32581 + Interview Questions in Mathematics Page 203 InterviewSolution

10101.	Solve the quadratic equations(1) x2 + 15x + 50 = 0(2) a2 − 5a + 6 = 0(3) y2 = y + 2(4) 6 − p2 = p(5) 30 = b2 − b(6) 2x2 = 5x − 12 = 0(7) 6y2 + y − 15 = 0(8) 6a2 + a = 5(9) 13m = 6(m2 + 1)(10) 0.2t2 − 0.04t = 0.03
Answer» Solve the quadratic equations (1) x² + 15x + 50 = 0 (2) a² − 5a + 6 = 0 (3) y² = y + 2 (4) 6 − p² = p (5) 30 = b² − b (6) 2x² = 5x − 12 = 0 (7) 6y² + y − 15 = 0 (8) 6a² + a = 5 (9) 13m = 6(m² + 1) (10) 0.2t² − 0.04t = 0.03

10101.

Solve the quadratic equations(1) x2 + 15x + 50 = 0(2) a2 − 5a + 6 = 0(3) y2 = y + 2(4) 6 − p2 = p(5) 30 = b2 − b(6) 2x2 = 5x − 12 = 0(7) 6y2 + y − 15 = 0(8) 6a2 + a = 5(9) 13m = 6(m2 + 1)(10) 0.2t2 − 0.04t = 0.03

Answer»

Solve the quadratic equations

(1) x² + 15x + 50 = 0

(2) a² − 5a + 6 = 0

(3) y² = y + 2

(4) 6 − p² = p

(5) 30 = b² − b

(6) 2x² = 5x − 12 = 0

(7) 6y² + y − 15 = 0

(8) 6a² + a = 5

(9) 13m = 6(m² + 1)

(10) 0.2t² − 0.04t = 0.03

Discussion

10102.	Question 22On dividing 57p2qr by 114pq, we geta) 14prb) 34prc) 12prd) 2pr
Answer» Question 22 On dividing $57 p^{2} q r$ by $114 p q$ , we get a) $\frac{1}{4} p r$ b) $\frac{3}{4} p r$ c) $\frac{1}{2} p r$ d) $2 p r$

Discussion

10103.	101.show that tan3x.tan2x.tanx=tan3x-tan2x-tanx
Answer» 101.show that tan3x.tan2x.tanx=tan3x-tan2x-tanx

Discussion

10104.	If 3 numbers a,b,c are in G.P., then loga,logb,logc are in:
Answer» If 3 numbers a,b,c are in G.P., then $l o g a, l o g b, l o g c$ are in:

Discussion

10105.	sin(theta), cos(theta) etc are simply a ratio. and a ratio is constant, then why differentiation of these trigonometric ratios are not zero?
Answer» sin(theta), cos(theta) etc are simply a ratio. and a ratio is constant, then why differentiation of these trigonometric ratios are not zero?

Discussion

10106.	What is finite and infinite arithmetic progression?
Answer» What is finite and infinite arithmetic progression?

Discussion

10107.	If the point P(p, q) is equidistant from the points A(a+b, b-a) and B(a-b, a+b), then
Answer» If the point P(p, q) is equidistant from the points A(a+b, b-a) and B(a-b, a+b), then

Discussion

10108.	The angle between two vectors a→ and b→ with magnitudes 3 and 4 respectively and a→·b→=23, is(a) π6 (b) π3 (c) π2 (d) 5π2
Answer» The angle between two vectors $\vec{a} and \vec{b}$ with magnitudes $\sqrt{3}$ and 4 respectively and $\vec{a} \cdot \vec{b} = 2 \sqrt{3}, is$ $(a) \frac{π}{6} (b) \frac{π}{3} (c) \frac{π}{2} (d) \frac{5 π}{2}$

Discussion

10109.	Determine the number nearest to 110000 but greater than 100000 which is exactly divisible by each of 8,15 and 21
Answer» Determine the number nearest to 110000 but greater than 100000 which is exactly divisible by each of 8,15 and 21

