8677 + Interview Questions in Maths in Class 14 Page 67 InterviewSolution

3301.	Let g(x)=1+x-[x] and f(x)={(-1",",x lt 0),(0",",x=0),(1",",x gt 0):}, then for all x, f[g(x)] is equal to
Answer» 0 1 X f(x) ANSWER :B

Discussion

3302.	ABCD is a square L and K are two point on AB s.t. BO = BK , AO= AL , O is the intersection point of diagonal .If angle LOK= Qfind tan Q
Answer» ANSWER :1

Discussion

3303.	sectheta+tantheta=2+sqrt(5), then sintheta will be
Answer» `(1)/(sqrt(5))` `(sqrt(3))/(2)` `(4)/(5)` `(2)/(sqrt(5))` Answer :B

Discussion

3304.	The value of denominator when (7sqrt3 - 5sqrt2)/(sqrt18 + sqrt48) is rationalised :
Answer» (A) 15 (B) 25 (C) 30 (D) 50 Answer :C

Discussion

3305.	The marked price of a bicycle is1100. A shopkeeper allows a discount of 10% and get a profit of 10 %. Find the cost price of the bicycle.
Answer» ANSWER :900

Discussion

3306.	If p^(2)+q^(2)+r^(2)=1, then the maximum vlaue of pqr is :
Answer» 1 `1/3sqrt3` 3 none of these Answer :B

Discussion

3307.	The students in three classes are in the ratio of 2:3:4. If 40 students are added in each clas, the ratio becomes 4:5:6. Find the total number of students in all the three classes is :
Answer» 270 180 126 135 Solution :2X + 4 = 4y ...(i) 3x + 40 = 5y ...(ii) 4x + 40 = 6y ...(III) Therefore 2x = 40 `IMPLIES x = 20` Hence, total number of students = 2x + 3x + 4x = 9x `9 xx 20 = 180 Alternatively It can be solved through options also.

Discussion

3308.	The product of two numbers is 24 times the difference of these two numbers. If the sum of these numbers is 14, the larger number is
Answer» ANSWER :x=8 ,or -42 `=> a; =8`

Discussion

3309.	Malvika wants to colour a cubical box from outside. In how many ways can she colour it if she wants to colour each face of the box with either blue or pink colour?
Answer» 6 12 10 18 Answer :C

Discussion

3310.	An N.G.O (non- government organisation) STRANGE working for the relief of Tsunami Victims in Srilanka consisting of 7 members S,T,R,A,N,G,E of the same family. The eldest one 'S' spoke to me "I have deployed equal number of brothers and sisters for medical relief and psychological counselling under the supervision of myself'. Later on the youngest member E spoke to me as "we have been working for rehabilitation and food supply as twice the number of sisters as the number of brothers have been deployed there, but I did not actually do any thing due to a severe injury in my leg". Then we can conclude that:
Answer» YOUNGEST PERSON is a lady eldest person's WIFE is youngest the BROTHER of S is youngest nothing can be said Answer :C

Discussion

3311.	Find the number of digits required to write down the number of pages in a 300 pages book.
Answer» 792 279 729 none of these Answer :A

Discussion

3312.	What is difference in production of rice in 1969-70 and 1979-80 ?
Answer» 149830 175752 53890 none of these Answer :A

Discussion

3313.	The ratio of weight of Ram and Shyam is 4 : 5. The weight of Ram is increased by 10%. Total weight of Ram and Shyam is increased by 82.5 kg. The percentage of increment in total weight is 15 %. Find the percent change in weight of Shyam.
Answer» ANSWER :0.19

Discussion

3314.	There is some average of 11 innings of a batsman. He scores 90 runs in 12^(th)innings then average is decreased by 5 runs. Find his current average
Answer» ANSWER :145

Discussion

3315.	A student on his birthday distributed on an average 5 chocolates per student. If on the arrival of the teacher and the headmaster to whom the student gives 10 and 15 chocolates respectively, the average chocolate distributed per head increases to 5.5. How many students were in the class?
Answer» ANSWER :28

Discussion

3316.	(15^(40))/(100)find R.
Answer» ANSWER :`Rto25`

Discussion

3317.	In a 1000 m race Ameesha gives a headstart of 100 m to Bipasha and beats her by 200m in the same race Ameesha gives a headstart of 100 m to Celina and beats her by 300 m by how many metres would Bipasha beat Celina in a 50 m race?
Answer» 6.66 m 7.143 m 8 m none of these Answer :B

