32581 + Interview Questions in Mathematics Page 193 InterviewSolution

9601.	Find the length of AD, if BD= 3.6 cm and DC = 6.4 cm.
Answer» Find the length of AD, if BD= 3.6 cm and DC = 6.4 cm.

Discussion

9602.	if x^2- 5x+1=0,then find the value of x^5+1/x^5
Answer» if x^2- 5x+1=0,then find the value of x^5+1/x^5

Discussion

9603.	Question 21 (ii)Find the sum:(4−1n)+(4−2n)+(4−3n)+⋯upto n terms
Answer» Question 21 (ii) Find the sum: $(4 - \frac{1}{n}) + (4 - \frac{2}{n}) + (4 - \frac{3}{n}) + \dots u p t o n t e r m s$

Discussion

9604.	From a point on the ground, the angles of elevation of the bottom and the top of a transmission tower which is fixed at the top of a 30 m high building are 45∘ and 60∘ respectively. Find the height of the tower.
Answer» From a point on the ground, the angles of elevation of the bottom and the top of a transmission tower which is fixed at the top of a 30 m high building are $45^{\circ}$ and $60^{\circ}$ respectively. Find the height of the tower.

Discussion

9605.	What are complex numbers?
Answer» What are complex numbers?

Discussion

9606.	Show that (a − b)2, (a2 + b2) and (a + b)2 are in A.P.
Answer» Show that (a − b)², (a² + b²) and (a + b)² are in A.P.

Discussion

9607.	The nth term of an AP is (7 - 4n). Find its common difference.
Answer» The nth term of an AP is (7 - 4n). Find its common difference.

Discussion

9608.	If →a,→b,→c are non collinear coplanar vectors represents −−→BC,−−→CA,−−→AB respectively, then which of the following is TRUE
Answer» If $\to a, \to b, \to c$ are non collinear coplanar vectors represents $- - \to B C, - - \to C A, - - \to A B$ respectively, then which of the following is TRUE

Discussion

9609.	Slow & Steady Ltd. invited applications for 10,000 Equity Shares of ₹ 10 each for public subscription. The amount of these shares was payable as:On application ₹ 1 per share, on allotment ₹ 2 per share, on first call ₹ 3 per share and on second and final call ₹ 4 per share.All sums payable on application, allotment and calls were duly received with the following exceptions: (i) A, who held 200 shares, failed to pay the money on allotments and calls.(ii) B, to whom 150 shares were allotted, failed to pay the money on first call and final call.(iii) C, who held 50 shares, did not pay the amount of second and final call.The shares of A, B and C were forfeited and were subsequently reissued for cash as fully paid-up at a discount of 5%.Pass necessary Journal entries to record these transactions in the books of X Ltd.
Answer» Slow & Steady Ltd. invited applications for 10,000 Equity Shares of ₹ 10 each for public subscription. The amount of these shares was payable as: On application ₹ 1 per share, on allotment ₹ 2 per share, on first call ₹ 3 per share and on second and final call ₹ 4 per share. All sums payable on application, allotment and calls were duly received with the following exceptions: (i) A, who held 200 shares, failed to pay the money on allotments and calls. (ii) B, to whom 150 shares were allotted, failed to pay the money on first call and final call. (iii) C, who held 50 shares, did not pay the amount of second and final call. The shares of A, B and C were forfeited and were subsequently reissued for cash as fully paid-up at a discount of 5%. Pass necessary Journal entries to record these transactions in the books of X Ltd.

Discussion

9610.	Number of points of discontinuity in [14cosx] and [14sinx] where [] is GIF
Answer» Number of points of discontinuity in [14cosx] and [14sinx] where [] is GIF

Discussion

9611.	A positive integer is of the form 3q + 1, q being a natural number. Can you write its square in any form other than 3m + 1, 3m or 3m + 2 for some integer m? Justify your answer.
Answer» A positive integer is of the form 3q + 1, q being a natural number. Can you write its square in any form other than 3m + 1, 3m or 3m + 2 for some integer m? Justify your answer.

Discussion

9612.

The mean of the following frequency distribution is 62.8 and the sum of all the frequencies is 50. Compute the missing frequency f1 and f2. Class: 0−20 20−40 40−60 60−80 80−100 100−120 Frequency: 5 f1 10 f2 7 9

Answer» The mean of the following frequency distribution is 62.8 and the sum of all the frequencies is 50. Compute the missing frequency f₁ and f₂.