Discussion

10110.	Two cars starf simultaneously from the same place and in same direction . The first car moves with a uniform speed of 10 km/h . The second car moves at a speed of 8km/hr in the first hour and then increases its speed by 0.5 km/hr in each succeeding hour . If both the cars move non stop , then how long will it take for the second car to overtake?
Answer» Two cars starf simultaneously from the same place and in same direction . The first car moves with a uniform speed of 10 km/h . The second car moves at a speed of 8km/hr in the first hour and then increases its speed by 0.5 km/hr in each succeeding hour . If both the cars move non stop , then how long will it take for the second car to overtake?

Discussion

10111.	Question 10A solid piece of iron in the form of a cuboid of dimensions 49cm×33cm×24cm, is moulded to form a solid sphere. Then, radius of the sphere is(A) 21 cm(B) 23 cm(C) 25 cm(D) 19 cm
Answer» Question 10 A solid piece of iron in the form of a cuboid of dimensions $49 c m \times 33 c m \times 24 c m$ , is moulded to form a solid sphere. Then, radius of the sphere is (A) 21 cm (B) 23 cm (C) 25 cm (D) 19 cm

Discussion

10112.	Question 62 The cost of a book marked at Rs 190 after paying a sales tax of 2% is Rs. 192.
Answer» Question 62 The cost of a book marked at Rs 190 after paying a sales tax of 2% is Rs. 192.

10112.

Question 62 The cost of a book marked at Rs 190 after paying a sales tax of 2% is Rs. 192.

Answer»

Question 62

The cost of a book marked at Rs 190 after paying a sales tax of 2% is Rs. 192.

Discussion

10113.	Determine whether the triangle having sides (a-1) cm, 2√a cm and (a+1)cm is a right angled triangle.
Answer» Determine whether the triangle having sides (a-1) cm, $2 \sqrt{a}$ cm and (a+1)cm is a right angled triangle.

Discussion

10114.	9. Let a and b be natural numbers such that 2a - b, a - 2b, a + b are all distinct squares. What is the smallest possible value of b
Answer» 9. Let a and b be natural numbers such that 2a - b, a - 2b, a + b are all distinct squares. What is the smallest possible value of b

Discussion

10115.	Find the roots of the given equation, if they exist, by applying the quadratic formula: 3a2x2+8abx+4b2=0,a≠0
Answer» Find the roots of the given equation, if they exist, by applying the quadratic formula: $3 a^{2} x^{2} + 8 a b x + 4 b^{2} = 0, a \neq 0$

Discussion

10116.	Question 14Prove that √p+√q is irrational, where p and q are primes.
Answer» Question 14 Prove that $\sqrt{p} + \sqrt{q}$ is irrational, where p and q are primes.

Discussion

10117.	Ms. Rana goes for shopping to buy a leather coat which costs ₹ 735. The rate of sales tax is 5%. She tells the shopkeeper to reduce the price to such an extent that she has to pay ₹ 735, inclusive of sales tax. Find the reduction needed at the price of the coat.
Answer» Ms. Rana goes for shopping to buy a leather coat which costs ₹ 735. The rate of sales tax is 5%. She tells the shopkeeper to reduce the price to such an extent that she has to pay ₹ 735, inclusive of sales tax. Find the reduction needed at the price of the coat.

Discussion

10118.	If the lines given by 3x + 2ky = 2 and 3x + 5y = 1 are parallel, then find the value of 'k'.
Answer» If the lines given by 3x + 2ky = 2 and 3x + 5y = 1 are parallel, then find the value of 'k'.

Discussion

10119.	20. Two circles of radius r and R touch each other externally then the radius of circle which touches both of them externally and also their direct common tangent is
Answer» 20. Two circles of radius r and R touch each other externally then the radius of circle which touches both of them externally and also their direct common tangent is

Discussion

10120.	From the top of a 7m high building, the angle of elevation of top of the cable tower is 60° and the angle of depression of it's foot is 45°. Determine the height of the tower.
Answer» From the top of a 7m high building, the angle of elevation of top of the cable tower is 60° and the angle of depression of it's foot is 45°. Determine the height of the tower.

