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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.
| 96751. |
Fill in the BlanksThe combination of rational and irrational number is called ____ number. |
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Answer» The combination of rational and irrational number is called Real number |
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| 96752. |
x2 |
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Answer» \(f(x) =\begin{cases}ax^2 & \quad \text{0<} x \text{<1}\\x+3 & \quad \text{1<}x< \text{2}\\4& \quad \text{x} = \text{1}\end{cases}\) f(x) is not continuous at x = 1 Left hand limit of f(x) at x = 1 is f(1-) = \(\lim\limits_{x \to 1^-}\) f(x) = \(\lim\limits_{x \to 1}\) ax2 = a Right hand limit of f(x) at x = 1 is f(1+) = \(\lim\limits_{x \to 1^+}\) f(x) = \(\lim\limits_{x \to 1}\) (x + 3) = 1 + 3 = 4 f(1) = 4 ∵ f(1+) = f(1) and f is not continuous at x = 1. Therefore f(1-) ≠ f(1+) ⇒a ≠ 4 (∵ f (1-)= a) Hence, a ∈ R-{4}, then f(x) is not continuous at x = 1. |
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| 96753. |
Express the following numbers as a product of powers of prime factors:(i) 72 (ii) 432 (iii) 1000 (iv) 16000 |
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Answer» (i) 72 = 2×2×2×3×3 = 23×32 (ii) 432 = 2×2×2×2×3×3×3 = 24×33 (iii) 1000 = 2×2×2×5×5×5 = 23×53 (iv) 16000 = 2×2×2×2×2×2×2×5×5×5 = 27×53 |
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| 96754. |
If a and b are co-prime numbers, then find the HCF (a, b). |
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Answer» The HCF (a, b) is 1 |
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| 96755. |
What will curved surface area of Hemisphere whose volume is 19404 cm3.(a) 2772 cm2(b) 3696 cm2(c) 3632 cm2(d) 2316 cm2 |
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Answer» What will curved surface area of Hemisphere whose volume is 19404 cm3.2772 cm2 |
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| 96756. |
On comparing the ratios of the coefficients, find out whether the pair of equations x – 2y = 0 and 3x + 4y - 20 = 0 is consistent or inconsistent. |
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Answer» x – 2y = 0 3x + 4y - 20 = 0 \(\frac{1}{3}\) ≠ \(\frac{-2}{4}\) As, \(\frac{a1}{a2}\) ≠ \(\frac{b1}{b2}\) is one condition for consistency. Therefore, the pair of equations is consistent. |
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| 96757. |
Define fundamental theorem of arithmetic |
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Answer» "Every composite number can be factorized as a product of primes, and this factorization is unique, apart from the order in which the prime factors occur." |
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| 96758. |
Express 156 as the product of primes. |
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Answer» 156 = 22 x 3 x 13 |
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| 96759. |
Let \( \lambda \) be an integer. If the shortest distance between the lines\( x-\lambda=2 y-1=-2 z \) and \[ x=y+2 \lambda=z-\lambda \] is \( \frac{\sqrt{7}}{2 \sqrt{2}} \) then the value of \( |\lambda| \) is |
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Answer» We know that distance between two show line \(\frac{x-x_1}{a_1}=\frac{y-y_1}{b_1}=\frac{z-z_1}{c_1}\) and \(\frac{x-x_2}{a_2}=\frac{y-y_2}{b_2}=\frac{z-z_2}{c_2}\) is d = \(\cfrac{\begin{vmatrix}x_2-x_1&y_2-y_1&z_2-z_1\\a_1&b_1&c_1\\a_2&b_2&c_2\end{vmatrix}}{\sqrt{(b_1c_2-b_2c_1)^2+(c_1a_2-c_2a_1)^2+(a_1b_2-a_2b_1)^2}}\) Given lines are x - λ = 2y - 1 = -2z ⇒ \(\frac{x-\lambda}1=\cfrac{y-\frac12}{\frac12}=\cfrac{z}{\frac{-1}2}\) and x = y + 2λ = z - λ ⇒ \(\frac{x-0}1 = \frac{y-(-2\lambda)}1 = \frac{z-\lambda}1\) \(\therefore\) x1 = λ, y1 = 1/2, z1 = λ a1 = 1, b1 = 1, c2 = 1 and a2 = 1, b2 = 1 c2 = 1 \(\therefore\) d = \(\cfrac{\begin{vmatrix}0-\lambda&-2\lambda-1/2&\lambda-0\\1&1/2&-1/2\\1&1&1\end{vmatrix}}{\sqrt{(1/2+1/2)^2+(-1/2-1)^2+(1-1/2)^2}}\) Given that distance between them is \(\frac{\sqrt7}{2\sqrt2}\) \(\therefore\) \(\cfrac{\begin{vmatrix}-\lambda&-2\lambda-1/2&\lambda\\1&1/2&-1/2\\1&1&1\end{vmatrix}}{\sqrt{1+9/4+1/4}}\) \(=\frac{\sqrt7}{2\sqrt2}\) ⇒ \(\cfrac{-\lambda\begin{vmatrix}1/2&-1/2\\1&1\end{vmatrix}+(2\lambda+1/2)\begin{vmatrix}1&-1/2\\1&1\end{vmatrix}+\lambda\begin{vmatrix}1&1/2\\1&1\end{vmatrix}}{\sqrt{\frac72}}\) = \(\frac{\sqrt7}{2\sqrt2}\) ⇒ -λ(1/2 + 1/2) + (2λ + 1/2)(1 + 1/2) + λ(1 - 1/2) = \(\frac{\sqrt7}{2\sqrt2}\times\frac{\sqrt7}{\sqrt2}\) ⇒ -λ + 3λ + 3/4 + λ/2 = 7/4 ⇒ \(\frac{2\lambda+6\lambda+\lambda}2\) = \(\frac74-\frac34 = \frac44=1\) ⇒ 5λ = 2 ⇒ λ = 2/5 |
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| 96760. |
Write a quadratic polynomial, sum of whose zeroes is 2 and product is -8. |