Class:	0−20	20−40	40−60	60−80	80−100	100−120
Frequency:	5	f₁	10	f₂	7	9

Discussion

9613.	The LCM of (x−3)2(x+4) and (x−3)(x+4)2 is:
Answer» $The LCM of (x - 3)^{2} (x + 4) and (x - 3) (x + 4)^{2} is :$

Discussion

9614.	9^n-8n-1 is divisible by 64 is (1) Always true (2)Always false (3)Always true for rational values of n (4)Always true for irrational values of n
Answer» 9^n-8n-1 is divisible by 64 is (1) Always true (2)Always false (3)Always true for rational values of n (4)Always true for irrational values of n

Discussion

9615.	A flag pole 18 m high casts a shadow 9.6 cm long. The distance of the top of the pole from the far end of the shadow is _________.
Answer» A flag pole 18 m high casts a shadow 9.6 cm long. The distance of the top of the pole from the far end of the shadow is _________.

Discussion

9616.	In ∆ABC, AD and BE are altitude. Prove that ar∆DECar∆ABC=DC2AC2.
Answer» In ∆ABC, AD and BE are altitude. Prove that $\frac{ar (∆ DEC)}{ar (∆ ABC)} = \frac{{DC}^{2}}{{AC}^{2}}$ .

Discussion

9617.	Calculate the Mean of the given distribution, using Assumed mean Method.MarksNo. of Students10−20220−30630−401040−501250−60960−70870−80480−90348.89
Answer» Calculate the Mean of the given distribution, using Assumed mean Method. $\begin{matrix} Marks & No. of Students 10 - 20 & 2 20 - 30 & 6 30 - 40 & 10 40 - 50 & 12 50 - 60 & 9 60 - 70 & 8 70 - 80 & 4 80 - 90 & 3 \end{matrix}$ 48.89

9617.

Calculate the Mean of the given distribution, using Assumed mean Method.MarksNo. of Students10−20220−30630−401040−501250−60960−70870−80480−90348.89

Answer»

Calculate the Mean of the given distribution, using Assumed mean Method.

$\begin{matrix} Marks & No. of Students 10 - 20 & 2 20 - 30 & 6 30 - 40 & 10 40 - 50 & 12 50 - 60 & 9 60 - 70 & 8 70 - 80 & 4 80 - 90 & 3 \end{matrix}$

48.89

Discussion

9618.	Question 12AB and AC are two chords of a circle of radius r such that AB = 2AC. If p an q are the distances of AB an AC from the centre, prove that 4q2=p2+3r2.
Answer» Question 12 AB and AC are two chords of a circle of radius r such that AB = 2AC. If p an q are the distances of AB an AC from the centre, prove that $4 q^{2} = p^{2} + 3 r^{2}$ .

Discussion

9619.	Find the area of the sector whose arc is making an angle of 60∘ at the center of a circle of radius 3.2 cm. What will be the area of the balance sector? [3 MARKS]
Answer» Find the area of the sector whose arc is making an angle of $60^{\circ}$ at the center of a circle of radius 3.2 cm. What will be the area of the balance sector? [3 MARKS]

Discussion

9620.	Construct a ∆ABC in which ∠B = 45°, ∠C = 60° and the perpendicular from the vertex A to base BC is 4.5 cm.
Answer» Construct a ∆ABC in which ∠B = 45°, ∠C = 60° and the perpendicular from the vertex A to base BC is 4.5 cm.

Discussion

9621.	ntA straight rod partially immersed in water appears to be inclined at 45 degree with the surface when viewed vertically through air.What is the actual inclination of rod with water?n nta)30 degreen ntb)45 degreen ntc)33 degreen ntd)180 degreen
Answer» ntA straight rod partially immersed in water appears to be inclined at 45 degree with the surface when viewed vertically through air.What is the actual inclination of rod with water?n nta)30 degreen ntb)45 degreen ntc)33 degreen ntd)180 degreen

Discussion

9622.	5. one of the diagonal s of a rhombus of perimeter is 140 M is 60 M find its area and length of the Other diagonal
Answer» 5. one of the diagonal s of a rhombus of perimeter is 140 M is 60 M find its area and length of the Other diagonal

Discussion

9623.	Suppose that there is a conical strainer as shown in the given figure.The radius of its broadest end is 6 cm and length is 8 cm. Now if 2 cm2 of strainer has an average of 8 tiny holes, then find the total number of holes in the entire strainer.
Answer» Suppose that there is a conical strainer as shown in the given figure.The radius of its broadest end is 6 cm and length is 8 cm. Now if 2 ${c m}^{2}$ of strainer has an average of 8 tiny holes, then find the total number of holes in the entire strainer.

