that represent the given statement.

Discussion

7375.	Question 57State whether the following statement is True or False.A cylinder is a 3 - D shape having two circular faces of different radii.
Answer» Question 57 State whether the following statement is True or False. A cylinder is a 3 - D shape having two circular faces of different radii.

Discussion

7376.	The midpoint of the line joining the points (0,0) and (-8, -6) is
Answer» The midpoint of the line joining the points (0,0) and (-8, -6) is

Discussion

7377.	Find the HCF of 360 and 18144 by prime factorization.
Answer» Find the HCF of 360 and 18144 by prime factorization.

Discussion

7378.	If x=cotA+cosA and y=cotA-cosA, prove that x-yx+y2+x-y22=1.
Answer» If $x = cotA + cosA$ and $y = cotA - cosA$ , prove that ${(\frac{x - y}{x + y})}^{2} + {(\frac{x - y}{2})}^{2} = 1$ .

Discussion

7379.	The sequence of numbers 5, - 2, -9, -16, ... is
Answer» The sequence of numbers 5, - 2, -9, -16, ... is

Discussion

7380.	Find the sum of the first 24 terms of an AP whose nth term is given by tn=3+2n.
Answer» Find the sum of the first $24$ terms of an AP whose $n^{th}$ term is given by $t_{n} = 3 + 2 n .$

Discussion

7381.

Journalise the following transactions of Ram Delhi: 2018 ₹ Jan. 1 Ram commenced business with cash 30,000 Jan. 2 Open a bank account with Union Bank by cheque from saving account 21,000 Jan. 3 Purchased goods from Rahul in cash 10,000 Jan. 7 Withdrew cash from bank for office use 3,000 Jan. 10 Sold goods to Hari, Delhi on credit 5,000 Jan. 15 Purchased goods from Shyam, Meerut (UP) 15,000 Jan. 20 Cash sales 3,000 Jan. 25 Paid to Shyam 14,750 Discount Received 250 Jan. 31 Paid Salaries 10,000 CGST and SGST is levied 6% each on intra-state sale and purchase. IGST is levied 12% on inter-state sale and purchase.

Answer» Journalise the following transactions of Ram Delhi:

2018		₹
Jan. 1	Ram commenced business with cash	30,000
Jan. 2	Open a bank account with Union Bank by cheque from saving account	21,000
Jan. 3	Purchased goods from Rahul in cash	10,000
Jan. 7	Withdrew cash from bank for office use	3,000
Jan. 10	Sold goods to Hari, Delhi on credit	5,000
Jan. 15	Purchased goods from Shyam, Meerut (UP)	15,000
Jan. 20	Cash sales	3,000
Jan. 25	Paid to Shyam	14,750
	Discount Received	250
Jan. 31	Paid Salaries	10,000

CGST and SGST is levied 6% each on intra-state sale and purchase. IGST is levied 12% on inter-state sale and purchase.

Discussion

7382.	find the sum to n terms whose nth term is given by n(n+1)(n-1)
Answer» find the sum to n terms whose nth term is given by n(n+1)(n-1)

Discussion

7383.	Arun purchased a book costing Rs. 500. If rate of sales tax is 5% , then the amount paid by him is Rs.___
Answer» Arun purchased a book costing Rs. 500. If rate of sales tax is 5% , then the amount paid by him is Rs.___

Discussion

7384.	42. If a+b+c ≠ 0 ,then prove that a3+b3+c3=3abc,only when a = b = c.
Answer» 42. If a+b+c ≠ 0 ,then prove that a3+b3+c3=3abc,only when a = b = c.