Discussion

10121.	Which term of the sequence –1, 3, 7, 11, ..... , is 95 ?
Answer» Which term of the sequence –1, 3, 7, 11, ..... , is 95 ?

Discussion

10122.	In the given figure, ∠CAB=90o and AD⊥BC. Show that ΔBDA∼ΔBAC. If AC = 75 cm, AB = 1 m and BC = 1.25 m, find AD.
Answer» In the given figure, $∠ C A B = 90^{o}$ and $A D ⊥ B C$ . Show that $Δ B D A \sim Δ B A C$ . If AC = 75 cm, AB = 1 m and BC = 1.25 m, find AD.

Discussion

10123.	How to use natural tangents tables?
Answer» How to use natural tangents tables?

Discussion

10124.	If x=3+12, find the value of 4x3+2x2-8x+7.
Answer» If $x = \frac{\sqrt{3} + 1}{2},$ find the value of $4 x^{3} + 2 x^{2} - 8 x + 7$ .

Discussion

10125.	What is the probability that a non-leap year has 53 Sundays?(a) 67(b) 17(c) 57(d) None of these
Answer» What is the probability that a non-leap year has 53 Sundays? (a) $\frac{6}{7}$ (b) $\frac{1}{7}$ (c) $\frac{5}{7}$ (d) None of these

Discussion

10126.	If (a,b) is the mid-point of the line segment joining the points A (10, -6) , B (k,4) and a-2b = 18 , find the value of k and the distance AB.
Answer» If (a,b) is the mid-point of the line segment joining the points A (10, $-$ 6) , B (k,4) and a $-$ 2b = 18 , find the value of k and the distance AB.

Discussion

10127.	The length of rectangular field is 3 times its breadth. If the area of the field is 147 sq. m. find its length.
Answer» The length of rectangular field is 3 times its breadth. If the area of the field is 147 sq. m. find its length.

Discussion

10128.	Question 12A triangle ABC is drawn to circumscribe a circle of radius 4 cm such that the tangents BD and DC into which BC is divided by the point of contact D are of lengths 8 cm and 6 cm respectively. Find the sides AB and AC.
Answer» Question 12 A triangle ABC is drawn to circumscribe a circle of radius 4 cm such that the tangents BD and DC into which BC is divided by the point of contact D are of lengths 8 cm and 6 cm respectively. Find the sides AB and AC.

Discussion

10129.	Find the area of the region bounded by the following two circles:x²+y²=4(x-2)²+y²=4
Answer» Find the area of the region bounded by the following two circles: x²+y²=4 (x-2)²+y²=4

Discussion

10130.	Find the number of terms in the following AP: 18,312,13,...−47
Answer» Find the number of terms in the following AP: $18, \frac{31}{2}, 13, . . . - 47$

Discussion

10131.	A sum of Rs. 1400 is to be used to give seven cash prizes to students of a school for their overall academic performance. If each prize is Rs. 40 less than the preceding price, find the value of each of the prizes.
Answer» A sum of Rs. 1400 is to be used to give seven cash prizes to students of a school for their overall academic performance. If each prize is Rs. 40 less than the preceding price, find the value of each of the prizes.

Discussion

10132.	the hypotenuse of a right angled triangle is 3√5 cm if the smaller side is tripled and the larger side is doubled the new hypotenuse becomes 15 cm find the length of each side of triangle
Answer» the hypotenuse of a right angled triangle is 3√5 cm if the smaller side is tripled and the larger side is doubled the new hypotenuse becomes 15 cm find the length of each side of triangle

Discussion

10133.	x+7y=10 ; 3x - 2y =7
Answer» x+7y=10 ; 3x - 2y =7

Discussion

10134.	When the list price of a book is increased by Rs. 10, a person can buy 10 books less for Rs. 1200. The original price of the book was ______.
Answer» When the list price of a book is increased by Rs. 10, a person can buy 10 books less for Rs. 1200. The original price of the book was ______.