9623.

Suppose that there is a conical strainer as shown in the given figure.The radius of its broadest end is 6 cm and length is 8 cm. Now if 2 cm2 of strainer has an average of 8 tiny holes, then find the total number of holes in the entire strainer.

Answer»

Suppose that there is a conical strainer as shown in the given figure.The radius of its broadest end is 6 cm and length is 8 cm. Now if 2 ${c m}^{2}$ of strainer has an average of 8 tiny holes, then find the total number of holes in the entire strainer.

Discussion

9624.	Question 3A, B and C are three points on a circle, prove that perpendicular bisectors of AB, BC and CA are concurrent.
Answer» Question 3 A, B and C are three points on a circle, prove that perpendicular bisectors of AB, BC and CA are concurrent.

Discussion

9625.	Divide 32 into four parts which are the four terms of an AP such that the product of the first and the fourth term is to the product of the second and the third term is 7 : 15. [CBSE 2014]
Answer» Divide 32 into four parts which are the four terms of an AP such that the product of the first and the fourth term is to the product of the second and the third term is 7 : 15. [CBSE 2014]

Discussion

9626.	(4+√3)× ________ results in a rational number.
Answer» $(4 + \sqrt{3}) \times$ ________ results in a rational number.

Discussion

9627.	What is the probability of not picking a face card when you draw randomly from a pack of 52 cards?
Answer» What is the probability of not picking a face card when you draw randomly from a pack of 52 cards?

Discussion

9628.	In the given figure, common tangents AB and CD to the two circle with centres O1 and O2 intersect at E. Prove that AB = CD [CBSE 2014]
Answer» In the given figure, common tangents AB and CD to the two circle with centres O₁ and O₂ intersect at E. Prove that AB = CD [CBSE 2014]

Discussion

9629.	A, B and C are partners sharing profits in the ratio of 4/9 : 3/9 : 2/9. B retires and his capital after making adjustments for reserves and gain (profit) on revaluation stands at ₹ 1,39,200. A and C agreed to pay him ₹ 1,50,000 in full settlement of his claim. Record necessary Journal entry for adjustment of goodwill if the new profit-sharing ratio is decided at 5 : 3.
Answer» A, B and C are partners sharing profits in the ratio of 4/9 : 3/9 : 2/9. B retires and his capital after making adjustments for reserves and gain (profit) on revaluation stands at ₹ 1,39,200. A and C agreed to pay him ₹ 1,50,000 in full settlement of his claim. Record necessary Journal entry for adjustment of goodwill if the new profit-sharing ratio is decided at 5 : 3.

Discussion

9630.	From the top of a lighthouse H m tall, a person observes the angle of depression of a boat to be 60∘. Another person who is H3 m from the top of a lighthouse observes the angle of depression of another boat directly behind the first boat to be 45∘. Find the distance between the two boats. (Take √3 = 1.7)
Answer» From the top of a lighthouse H m tall, a person observes the angle of depression of a boat to be $60^{\circ}$ . Another person who is $\frac{H}{3}$ m from the top of a lighthouse observes the angle of depression of another boat directly behind the first boat to be $45^{\circ}$ . Find the distance between the two boats. (Take $\sqrt{3}$ = 1.7)

9630.

From the top of a lighthouse H m tall, a person observes the angle of depression of a boat to be 60∘. Another person who is H3 m from the top of a lighthouse observes the angle of depression of another boat directly behind the first boat to be 45∘. Find the distance between the two boats. (Take √3 = 1.7)

Answer»

From the top of a lighthouse H m tall, a person observes the angle of depression of a boat to be $60^{\circ}$ . Another person who is $\frac{H}{3}$ m from the top of a lighthouse observes the angle of depression of another boat directly behind the first boat to be $45^{\circ}$ . Find the distance between the two boats.