Discussion

7385.	Three points on the ground form an equilateral triangle. There is a vertical pillar at point A. The angle of elevation of the top of the tower is 60 from the midpoint of bc and tetha from midpoint of ab.find tan tetha
Answer» Three points on the ground form an equilateral triangle. There is a vertical pillar at point A. The angle of elevation of the top of the tower is 60 from the midpoint of bc and tetha from midpoint of ab.find tan tetha

Discussion

7386.	Solve the following quadratic equations by factorization:10x-1x=3
Answer» Solve the following quadratic equations by factorization: $10 x - \frac{1}{x} = 3$

Discussion

7387.	In the given figure, if AP = 10 cm, then BP = (a) 91cm(b) 127cm(c) 119cm(d) 109cm
Answer» In the given figure, if AP = 10 cm, then BP = (a) $\sqrt{91} c m$ (b) $\sqrt{127} c m$ (c) $\sqrt{119} c m$ (d) $\sqrt{109} c m$

Discussion

7388.	A 1.8 m tall man is standing at some distance from a 31.8 m tall building. The angle of elevation from his eyes to the top of the building increases from 30∘ to 60∘ as he walks towards the building. Find the distance he walked towards the building.
Answer» A 1.8 m tall man is standing at some distance from a 31.8 m tall building. The angle of elevation from his eyes to the top of the building increases from $30^{\circ}$ to $60^{\circ}$ as he walks towards the building. Find the distance he walked towards the building.

Discussion

7389.	What is the ratio ABBC for the line segment AB following the construction method below? Step 1. A ray is extended from A and 30 arcs of equal lengths are cut, cutting the ray at A1,A2,...,A30 Step 2. A line is drawn from A30 to B and a line parallel to A30B is drawn, passing through the point A17.
Answer» What is the ratio $\frac{A B}{B C}$ for the line segment AB following the construction method below? Step 1. A ray is extended from A and 30 arcs of equal lengths are cut, cutting the ray at $A_{1}, A_{2}, . . ., A_{30}$ Step 2. A line is drawn from $A_{30}$ to $B$ and a line parallel to $A_{30} B$ is drawn, passing through the point $A_{17}$ .

Discussion

7390.	If a pool has to be constructed with a boundary of width 14 m consisting of two straight sections 120 m long joining semi-circular ends whose inner radius is 35 m. Then, the area of the boundary is
Answer» If a pool has to be constructed with a boundary of width 14 m consisting of two straight sections 120 m long joining semi-circular ends whose inner radius is 35 m. Then, the area of the boundary is

Discussion

7391.	∆MNT ~ ∆QRS. Length of altitude drawn from point T is 5 and length of altitude drawn from point S is 9. Find the ratio A∆MNTA∆QRS.
Answer» ∆MNT ~ ∆QRS. Length of altitude drawn from point T is 5 and length of altitude drawn from point S is 9. Find the ratio $\frac{A (∆ MNT)}{A (∆ QRS)}$ .

Discussion

7392.	There are two taps opening into a tank. If both are opened, the tank would be full in 12 minutes. The time taken for it to fill with only the small tap open, is 10 minutes more than the time to fill with only the large tap open. What is the time taken to fill the tank with only the small tap open?
Answer» There are two taps opening into a tank. If both are opened, the tank would be full in 12 minutes. The time taken for it to fill with only the small tap open, is 10 minutes more than the time to fill with only the large tap open. What is the time taken to fill the tank with only the small tap open?

Discussion

7393.	What is the algebraic sum of deviation of a frequency distribution about its mean?
Answer» What is the algebraic sum of deviation of a frequency distribution about its mean?

Discussion

7394.	If cos θ=34, then find the value of 9tan2 θ + 9.
Answer» If $\cos θ = \frac{3}{4}$ , then find the value of 9tan² θ + 9.

Discussion

7395.	Solve each of the following systems of equations graphically: 3x+2y=12,5x−2y=4.
Answer» Solve each of the following systems of equations graphically: $3 x + 2 y = 12, 5 x - 2 y = 4.$

7395.

Solve each of the following systems of equations graphically: 3x+2y=12,5x−2y=4.

