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InterviewSolution
This section includes InterviewSolutions, each offering curated multiple-choice questions to sharpen your knowledge and support exam preparation. Choose a topic below to get started.
| 301. |
There are m arithmetic means between 5 and -16 such that the ratio of the 7th mean to the (m-7)th mean is 1:4. Find the value of m. |
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Answer» Solution :LET `A_(1),A_(2),...,A_(m)`be m arithmetic means between 5 and -16. `:. 5,A_(1),A_(2),A_(3),...A_(m)-16` are in A.P. `:. T_(m+2)=-16 RARR 5+(m+1)d=-16` `rArr d=(-21)/(m+1)` `rArr (A_(7))/(A_(m-7))=(1)/(4) rArr(T_(8))/(T_(m-6))=(1)/(4)` `rArr (5+7d)/(5+(m-7)d)=(1)/(4) rArr (5+7((-21)/(m+1)))/ (5+(m-7)((-21)/(m+1)))=(1)/(4)` `rArr 20-(588)/(m+1)=5-(21(m-7))/(m+7)` `rArr 20m+20-588=5m+5-21m+147` `rArr36m=720` `rArr m=20` |
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| 302. |
from the adjoining figure, prove that trianglePQR~triangleABC. Hence prove that (PR)/(AC)= sqrt((PQ)/(AB).(QR)/(BC)). |
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| 303. |
The radius of the base of a right circular cylinder is doubled and the height is halved . What is the ratio of volume of the new cylinder to the original cylinder ? |
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| 304. |
Two dice are thrown at the same time . Find the probability of getting the sum on dice is less than or equal to 12 . |
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| 305. |
Let A=[{:(,2,1),(,0,-2):}], B=[{:(,4,1),(,-3,-2):}] and C=[{:(,-3,2),(,-1,4):}]. Find A^2+AC-5B. |
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| 306. |
Statements: 1. All cars are cats. 2. All fans are cats. Conclusions: 1. All cars are fans. 2. Some fans are cars. |
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Answer» If only conclusion I FOLLOWS, |
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| 307. |
State whether the following statements are true of false. If false, give a reason. The matrices A_(2 xx 3) and B_(2 xx 3) are conformable for substraction. |
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| 308. |
Smt. Anagha Doshi purchased 22 shares of FV 100 for Market Value of 660. Find the sum invested. After taking 20% dividend, she sold all the shares when market value was 650. She paid 0.1% brokerage for each trading done. Find the percent of profit or loss in the share trading.(Write your answer to the nearest integer) |
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| 309. |
Find the (i) 30th term of the AP 10,7,4,…. (ii) 11th term fo the AP: -3, -1/2, 2……. |
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Answer» (II) `=22`. |
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| 311. |
Express each of the following as a fraction in simplest form :0.overline(8) (ii) 2.overline(4) (iii)0.overline(24) (iv)0.1overline2(vi)0.00608 |
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| 312. |
Show graphically the system of linear equationsx + 2y = 3and 4x + 3y = 2. |
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Answer» <P> SOLUTION :For equation, x + 2y = 3implies2y = 3 - ximplies `y = (3-x)/(2)` `{:(x,-3,-1,1),(y = (3-x)/(2),3,2,1):}` For equation, 4x + 3y = 2 `implies ""3y = 2 - 4x ""implies"" y =(2-4x)/(3)` `{:(x,-4,-1,2),(y = (2-4x)/(3),6,2,-2):}` Now PLOT the points A(-3, 3), B(-1, 2), C(1, 1) and P(-4, 6), Q(-1, 2), R(2, -2) on the same graph paper.  We observe that the two lines INTERSECT at POINT (-1, 2). Hence,`{:(x = - 1),(y = 2):}}` is the solution of the given system of equation. |
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| 313. |
Write first four terms of the AP, when the first term a and the common difference d are give as follows: (i) a=10,d=10 (ii) a=-2,d=0 (iii) a=4,d=-3 (iv) a=-1,d=1/2 (v) a=-1.25,d=-0.25 |
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| 314. |
State wether the following statements are true or false:(a) Prime factors of 6 are 2 and 3, represents a Statement.(b) Students can take French or Spanish as their third language. The "OR" used in the statement here is "INCLUSIVE OR".(c) Two lines intersect at a point or are parallel. The "OR" used in the statement here is "EXCLUSIVE OR".(d) The Compound statement "sqrt(2) is a rational number or an irrational number" is True.(e) The Compound Statement "All integers are either even or odd" is False. |
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Answer» (B)False (C)True (d)True (e)True |
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| 315. |
Determine the value of k for which k^2+4k + 8, 2k^2+ 3k + 6 and 3k^2 +4k + 4 are in A.P. |
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| 316. |
A right circular cone is of the height 3.6 cm and radius of its base is 1.6 cm . It is melted and recasted into a right circular cone with radius of its base 1.2 cm. Find the height of the cone so formed. |
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| 317. |
Can y + 1 be the remainder on division of a polynomial p(y) by y-5? Give reason. |
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| 319. |