Discussion

3318.	Total number of ways in which 20 mangoes can be distributed among 4 persons is :
Answer» `""^(20)C_3` `""^(23)C_3` `""^(24)C_4` `(20!)/(4!)` Answer :B

Discussion

3319.	If the shadow of a tower is 30 m when the sun's altitude is 30^(@) what is the length of the shadow when the sun's altiutude is 60^(@)?
Answer» `10sqrt3`m 20m 10m 12m Answer :C

Discussion

3320.	The true discount on a certain sum of money due 4 yr hence is X 75 and the simple interest on the same sum for the same time and at the same rate of interest is X 225. Find the rate per cent.
Answer» 0.25 0.5 0.31 0.45 Answer :B

Discussion

3321.	PQ is a chord of length 8 cm to a circle of radius 5 cm. The tangents at P and Q intersect at a point T. Find the length of the tangent TP.
Answer» `(16)/(3)` CM `(20)/(3)` cm `(18)/(5)` cm `(19)/(6)` cm Answer :B

Discussion

3322.	Find the number of Zeros at the end ofthe product - 2^1 xx 5^2 xx 2^3 xx 5^4 xx2^5 xx 5^6 xx 2^7 xx 5^8 xx 2^9 xx5^10
Answer» ANSWER :25

Discussion

3323.	Anjuli has written all the letters (or characters) of English alphabets (i.e., A,B,C,D,……Y,Z) horizontally in a single line. She started counting as A - 1, B- 2, C- 3, D - 4, ….Y - 25, Z - 26 and reversed back as Y - 27, X - 28, W - 29, V - 30,…..B-50, A - 51 and further reversed back as B - 52, C - 53, D - 54,.. etc. She continued counting till she reached the 777th character. At which letter or character she stopped counting ?
Answer» Y B R NONE of these Answer :A

Discussion

3324.	If x=asinthetaandy=btantheta, then the value of (a^(2))/(x^(2))-(b^(2))/(y^(2))=?
Answer» 5 `-1` 1 3 Answer :C

Discussion

3325.	Simplify the following ratios:2 1/3:3 1/2
Answer» SOLUTION :`2 1/3:3 1/2=7/3:7/2=(7/3)/(7/2)=2/3 or 2:3`

Discussion

3326.	A person deposited Rs. 500 for 4 years and Rs, 600 for 3 years at the same rate of simple interest in a bank. Altogether he received Rs. 190 as interest. The rate of simple interest per annum was :
Answer» ANSWER :0.05

Discussion

3327.	A helicopter is in a stationary position at a certain height over the lake. At a point 200 m above the surface of the lake, the angle of elevation of the helicopter is 45^(@). At the same time, the angle of depression of its reflection in the lake is 75^(@). Calculate the height of the helicopter from the surface of the lake :
Answer» `(200)/SQRT3` m `200sqrt3` m 200 m 150 m Answer :B

Discussion

3328.	There are three straight lines dividing the circle into maximum possible number of regions. If three additional lines are drawn, what is the maximum possible number of additional regions that can be formed in the circle?
Answer» (A) 6 (B) 9 (C) 14 (D) none of these Answer :D

Discussion

3329.	If tantheta=(1)/(2)andtanphi=(1)/(3), then theta+phi=?
Answer» `(PI)/(6)` 0 `(pi)/(4)` `pi` ANSWER :C

Discussion

3330.	If sum of the roots is-11 and product of the roots is 24,
Answer» 1.both the ROOTS He right-side of the X-axis 2.both the roots LIE left-side of the Y-axis. 3.roots lie on both the sides of the Y-axis 4.one root is ZERO and ANOTHER root is IMAGINARY number Answer :B

Discussion

3331.	If(a+b+c=0, find the nature of the roots of ttie equation(c^2-ab)x^2-2(a^2-bc)x+(b^2-ac)=0.
Answer» Imaginaiy Real and equal Non-real Irrational Answer :B

Discussion

3332.	A 220 m long train is running at 120 km/h. In what time, will it pass a man running in the direction opposite to that of the train at 12 km/h?
Answer» ANSWER :`=6S`