Answer»

Solve each of the following systems of equations graphically:

$3 x + 2 y = 12, 5 x - 2 y = 4.$

Discussion

7396.	If (x−3) and (x−2) are two factors of the polynomial x3−6x2+11x−6,then find the third factor.
Answer» $If (x - 3) and (x - 2) are two factors of the polynomial x^{3} - 6 x^{2} + 11 x - 6, then find the third factor.$

Discussion

7397.	Question 8 Write ‘True’ or ‘False’ and justify your answer in the following An open metallic bucket is in the shape of a frustum of a cone, mounted on a hollow cylindrical base made of the same metallic sheet. The surface area of the metallic sheet used is equal to curved surface area of frustum of a cone + area of circular base + curved surface area of cylinder
Answer» Question 8 Write ‘True’ or ‘False’ and justify your answer in the following An open metallic bucket is in the shape of a frustum of a cone, mounted on a hollow cylindrical base made of the same metallic sheet. The surface area of the metallic sheet used is equal to curved surface area of frustum of a cone + area of circular base + curved surface area of cylinder

Discussion

7398.	What is the mean of 70, 75, 80, 85, and 90?
Answer» What is the mean of 70, 75, 80, 85, and 90?

Discussion

7399.	Question 1 (iii) Fill in the blanks in the following table, given that a is the first term, d the common difference and an the nth term of the A.P. adnan(iii)……−318−5
Answer» Question 1 (iii) Fill in the blanks in the following table, given that a is the first term, d the common difference and $a_{n}$ the $n^{t h}$ term of the A.P. $\begin{matrix} a & d & n & a_{n} (i i i) & \dots \dots & - 3 & 18 & - 5 \end{matrix}$

Discussion

7400.	Question 3To conduct Sports Day activities, in your rectangular shaped school ground ABCD, lines have been drawn with chalk powder at a distance of 1 m each. 100 flower pots have been placed at a distance of 1 m from each other along AD, as shown in the following figure. Niharika runs 14th the distance AD on the 2nd line and posts a green flag. Preet runs 15th the distance AD on the eighth line and posts a red flag. What is the distance between both the flags? If Rashmi has to post a blue flag exactly halfway between the line segment joining the two flags, where should she post her flag?
Answer» Question 3 To conduct Sports Day activities, in your rectangular shaped school ground ABCD, lines have been drawn with chalk powder at a distance of 1 m each. 100 flower pots have been placed at a distance of 1 m from each other along AD, as shown in the following figure. Niharika runs $\frac{1}{4}$ th the distance AD on the 2nd line and posts a green flag. Preet runs $\frac{1}{5}$ th the distance AD on the eighth line and posts a red flag. What is the distance between both the flags? If Rashmi has to post a blue flag exactly halfway between the line segment joining the two flags, where should she post her flag?

Discussion

Explore topic-wise InterviewSolutions in .

Sonam and radha drive around a circular sports field.sonam takes 16 min to complete 1round while radha takes 20 min. If both started at same point and at same point, then after how much time they meet at the starting point.

In the given figure, PA and PB are two tangents to the circle with centre O. If ∠ APB = 60o then find the measure of ∠ OAB.

In a △ABC, right angled at B, AB + AC = 25 units, and BC = 5 units.What is sinC?

Question 1For some integer m, every even integer is of the formA) mB) m + 1C) 2mD) 2m + 1

if the coordinates of the midpoints of the side of the triangle are (4,-3),(-3,1),(3,-2) then the coordinates of the side of the triangle are

Fond the HCF of 65 and 117 and express it in the form 65n + 117n.

In ABC ,Given that DE//BC , D is the midpoint of AB and E is a midpoint of AC. The ratio AE : EC is ____.

If 2x^3 + ax^2 + bx - 6 has (x-1) as a factor and leaves a remainder 2 when divided by (x-2),find the relations between 'a' and 'b'.

Show that for any set A and B, A=(A∩B)∪(A−B) and A∪(B−A)=(A∪B)

2361 = ( 784 × Q ) + RFind the value of Q and R.

A person eats a 100 g of rice and 100 g of flour in a day. He eats pulses equal to 13rd of the total quantity of rice and flour. What is the quantity of pulses eaten by him in 6 days?

In fig., PQ is parallel to MN. If KPPM=413 and KN = 20.4 cm. Find KQ [2 MARKS]

The radii of the internal and external surfaces of a metallic spherical shell are 3 cm and 5 cm respectively. It is melted and recast into a solid right circular cylinder of height 1023 cm. Find the diameter of the base of the cylinder.