(Take $\sqrt{3}$ = 1.7)

Discussion

9631.	Insert 3 A.M's between 10 and-2. And also show that the sum of these A.M's is 3 times the single arithmetic between 10 and-2
Answer» Insert 3 A.M's between 10 and-2. And also show that the sum of these A.M's is 3 times the single arithmetic between 10 and-2

Discussion

9632.	Which is the factored form of 3a2−24ab+48b2
Answer» Which is the factored form of ${3 a}^{2} - 24 a b + 48 b^{2}$

Discussion

9633.	34. If d1and d2 (d2>d1) are the diameters of two concentric circles and c is the length of a chord of a circle which is tangent to the other circle,prove d2×d2=c2×c2/4 +d1×d1
Answer» 34. If d1and d2 (d2>d1) are the diameters of two concentric circles and c is the length of a chord of a circle which is tangent to the other circle,prove d2×d2=c2×c2/4 +d1×d1

Discussion

9634.	From a circular piece of cardboard of radius 3 cm two sectors of 90° have been cut off. Find the perimeter of the remaining portion nearest hundredth centimeters (Take π = 22/7).
Answer» From a circular piece of cardboard of radius 3 cm two sectors of 90° have been cut off. Find the perimeter of the remaining portion nearest hundredth centimeters (Take π = 22/7).

Discussion

9635.	Question 8 (ii)The distance (in km) of 40 engineers from their residence to their place of work were found as follows. 5310202511137123119101217181132171627978351215183121429615157612What is the empirical probability that an engineer lives:(ii) more than or equal to 7 km from her place of work?
Answer» Question 8 (ii) The distance (in km) of 40 engineers from their residence to their place of work were found as follows. $\begin{matrix} 5 & 3 & 10 & 20 & 25 & 11 & 13 & 7 & 12 & 31 19 & 10 & 12 & 17 & 18 & 11 & 32 & 17 & 16 & 2 7 & 9 & 7 & 8 & 3 & 5 & 12 & 15 & 18 & 3 12 & 14 & 2 & 9 & 6 & 15 & 15 & 7 & 6 & 12 \end{matrix}$ What is the empirical probability that an engineer lives: (ii) more than or equal to 7 km from her place of work?

Discussion

9636.

The arithmetic mean of the following frequency distribution is 53. Find the value of x. Class 0 – 20 20 – 40 40 – 60 60 – 80 80 – 100 Frequency 12 15 32 x 13

Answer» The arithmetic mean of the following frequency distribution is 53. Find the value of x.

Class	0 – 20	20 – 40	40 – 60	60 – 80	80 – 100
Frequency	12	15	32	x	13

Discussion

9637.	Given that a:b::c:d, then which of the following follows Componendo and Dividendo property?
Answer» Given that a:b::c:d, then which of the following follows Componendo and Dividendo property?

Discussion

9638.	Raman deposited Rs. 200 per month for 36 months in a bank's recurring deposit account. If the bank pays an interest at the rate of 15% per annum, find the amount he gets on maturity.
Answer» Raman deposited Rs. 200 per month for 36 months in a bank's recurring deposit account. If the bank pays an interest at the rate of 15% per annum, find the amount he gets on maturity.

Discussion

9639.	Find the equation of the circle with centre (-2,3) and radius 4
Answer» Find the equation of the circle with centre (-2,3) and radius 4

Discussion

9640.	The hypotenuse of a right triangle is 26 cm long. If one of the remaining two sides is 10 cm long, the length of the other side is(a) 25 cm(b) 23 cm(c) 24 cm(d) 22 cm
Answer» The hypotenuse of a right triangle is 26 cm long. If one of the remaining two sides is 10 cm long, the length of the other side is (a) 25 cm (b) 23 cm (c) 24 cm (d) 22 cm

Discussion

9641.	Consider the following graph:The number of strongly connected components of the graph are_________.4
Answer» Consider the following graph: The number of strongly connected components of the graph are_________. 4

Discussion

9642.	If A and B are two events such that P(A∩B) = 13, P(A∪B)=56 and P(B)=13, then P(A)=_____________.
Answer» If A and B are two events such that $P (A \cap B) = \frac{1}{3}, P (A \cup B) = \frac{5}{6} and P (B) = \frac{1}{3}$ , then P(A)=_____________.