Discussion

3333.	Find the value of 1/(log_(3)e) + 1/(log_(3)e^(2)) + 1/(log_(3)e^(4))+……….. Is:
Answer» `log_(e)9` 0 1 `log_(e) 270` Answer :A

Discussion

3334.	If A B, C are any three sets, then :
Answer» `A - (B UU C) = (A-B) uu (A-C)` `A- (BuuC)= (A-B) NN (A-C)` `A - (BuuC) =(A-B) uu (A-C)` `A - (B uu C) = (A uu B) - (A uu C)` Answer :b

Discussion

3335.	The odds against a husband who is 50 years old, living till he is 70 are 7:5 and the adds against his wife who is now 40, living till she is 60 are 5:3 Find the probability that the couple will be alive 20 years hence.
Answer» A.`21/32` B.`5/32` C.`15/32` D.`12/35` ANSWER :B

Discussion

3336.	i) Prove that: (1-sin2A)/(1+sin2A) = tan^(2)(pi/4-A) ii) If costheta=1/2(x+1/x), then prove that: cos2theta=1/2(x^(2)+1/x^(2)) and cos3theta=1/2(x^(3)+1/x^(3))
Answer» `secA+tanA` `TAN((PI)/(4)-A)` `tan((pi)/(4)+(A)/(2))` `tan((pi)/(4)-(A)/(2))` ANSWER :B

Discussion

3337.	OABC is a rhombus whose the vertices A, B and C lie on a circle of radius 10cm and with centre O.Find the area ofthe rhombus.
Answer» `30sqrt(3)CM^(2)` `50sqrt(3)cm^(2)` `10sqrt(3)cm^(2)` `100sqrt(3)cm^(2)` ANSWER :B

Discussion

3338.	10 gallons are drawn from a cask full of wine, It is then filled with water, 10 gallons of the mixture are drawn and the cask is again filled with water. After such four operations, the quantity of wine now left in the cask to that of water in it is 256: 369. How much does the cask hold?
Answer» 50 GALLONS 55 gallons 60 gallons 65 gallons ANSWER :A

Discussion

3339.	A and B have to write 810 and 900 pages respectively in the same time period. But A completes his work 3 days ahead of time and B completes 6 days ahead of time. How many pages did A write per hour if B wrote 21 pages more in each hour?
Answer» 45 72 54 100 Answer :C

Discussion

3340.	Two men A and B start from place X walking at 4 ½ kmph and 5 ¾ kmph respectively. How many km apart they are at the end of 3 ½ hours if they are walking in the same direction ?
Answer» A) `2 9/7 km` B) `3 7/5 km` C) `1 3/4 km` D) `4 3/8 km` ANSWER :D

Discussion

3341.	Solve the following problems based on the following information An industrial corrisor is laid out along the special Economic Zone (SEZ), which is in the shape of a regular polygon. Every vertex of the SEZ has exactly one manufacturing plant. A particular road connects any two plants. No single road connects directly more than two plants. Engineershave laid down all the possible roads connecting all the plants with each other. Each road is designed to offer the shortest distance between any two plants. Also, engineers have laid down all the possible rail-loops. Each loop connect any three plants. Every loop is designed along the shortest possible distance between any two plants connected through that loop. Wherever any two or more than two roads intersect inside the SEZ (poygon), exactly one government office is to be built there. Wherever any two or more than five roads intersect inside the SEZ (poygon), exactly one airport is to be built there. Maximum how many government offices are there if the SEZ has 49 plants?
Answer» 0 7 50 none of the above Answer :A

Discussion

3342.	Find min^(m) value of sin^(2)alpha +cosec^(2)alpha+cos^(2)beta+sec^(2)beta+tan^(2)gamma+cot^(2)gamma=?
Answer» ANSWER :6

Discussion

3343.	Solve the following problems based on the following information An industrial corrisor is laid out along the special Economic Zone (SEZ), which is in the shape of a regular polygon. Every vertex of the SEZ has exactly one manufacturing plant. A particular road connects any two plants. No single road connects directly more than two plants. Engineershave laid down all the possible roads connecting all the plants with each other. Each road is designed to offer the shortest distance between any two plants. Also, engineers have laid down all the possible rail-loops. Each loop connect any three plants. Every loop is designed along the shortest possible distance between any two plants connected through that loop. Wherever any two or more than two roads intersect inside the SEZ (poygon), exactly one government office is to be built there. Wherever any two or more than five roads intersect inside the SEZ (poygon), exactly one airport is to be built there. Maximum how many warehouse are there if the SEZ has 25 plants?
Answer» 7220 12650 14400 none of these Answer :B