Question 1There are two cuboidal boxes as shown in the adjoining figure. Which box requires the lesser amount of material to make?

If 2x – 3y + 1, x + y – 1 and 3x – y – 9 denote the three sides of an equilateral triangle. Find its perimeter.

Which measure of central tendency will a shoe manufacturer make use of to determine the size(s) which he should manufacture in maximum quantity?

P and Q are two points observed from the top of a building 10√3m high. If the angles of depression of the points are complementary, find the distance of two points from the building if PQ = 20m.

Solve the solution 14/x+3-1=3/x+1,x not equal -3,-1,for x.

Question 1 (iv)Find the roots of the quadratic equations by using the quadratic formula in the following question.−x2+7x−10=0

Use Euclid’s division lemma to show that the cube of any positive integer is of the form9m, 9m + 1 or 9m + 8.

A circular field has a circumference 360 km. three cyclists start together and can cycle 48 , 60 and 72 km a day round the field when will they meet again.

In a Fig., D is a point on hypotenuse AC of triangle ABC , such that BD is perpendicular to AC, DM is perpendicular to BC and DN is perpendicular to AB. Prove that: (1). DM^2=DN\ast MC (2). DN^2=DM\ast AN

Adding 6 to numerator of a fraction , the numerator becomes twice the denominator. Write the equation(s) that represent the given statement.

Question 57State whether the following statement is True or False.A cylinder is a 3 - D shape having two circular faces of different radii.

The midpoint of the line joining the points (0,0) and (-8, -6) is

Find the HCF of 360 and 18144 by prime factorization.

If x=cotA+cosA and y=cotA-cosA, prove that x-yx+y2+x-y22=1.

The sequence of numbers 5, - 2, -9, -16, ... is

Find the sum of the first 24 terms of an AP whose nth term is given by tn=3+2n.

find the sum to n terms whose nth term is given by n(n+1)(n-1)

Arun purchased a book costing Rs. 500. If rate of sales tax is 5% , then the amount paid by him is Rs.___

42. If a+b+c ≠ 0 ,then prove that a3+b3+c3=3abc,only when a = b = c.

Three points on the ground form an equilateral triangle. There is a vertical pillar at point A. The angle of elevation of the top of the tower is 60 from the midpoint of bc and tetha from midpoint of ab.find tan tetha

Solve the following quadratic equations by factorization:10x-1x=3

In the given figure, if AP = 10 cm, then BP = (a) 91cm(b) 127cm(c) 119cm(d) 109cm

A 1.8 m tall man is standing at some distance from a 31.8 m tall building. The angle of elevation from his eyes to the top of the building increases from 30∘ to 60∘ as he walks towards the building. Find the distance he walked towards the building.

What is the ratio ABBC for the line segment AB following the construction method below? Step 1. A ray is extended from A and 30 arcs of equal lengths are cut, cutting the ray at A1,A2,...,A30 Step 2. A line is drawn from A30 to B and a line parallel to A30B is drawn, passing through the point A17.

If a pool has to be constructed with a boundary of width 14 m consisting of two straight sections 120 m long joining semi-circular ends whose inner radius is 35 m. Then, the area of the boundary is

∆MNT ~ ∆QRS. Length of altitude drawn from point T is 5 and length of altitude drawn from point S is 9. Find the ratio A∆MNTA∆QRS.

There are two taps opening into a tank. If both are opened, the tank would be full in 12 minutes. The time taken for it to fill with only the small tap open, is 10 minutes more than the time to fill with only the large tap open. What is the time taken to fill the tank with only the small tap open?

What is the algebraic sum of deviation of a frequency distribution about its mean?

If cos θ=34, then find the value of 9tan2 θ + 9.

Solve each of the following systems of equations graphically: 3x+2y=12,5x−2y=4.

If (x−3) and (x−2) are two factors of the polynomial x3−6x2+11x−6,then find the third factor.

What is the mean of 70, 75, 80, 85, and 90?

Question 1 (iii) Fill in the blanks in the following table, given that a is the first term, d the common difference and an the nth term of the A.P. adnan(iii)……−318−5