Discussion

10135.	Find the cardial number of A×B, such that A = {1, 2, 3} and B = {a, b}.6
Answer» Find the cardial number of $A \times B$ , such that A = {1, 2, 3} and B = {a, b}. 6

Discussion

10136.

On a dart board of radius 50 cm, what is the probability that you hit the bull's eye of radius 5 cm?

Answer»

On a dart board of radius 50 cm, what is the probability that you hit the bull's eye of radius 5 cm?

Discussion

10137.	On 1st April, 2018, A, B and C commenced business in partnership sharing profits and losses in proportion of 1/2, 1/3 and 1/6 respectively. They paid into their Bank A/c as their capitals ₹ 22,000; ₹ 10,000 by A, ₹ 7,000 by B and ₹ 5,000 by C. During the year, they drew ₹ 5,000; being ₹ 1,900 by A, ₹ 1,700 by B and ₹ 1,400 by C.On 31st March, 2019, they dissolved their partnership, A taking up Stock at an agreed valuation of ₹ 5,000, B taking up Furniture at ₹ 2,000 and C taking up Debtors at ₹ 3,000. After paying up their Creditors, there remained a balance of ₹ 1,000 at Bank. Prepare necessary accounts showing the distribution of the cash at the Bank and of the further cash brought in by any partner or partners as the case required.
Answer» On 1st April, 2018, A, B and C commenced business in partnership sharing profits and losses in proportion of 1/2, 1/3 and 1/6 respectively. They paid into their Bank A/c as their capitals ₹ 22,000; ₹ 10,000 by A, ₹ 7,000 by B and ₹ 5,000 by C. During the year, they drew ₹ 5,000; being ₹ 1,900 by A, ₹ 1,700 by B and ₹ 1,400 by C. On 31st March, 2019, they dissolved their partnership, A taking up Stock at an agreed valuation of ₹ 5,000, B taking up Furniture at ₹ 2,000 and C taking up Debtors at ₹ 3,000. After paying up their Creditors, there remained a balance of ₹ 1,000 at Bank. Prepare necessary accounts showing the distribution of the cash at the Bank and of the further cash brought in by any partner or partners as the case required.

Discussion

10138.	Question 4 The number of polynomials having zeroes as –2 and 5 is (A) 1 (B) 2 (C) 3 (D) more than 3
Answer» Question 4 The number of polynomials having zeroes as –2 and 5 is (A) 1 (B) 2 (C) 3 (D) more than 3

Discussion

10139.	Fill in the blank with a modal auxiliary showing certainty. If computers are used in poorly lit places, users ____ suffer from headaches.
Answer» Fill in the blank with a modal auxiliary showing certainty. If computers are used in poorly lit places, users ____ suffer from headaches.

10139.

Fill in the blank with a modal auxiliary showing certainty. If computers are used in poorly lit places, users ____ suffer from headaches.

Answer»

Fill in the blank with a modal auxiliary showing certainty.

If computers are used in poorly lit places, users ____ suffer from headaches.

Discussion

10140.	A chord AB of a circle is equal to the radius of the circle. Find the angles subtended by the chord at points on the major arc and the minor arc, respectively.
Answer» A chord AB of a circle is equal to the radius of the circle. Find the angles subtended by the chord at points on the major arc and the minor arc, respectively.

Discussion

10141.	zeroes of x2−32x−68 are
Answer» zeroes of $x^{2} - 32 x - 68$ are

Discussion

10142.	The sum of first 16 terms of the AP 10, 6, 2, ... is (a) 320 (b) -320 (c) -352 (d) -400
Answer» The sum of first 16 terms of the AP 10, 6, 2, ... is (a) 320 (b) -320 (c) -352 (d) -400

Discussion

10143.	A cone, a hemisphere and a cylinder stand on equal bases and have the same height. What is the ratio of their volumes?
Answer» A cone, a hemisphere and a cylinder stand on equal bases and have the same height. What is the ratio of their volumes?