Discussion

3344.	Two bike riders ride in opposite directions around a circular track, starting at the same time from the same point. Biker A rides at a speed of 16 kmph and biker B rides at a speed of 14 kmph. If the track has a diameter of 40 km, after how much time (in hours) will the two bikers meet?
Answer» A) 6.52 B) 8.14 C) 4.18 D) 5.02 Answer :C

Discussion

3345.	Answer these questions based on the following information. A group consists of four straight couple. That means each couple is having a male and a female. In how many ways can they be seated around a circular table such that the men and women occupy the altenate positions?
Answer» 288 144 72 720 Answer :B

Discussion

3346.	Answer these questions based on the following information.A group consists of four straight couple. That means each couple is having a male and a femal. In how many ways can they be seated on the single bench such that all the men sit together and all the women sit together?
Answer» 384 275 184 none of these Answer :A

Discussion

3347.	A group consists of four straight couple. That means each couple is having a male and a female. In how many ways can they be arranged in a straight line such that no two men were sitting together?
Answer» 1242 1440 3880 2880 Answer :D

Discussion

3348.	If 2sec^(2)theta+tan^(2)theta=17, then find cottheta=?
Answer» ANSWER :`(1)/(SQRT(5))`

Discussion

3349.	Sapna borrowed some money on compound interest and returned it in three years in equal annual instalments. If the rate of interest is 15% per annum and annual instalment is ₹ 486680, find the sum borrowed :
Answer» 1112220 1111200 1122000 none of these Answer :B

Discussion

3350.	In the given figure, AP = 2 cm, BP = 6 cm and CP = 3 cm. Find DP :
Answer» 6 cm 4 cm 2 cm 3 cm Answer :B

Discussion

Explore topic-wise InterviewSolutions in .

Let g(x)=1+x-[x] and f(x)={(-1",",x lt 0),(0",",x=0),(1",",x gt 0):}, then for all x, f[g(x)] is equal to

ABCD is a square L and K are two point on AB s.t. BO = BK , AO= AL , O is the intersection point of diagonal .If angle LOK= Qfind tan Q

sectheta+tantheta=2+sqrt(5), then sintheta will be

The value of denominator when (7sqrt3 - 5sqrt2)/(sqrt18 + sqrt48) is rationalised :

The marked price of a bicycle is1100. A shopkeeper allows a discount of 10% and get a profit of 10 %. Find the cost price of the bicycle.

If p^(2)+q^(2)+r^(2)=1, then the maximum vlaue of pqr is :

The students in three classes are in the ratio of 2:3:4. If 40 students are added in each clas, the ratio becomes 4:5:6. Find the total number of students in all the three classes is :

The product of two numbers is 24 times the difference of these two numbers. If the sum of these numbers is 14, the larger number is

Malvika wants to colour a cubical box from outside. In how many ways can she colour it if she wants to colour each face of the box with either blue or pink colour?

Find the number of digits required to write down the number of pages in a 300 pages book.

What is difference in production of rice in 1969-70 and 1979-80 ?

The ratio of weight of Ram and Shyam is 4 : 5. The weight of Ram is increased by 10%. Total weight of Ram and Shyam is increased by 82.5 kg. The percentage of increment in total weight is 15 %. Find the percent change in weight of Shyam.

There is some average of 11 innings of a batsman. He scores 90 runs in 12^(th)innings then average is decreased by 5 runs. Find his current average

A student on his birthday distributed on an average 5 chocolates per student. If on the arrival of the teacher and the headmaster to whom the student gives 10 and 15 chocolates respectively, the average chocolate distributed per head increases to 5.5. How many students were in the class?

(15^(40))/(100)find R.

In a 1000 m race Ameesha gives a headstart of 100 m to Bipasha and beats her by 200m in the same race Ameesha gives a headstart of 100 m to Celina and beats her by 300 m by how many metres would Bipasha beat Celina in a 50 m race?