A bag contains 3 red balls and 5 black balls. A ball is drawn at random from the bag. What is the probability that the ball drawn is (i) red? (ii) not red? |
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| 320. |
Solve the following pair of linear equations graphically : x+3y=6, 2x-3y=12 Also shade the region bounded by the line 2x-3y=12 and both the co-ordinate axes. |
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| 321. |
Check whether the following equations are consistent or inconsistent. Solve them graphically. 4/3x+2y = 8, 2x+3y = 12 |
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| 322. |
Arun said, “this girl is the wife of the grandson of my mother.” Who is Arun to the girl? |
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Answer» Father |
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| 323. |
Anil introduces Rohit as the son of the only brother of his father's wife. How is Rohit related to Anil? |
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Answer» SON |
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| 324. |
Write the common difference of the arithmetic progression whose nth term is a] n^(2) + 5 b] 2n^(2) -6 |
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Answer» `a_(1) = 1^(2) + 5=1 +5 =6` `a_(2) = 2^(2) + 5=4 +5 =9` `d=a_(2) -a_(1)= 9 -6 =3` B] `a= 2n^(2) -6` `a_(1) = 2(1)^(2) -6 =2 =-4` `a_(2) = 2 (2)^(2) -6 =8 -6 =2`. `d=a_(2) - a_(1) = 2- (-4)=6` |
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| 325. |
Who among P, Q, T, V and M is exactly in the middle when they are arranged in ascending order of their heights? I. V is taller than Q but shorter than M. II. T is taller than Q and M but shorter than P. |
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Answer» the data in statement I alone are sufficient to answer the question, while the data in statement II alone are not sufficient to answer the question, From II, we have : `TgtQ,TgtM,PgtT` Combining the above two, we have : `PgtTgtMgtVgtQ" i.e. "QltVltMltTltP`. Clearly, M is in the MIDDLE. |
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| 326. |
What is Rohan's rank from the top in the class of 30 students? I. Meera is 4 ranks below Rohan and twenty-first from the bottom. II. Arjun is two ranks above Rohan and is twenty-seventh from the bottom. |
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Answer» Solution :From I, it is clear that Rohan has (1 + 3 + 20) = 24 students below him in rank, NAMELY Meera, 20 students below Meera and 3 students between Rohan and Meera. Thus, there are [30- (24 + 1)] = 5 students above Rohan in rank. So Rohan is `6^(th)` from top. From II, we find that Arjun is `27^(th)` from the bottom i.e. `4^(th)` from the top. Since Arjun is two ranks above Rohan, so Rohan is `6^(th)` from the top. Thus, either I alone or II alone is sufficient to ANSWER the given quention. |
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| 327. |
Which of the following is not CORRECT ?? |
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Answer» ` sintheta = (-1)//(5)` |
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| 328. |
A boy standing on a horizontal plane finds a bird flying at a distane of 100 mfrom him at an elevation of 30^(@). A girl standing on the roof of a 20 m high building finds the angle of elevation of the same bird to be 45^(@). Boy and girl are on the opposite sides of the bird. Find the distance of the bird from the girl. |
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| 329. |
The sum of first 6 terms of an A.P. is 42. If its 10th and 30th terms are in the ratio 1 : 3, find a_8 and a_12. |
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| 330. |
Solve each the following pairs of equations by reducing them to a pair of linear equations. (vi) 2/x + 3/y = 13 5/x - 4/y = -2 |
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| 331. |
The radiusof a cone is 7 cm and slant height is 10 cm. Find the total surface area of the cone. |
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| 332. |
Two angles are complementary. The larger angle is 3^(@) less than twice the measure of the smaller angle. Find the measure of each angle. |
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| 333. |
A die is thrown once. The probabilty of getting a prime number is: |
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Answer» `2/3` |
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| 334. |
If A=[{:(,5,4),(,3,-1):}], B=[{:(,2,1),(,0,4):}] and C=[{:(,-3,2),(,1,0):}], find : (i) A+C (ii) B-A (iii) A+B-C |
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Answer» (II) `[{:(,-3,-3),(,-3,5):}]` (iii) `[{:(,10,3),(,2,3):}]` |
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| 335. |
If ( x^(2) - x -2)is a factorofx^(3) +3x^(2) +ax+ bcalculate the values of a and b . Write all the factor of the given expression. |
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| 336. |