Discussion

9643.	A water fountain sprinkles water all around it. If the speed of water coming out of the fountain is v, find the total area around the fountain that gets wet, in terms ofπ, g and v
Answer» A water fountain sprinkles water all around it. If the speed of water coming out of the fountain is v, find the total area around the fountain that gets wet, in terms ofπ, g and v

Discussion

9644.	if two chords PQ and RS of a circle with centre O intersect each other at M such that PM = MS, then prove that MR = MQ
Answer» if two chords PQ and RS of a circle with centre O intersect each other at M such that PM = MS, then prove that MR = MQ

Discussion

9645.	Find the greatest number that will divide 445, 572 and 699 leaving remainder 4,5,6 effectively
Answer» Find the greatest number that will divide 445, 572 and 699 leaving remainder 4,5,6 effectively

Discussion

9646.	Find the domain and range of the real function f. defined by f(x)=\|x−1\|
Answer» Find the domain and range of the real function $f$ . defined by $f (x) = \| x - 1 \|$

Discussion

9647.	In an isosceles triangle ABC if AC = BC and AB2 = 2AC2, then ∠C =(a) 30°(b) 45(c) 90°(d) 60°
Answer» In an isosceles triangle ABC if AC = BC and AB² = 2AC², then ∠C = (a) 30° (b) 45 (c) 90° (d) 60°

Discussion

9648.	Find the equation of the line passing through the points (1, 8) and (2, 7)
Answer» Find the equation of the line passing through the points (1, 8) and (2, 7)

Discussion

9649.	Find the roots of the equation 2x2−7x−39=0 by the method of factorization.
Answer» Find the roots of the equation $2 x^{2} - 7 x - 39 = 0$ by the method of factorization.

Discussion

9650.

The decorative block shown in Fig. is made of two solids - a cube and a hemisphere. The base of the block is a cube with edge 5 cm, and the hemisphere fixed on the top has a diameter of 4.2 cm. Find the total surface area of the block. (Take π=227)

Answer»

The decorative block shown in Fig. is made of two solids - a cube and a hemisphere. The base of the block is a cube with edge 5 cm, and the hemisphere fixed on the top has a diameter of 4.2 cm. Find the total surface area of the block. (Take $π = \frac{22}{7}$ )

Discussion

Explore topic-wise InterviewSolutions in .

Find the length of AD, if BD= 3.6 cm and DC = 6.4 cm.

if x^2- 5x+1=0,then find the value of x^5+1/x^5

Question 21 (ii)Find the sum:(4−1n)+(4−2n)+(4−3n)+⋯upto n terms

From a point on the ground, the angles of elevation of the bottom and the top of a transmission tower which is fixed at the top of a 30 m high building are 45∘ and 60∘ respectively. Find the height of the tower.

What are complex numbers?

Show that (a − b)2, (a2 + b2) and (a + b)2 are in A.P.

The nth term of an AP is (7 - 4n). Find its common difference.

If →a,→b,→c are non collinear coplanar vectors represents −−→BC,−−→CA,−−→AB respectively, then which of the following is TRUE

Number of points of discontinuity in [14cosx] and [14sinx] where [] is GIF

A positive integer is of the form 3q + 1, q being a natural number. Can you write its square in any form other than 3m + 1, 3m or 3m + 2 for some integer m? Justify your answer.

The mean of the following frequency distribution is 62.8 and the sum of all the frequencies is 50. Compute the missing frequency f1 and f2. Class: 0−20 20−40 40−60 60−80 80−100 100−120 Frequency: 5 f1 10 f2 7 9

The LCM of (x−3)2(x+4) and (x−3)(x+4)2 is:

9^n-8n-1 is divisible by 64 is (1) Always true (2)Always false (3)Always true for rational values of n (4)Always true for irrational values of n

A flag pole 18 m high casts a shadow 9.6 cm long. The distance of the top of the pole from the far end of the shadow is _________.

In ∆ABC, AD and BE are altitude. Prove that ar∆DECar∆ABC=DC2AC2.