Total number of ways in which 20 mangoes can be distributed among 4 persons is :

If the shadow of a tower is 30 m when the sun's altitude is 30^(@) what is the length of the shadow when the sun's altiutude is 60^(@)?

The true discount on a certain sum of money due 4 yr hence is X 75 and the simple interest on the same sum for the same time and at the same rate of interest is X 225. Find the rate per cent.

PQ is a chord of length 8 cm to a circle of radius 5 cm. The tangents at P and Q intersect at a point T. Find the length of the tangent TP.

Find the number of Zeros at the end ofthe product - 2^1 xx 5^2 xx 2^3 xx 5^4 xx2^5 xx 5^6 xx 2^7 xx 5^8 xx 2^9 xx5^10

If x=asinthetaandy=btantheta, then the value of (a^(2))/(x^(2))-(b^(2))/(y^(2))=?

Simplify the following ratios:2 1/3:3 1/2

A person deposited Rs. 500 for 4 years and Rs, 600 for 3 years at the same rate of simple interest in a bank. Altogether he received Rs. 190 as interest. The rate of simple interest per annum was :

There are three straight lines dividing the circle into maximum possible number of regions. If three additional lines are drawn, what is the maximum possible number of additional regions that can be formed in the circle?

If tantheta=(1)/(2)andtanphi=(1)/(3), then theta+phi=?

If sum of the roots is-11 and product of the roots is 24,

If(a+b+c=0, find the nature of the roots of ttie equation(c^2-ab)x^2-2(a^2-bc)x+(b^2-ac)=0.

A 220 m long train is running at 120 km/h. In what time, will it pass a man running in the direction opposite to that of the train at 12 km/h?

Find the value of 1/(log_(3)e) + 1/(log_(3)e^(2)) + 1/(log_(3)e^(4))+……….. Is:

If A B, C are any three sets, then :

The odds against a husband who is 50 years old, living till he is 70 are 7:5 and the adds against his wife who is now 40, living till she is 60 are 5:3 Find the probability that the couple will be alive 20 years hence.

i) Prove that: (1-sin2A)/(1+sin2A) = tan^(2)(pi/4-A) ii) If costheta=1/2(x+1/x), then prove that: cos2theta=1/2(x^(2)+1/x^(2)) and cos3theta=1/2(x^(3)+1/x^(3))

OABC is a rhombus whose the vertices A, B and C lie on a circle of radius 10cm and with centre O.Find the area ofthe rhombus.

10 gallons are drawn from a cask full of wine, It is then filled with water, 10 gallons of the mixture are drawn and the cask is again filled with water. After such four operations, the quantity of wine now left in the cask to that of water in it is 256: 369. How much does the cask hold?

A and B have to write 810 and 900 pages respectively in the same time period. But A completes his work 3 days ahead of time and B completes 6 days ahead of time. How many pages did A write per hour if B wrote 21 pages more in each hour?

Two men A and B start from place X walking at 4 ½ kmph and 5 ¾ kmph respectively. How many km apart they are at the end of 3 ½ hours if they are walking in the same direction ?

Find min^(m) value of sin^(2)alpha +cosec^(2)alpha+cos^(2)beta+sec^(2)beta+tan^(2)gamma+cot^(2)gamma=?

Two bike riders ride in opposite directions around a circular track, starting at the same time from the same point. Biker A rides at a speed of 16 kmph and biker B rides at a speed of 14 kmph. If the track has a diameter of 40 km, after how much time (in hours) will the two bikers meet?

Answer these questions based on the following information. A group consists of four straight couple. That means each couple is having a male and a female. In how many ways can they be seated around a circular table such that the men and women occupy the altenate positions?

Answer these questions based on the following information.A group consists of four straight couple. That means each couple is having a male and a femal. In how many ways can they be seated on the single bench such that all the men sit together and all the women sit together?

A group consists of four straight couple. That means each couple is having a male and a female. In how many ways can they be arranged in a straight line such that no two men were sitting together?

If 2sec^(2)theta+tan^(2)theta=17, then find cottheta=?

Sapna borrowed some money on compound interest and returned it in three years in equal annual instalments. If the rate of interest is 15% per annum and annual instalment is ₹ 486680, find the sum borrowed :

In the given figure, AP = 2 cm, BP = 6 cm and CP = 3 cm. Find DP :