Discussion

10144.	If tanA =5/12 the value of (sinA+cosA)swcA
Answer» If tanA =5/12 the value of (sinA+cosA)swcA

Discussion

10145.	Question 6 Prove that a triangle must have atleast two acute angles.
Answer» Question 6 Prove that a triangle must have atleast two acute angles.

Discussion

10146.	Which of the following measures of central tendency is influenced by extreme values?(a) Mean(b) Median(c) Mode(d) None of these
Answer» Which of the following measures of central tendency is influenced by extreme values? (a) Mean (b) Median (c) Mode (d) None of these

Discussion

10147.	If the third term of a G.P. is 4 then find the product of its first 5 terms.
Answer» If the third term of a G.P. is 4 then find the product of its first 5 terms.

Discussion

10148.	Ramkali saved Rs.5 in the first week of a year and then increased her weekly saving by Rs.1.75. If in the nth week, her weekly savings become Rs.20.75, find n.
Answer» Ramkali saved $R s . 5$ in the first week of a year and then increased her weekly saving by $R s . 1.75$ . If in the $n^{t h}$ week, her weekly savings become $R s . 20.75$ , find $n$ .

Discussion

10149.	Choose the correct answer in each of the following questions:The common difference of the AP 1p,1-pp,1-2pp,... is [CBSE 2013](a) p (b) −p (c) −1 (d) 1
Answer» Choose the correct answer in each of the following questions: The common difference of the AP $\frac{1}{p}, \frac{1 - p}{p}, \frac{1 - 2 p}{p}, . . .$ is [CBSE 2013] (a) p (b) −p (c) −1 (d) 1

Discussion

10150.	How many litres of water would flow out of a pipe having an area of cross-section of 5cm2 in one minute, if the speed of water in the pipe is 30 cm/ sec?
Answer» How many litres of water would flow out of a pipe having an area of cross-section of $5 c m^{2}$ in one minute, if the speed of water in the pipe is 30 cm/ sec?

Discussion

Explore topic-wise InterviewSolutions in .

Solve the quadratic equations(1) x2 + 15x + 50 = 0(2) a2 − 5a + 6 = 0(3) y2 = y + 2(4) 6 − p2 = p(5) 30 = b2 − b(6) 2x2 = 5x − 12 = 0(7) 6y2 + y − 15 = 0(8) 6a2 + a = 5(9) 13m = 6(m2 + 1)(10) 0.2t2 − 0.04t = 0.03

Question 22On dividing 57p2qr by 114pq, we geta) 14prb) 34prc) 12prd) 2pr

101.show that tan3x.tan2x.tanx=tan3x-tan2x-tanx

If 3 numbers a,b,c are in G.P., then loga,logb,logc are in:

sin(theta), cos(theta) etc are simply a ratio. and a ratio is constant, then why differentiation of these trigonometric ratios are not zero?

What is finite and infinite arithmetic progression?

If the point P(p, q) is equidistant from the points A(a+b, b-a) and B(a-b, a+b), then

The angle between two vectors a→ and b→ with magnitudes 3 and 4 respectively and a→·b→=23, is(a) π6 (b) π3 (c) π2 (d) 5π2

Determine the number nearest to 110000 but greater than 100000 which is exactly divisible by each of 8,15 and 21

Question 10A solid piece of iron in the form of a cuboid of dimensions 49cm×33cm×24cm, is moulded to form a solid sphere. Then, radius of the sphere is(A) 21 cm(B) 23 cm(C) 25 cm(D) 19 cm

Question 62 The cost of a book marked at Rs 190 after paying a sales tax of 2% is Rs. 192.

Determine whether the triangle having sides (a-1) cm, 2√a cm and (a+1)cm is a right angled triangle.

9. Let a and b be natural numbers such that 2a - b, a - 2b, a + b are all distinct squares. What is the smallest possible value of b

Find the roots of the given equation, if they exist, by applying the quadratic formula: 3a2x2+8abx+4b2=0,a≠0

Question 14Prove that √p+√q is irrational, where p and q are primes.