A child prepares a poster on 'Save Energy'on a square sheetwhose each side measures 60 cm. At each cornerof the sheet. She draws a quadrant of radius17.5cm in whichshe shows the ways to save energy. At the centre, she draws a circle of diameter 21 cm and writes a slogan in it . Find the area of the remaining sheet .(a)write down the four waysby whichenergy can be saved.(b)Write a slogan on 'Save Energy' . (c)Why do we need to save energy ? |
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Answer» a (i)SAVING electricity by using CFLs, switchingoff APPLIANCES whennot in use. (ii)Saving WATER by using it efficiently. (iii)Saving petroleum resources by using public TRANSPORT. (iv)Using solar energy. (b) 'Save Energy, Save Environment'or any othergivne by students . (c)We should save energy to save our environment so that we can give a battertomorrowto the forthcominggenerations. |
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| 337. |
The taxi charges in Hyderabad are fixed, along with the charge for the distance covered. Upto first 3 km you will be charged a certain minimum amount. From there onwards you have to pay additionally for every kilometer travelled. For the first 10 km. the charge paid is Rs.166. For a journey of 15 km. the charge paid is Rs.256. i. What are the fixed charges and charge per km? ii. How much does a person have to pay for travelling a distance of 25 km? |
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| 338. |
Solve each the following pairs of equations by reducing them to a pair of linear equations. (ii) x+y/xy = 2 x-y/xy = 6 |
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| 339. |
Find all the zeros of p(x) = x^3-9x^2 – 12x + 20 if (x+2) is a factor of p(x). |
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| 340. |
Prove that : (tan theta)/(1 - cot theta) + (cot theta)/(1 - tan theta) = 1 + sec theta cosec theta . |
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| 342. |
Solve the following systems of inequalities for all xinRA milkman has 80% milk in this stock of 800 litres of adultered milk. How much 100% pure milk is to be added to it so that purity is between 90% and 95%? |
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| 343. |
Seema purchased a Dry fruits from 'Super market. The discount of 2% was given on the printed price of 9,000. Rate of GST charged was 12%. Find the purchase price of dry fruits. Also find amount of GST. |
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| 344. |
find the equation of cicle in each of the following cases ) (f)touches the y-axis at origin and having radius =6 units |
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| 346. |
If (x-1)^(2) is a factor of f (x)=x^(3)+bx+c , then find the remainder when f (x) is divided by (x-2). |
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Answer» 2 `:.` Third root =-2. (ii)Apply factro THEOREM. (iii)To obtain the remainder , USE the remaindertheorem. |
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| 347. |
You are given two series in two rows. In the first row, a full series is given which follows a specific pattern. The second row has a series, similar to the first series but only first element of this series is produced followed by (A), (B), (C), (D) and (E) for the subsequent elements. You have to complete the series starting with a given number and answer the question that follows. {:("3","40","176","537","1078","1079"),("1","A","B","C","D","E"):} What will come in place of E? |
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Answer» 839 `xx5+5^(2),xx4+4^(2),xx3+3^(2),xx2+2^(2),xx1+1^(2)`. So the new series is : 1, 30, 136, 417, 838, 839. |
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| 348. |
You are given two series in two rows. In the first row, a full series is given which follows a specific pattern. The second row has a series, similar to the first series but only first element of this series is produced followed by (A), (B), (C), (D) and (E) for the subsequent elements. You have to complete the series starting with a given number and answer the question that follows. {:("9","10","16","57","212","1085"),("2","A","B","C","D","E"):} What will come in place of C? |
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Answer» 37 `xx1+1^(2),xx2-2^(2),xx3+3^(2),xx4-4^(2),xx5-5^(2)`. So ACCORDINGLY, the new series BECOMES 2, 3, 2, 15, ____. |
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| 349. |
You are given two series in two rows. In the first row, a full series is given which follows a specific pattern. The second row has a series, similar to the first series but only first element of this series is produced followed by (A), (B), (C), (D) and (E) for the subsequent elements. You have to complete the series starting with a given number and answer the question that follows. {:("3","8","30","132","680","4110"),("4","A","B","C","D","E"):} What will come in place of C? |
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Answer» 156 `xx2+2,xx3+6,xx4+12,xx5+20,xx6+30` STARTING with 4, the new SERIES is 4, 10, 36, 156. |
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| 350. |
B takes 16 days less than A to do a certain piece of work. If both working together can complete the work in 15 days, in how many days will B alone complete the work ? |
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