Calculate the Mean of the given distribution, using Assumed mean Method.MarksNo. of Students10−20220−30630−401040−501250−60960−70870−80480−90348.89

Question 12AB and AC are two chords of a circle of radius r such that AB = 2AC. If p an q are the distances of AB an AC from the centre, prove that 4q2=p2+3r2.

Find the area of the sector whose arc is making an angle of 60∘ at the center of a circle of radius 3.2 cm. What will be the area of the balance sector? [3 MARKS]

Construct a ∆ABC in which ∠B = 45°, ∠C = 60° and the perpendicular from the vertex A to base BC is 4.5 cm.

ntA straight rod partially immersed in water appears to be inclined at 45 degree with the surface when viewed vertically through air.What is the actual inclination of rod with water?n nta)30 degreen ntb)45 degreen ntc)33 degreen ntd)180 degreen

5. one of the diagonal s of a rhombus of perimeter is 140 M is 60 M find its area and length of the Other diagonal

Suppose that there is a conical strainer as shown in the given figure.The radius of its broadest end is 6 cm and length is 8 cm. Now if 2 cm2 of strainer has an average of 8 tiny holes, then find the total number of holes in the entire strainer.

Question 3A, B and C are three points on a circle, prove that perpendicular bisectors of AB, BC and CA are concurrent.

Divide 32 into four parts which are the four terms of an AP such that the product of the first and the fourth term is to the product of the second and the third term is 7 : 15. [CBSE 2014]

(4+√3)× ________ results in a rational number.

What is the probability of not picking a face card when you draw randomly from a pack of 52 cards?

In the given figure, common tangents AB and CD to the two circle with centres O1 and O2 intersect at E. Prove that AB = CD [CBSE 2014]

Insert 3 A.M's between 10 and-2. And also show that the sum of these A.M's is 3 times the single arithmetic between 10 and-2

Which is the factored form of 3a2−24ab+48b2

34. If d1and d2 (d2>d1) are the diameters of two concentric circles and c is the length of a chord of a circle which is tangent to the other circle,prove d2×d2=c2×c2/4 +d1×d1

From a circular piece of cardboard of radius 3 cm two sectors of 90° have been cut off. Find the perimeter of the remaining portion nearest hundredth centimeters (Take π = 22/7).

Question 8 (ii)The distance (in km) of 40 engineers from their residence to their place of work were found as follows. 5310202511137123119101217181132171627978351215183121429615157612What is the empirical probability that an engineer lives:(ii) more than or equal to 7 km from her place of work?

The arithmetic mean of the following frequency distribution is 53. Find the value of x. Class 0 – 20 20 – 40 40 – 60 60 – 80 80 – 100 Frequency 12 15 32 x 13

Given that a:b::c:d, then which of the following follows Componendo and Dividendo property?

Raman deposited Rs. 200 per month for 36 months in a bank's recurring deposit account. If the bank pays an interest at the rate of 15% per annum, find the amount he gets on maturity.

Find the equation of the circle with centre (-2,3) and radius 4

The hypotenuse of a right triangle is 26 cm long. If one of the remaining two sides is 10 cm long, the length of the other side is(a) 25 cm(b) 23 cm(c) 24 cm(d) 22 cm

Consider the following graph:The number of strongly connected components of the graph are_________.4

If A and B are two events such that P(A∩B) = 13, P(A∪B)=56 and P(B)=13, then P(A)=_____________.

A water fountain sprinkles water all around it. If the speed of water coming out of the fountain is v, find the total area around the fountain that gets wet, in terms ofπ, g and v

if two chords PQ and RS of a circle with centre O intersect each other at M such that PM = MS, then prove that MR = MQ

Find the greatest number that will divide 445, 572 and 699 leaving remainder 4,5,6 effectively

Find the domain and range of the real function f. defined by f(x)=|x−1|

In an isosceles triangle ABC if AC = BC and AB2 = 2AC2, then ∠C =(a) 30°(b) 45(c) 90°(d) 60°

Find the equation of the line passing through the points (1, 8) and (2, 7)

Find the roots of the equation 2x2−7x−39=0 by the method of factorization.

The decorative block shown in Fig. is made of two solids - a cube and a hemisphere. The base of the block is a cube with edge 5 cm, and the hemisphere fixed on the top has a diameter of 4.2 cm. Find the total surface area of the block. (Take π=227)