Ms. Rana goes for shopping to buy a leather coat which costs ₹ 735. The rate of sales tax is 5%. She tells the shopkeeper to reduce the price to such an extent that she has to pay ₹ 735, inclusive of sales tax. Find the reduction needed at the price of the coat.

If the lines given by 3x + 2ky = 2 and 3x + 5y = 1 are parallel, then find the value of 'k'.

20. Two circles of radius r and R touch each other externally then the radius of circle which touches both of them externally and also their direct common tangent is

From the top of a 7m high building, the angle of elevation of top of the cable tower is 60° and the angle of depression of it's foot is 45°. Determine the height of the tower.

Which term of the sequence –1, 3, 7, 11, ..... , is 95 ?

In the given figure, ∠CAB=90o and AD⊥BC. Show that ΔBDA∼ΔBAC. If AC = 75 cm, AB = 1 m and BC = 1.25 m, find AD.

How to use natural tangents tables?

If x=3+12, find the value of 4x3+2x2-8x+7.

What is the probability that a non-leap year has 53 Sundays?(a) 67(b) 17(c) 57(d) None of these

If (a,b) is the mid-point of the line segment joining the points A (10, -6) , B (k,4) and a-2b = 18 , find the value of k and the distance AB.

The length of rectangular field is 3 times its breadth. If the area of the field is 147 sq. m. find its length.

Question 12A triangle ABC is drawn to circumscribe a circle of radius 4 cm such that the tangents BD and DC into which BC is divided by the point of contact D are of lengths 8 cm and 6 cm respectively. Find the sides AB and AC.

Find the area of the region bounded by the following two circles:x²+y²=4(x-2)²+y²=4

Find the number of terms in the following AP: 18,312,13,...−47

A sum of Rs. 1400 is to be used to give seven cash prizes to students of a school for their overall academic performance. If each prize is Rs. 40 less than the preceding price, find the value of each of the prizes.

the hypotenuse of a right angled triangle is 3√5 cm if the smaller side is tripled and the larger side is doubled the new hypotenuse becomes 15 cm find the length of each side of triangle

x+7y=10 ; 3x - 2y =7

When the list price of a book is increased by Rs. 10, a person can buy 10 books less for Rs. 1200. The original price of the book was ______.

Find the cardial number of A×B, such that A = {1, 2, 3} and B = {a, b}.6

On a dart board of radius 50 cm, what is the probability that you hit the bull's eye of radius 5 cm?

Question 4 The number of polynomials having zeroes as –2 and 5 is (A) 1 (B) 2 (C) 3 (D) more than 3

Fill in the blank with a modal auxiliary showing certainty. If computers are used in poorly lit places, users ____ suffer from headaches.

A chord AB of a circle is equal to the radius of the circle. Find the angles subtended by the chord at points on the major arc and the minor arc, respectively.

zeroes of x2−32x−68 are

The sum of first 16 terms of the AP 10, 6, 2, ... is (a) 320 (b) -320 (c) -352 (d) -400

A cone, a hemisphere and a cylinder stand on equal bases and have the same height. What is the ratio of their volumes?

If tanA =5/12 the value of (sinA+cosA)swcA

Question 6 Prove that a triangle must have atleast two acute angles.

Which of the following measures of central tendency is influenced by extreme values?(a) Mean(b) Median(c) Mode(d) None of these

If the third term of a G.P. is 4 then find the product of its first 5 terms.

Ramkali saved Rs.5 in the first week of a year and then increased her weekly saving by Rs.1.75. If in the nth week, her weekly savings become Rs.20.75, find n.

Choose the correct answer in each of the following questions:The common difference of the AP 1p,1-pp,1-2pp,... is [CBSE 2013](a) p (b) −p (c) −1 (d) 1

How many litres of water would flow out of a pipe having an area of cross-section of 5cm2 in one minute, if the speed of water in the pipe is 30 cm/ sec?