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Answer» Quadratic polynomial is given by x2 - (a + b)x + ab x2 - 2x - 8 |
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| 96761. |
State the fundamental Theorem of Arithmetic. |
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Answer» Every composite number can be expressed (factorized) as a product of primes, and this factorization is unique, apart from the order in which the factors occur. |
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| 96762. |
Given that HCF (96,404) is 4, find the LCM ( 96,404). |
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Answer» HCF X LCM = Product of two numbers LCM (96,404) = \(\frac{96\times404}{HCF(96,404)}\) = \(\frac{96\times404}{4}\) LCM = 9696 |
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| 96763. |
Number of necklaces of 8 coloured stoned made by 15 coloured stones. |
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Answer» Number of neckless of 8 coloured stone made by 15 coloured stone = 15C8 = \(\cfrac{15\times14\times13\times12\times11\times10\times9\times8!}{8!\times7\times6\times5\times4\times3\times2\times1}\) = 6435 |
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| 96764. |
The sum of all three-digit numbers less than or equal to 500, that are formed without using the digit 1 and they all are multiple of 11 is |
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Answer» Such numbers are 11 x 19, 11 x 20, 11 x 22, 11 x 23,....., 11 x 28, 11 x 30, 11 x 32,....., 11 x 37, 11 x 39, 11 x 40, 11 x 42,.....,11 x 45 Sum = 11 (19 + ..... + 45 - 21 - 29 - 31 - 38 - 41) = 11 (1 + ..... + 45 - 160 - (1 + 2 + 3 + ..... + 18)) = 11 (1035 - 160 - 171) = 11 x 704 = 7744 |
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| 96765. |
The radii of two circles are 8 cm and 6 cm respectively. Find the radius of the circle having area equal to the sum of the areas of the two circles. |
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Answer» Answer:Area of first circle = πr2 = π82 = 64π sq cm Area of second circle = π62 = 36π sq cm As per question; area of the largest circle = 64π + 36π = 100π sq cm Or, πr2 = 100π Or, r2 = 100 Or, r = 10 cm |
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| 96766. |
Permutation and combination |
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Answer» Arranging people, digits, numbers, alphabets, letters, and colours are examples of permutations. Selection of menu, food, clothes, subjects, the team are examples of combinations. |
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| 96767. |
Complete the incomplete sentences in the Paragraph by using either “much” or “many” or “a lot of” or “some” in the blanks.[Note: We usually use “a lot of” in positive sentences and “much”, “many” in negative and interrogative sentences.]How………… money has Rekha got? Ten rupees. How……….mangoes can she buy? She can buy about fourteen. But Rahul hasn’t got………money. He can’t buy……mangoes. He can buy…….bananas. Are there……..bananas in the shop? Yes, there are……….. Gopal has………money. He is rich. He will go to the big shop in the corner and buy……..things. Are there…..people in that shop? Not………., but there are…….women………..are buyingice-cream……… are buying toffees……….women are drinking coca-cola. |
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Answer» How much money has Rekha got? Ten rupees. How many mangoes can she buy? She canbuy about fourteen. But Rahul hasn’t got a lot of money. He can’t buy many mangoes. He can buy some bananas. Are there many bananas in the shop? Yes, there are a lot of. Gopal has a lot of money. He is rich. He will go to the big shop in the corner and buy many things. Are there many people in that shop? Not many but there are some women some are buying ice-cream some are buying toffees some women are drinking coca-cola. |
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| 96768. |
He felt that he ___ it wrong. A) has made B) made C) will make D) was made E) had made |
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Answer» Correct option is E) had made |
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| 96769. |
We _____ write an essay on the book after we’d read it. A) had to B) have to C) will have to D) must |
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Answer» Correct option is A) had to |
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| 96770. |
I couldn’t imagine what ___ to her. A) had happened B) has been happened C) will happen D) has been happening E) happens |
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Answer» Correct option is A) had happened |
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| 96771. |
Complete the incomplete sentences in the Paragraph below using there is, there are, is there, are there in the blanks. . . . . . . . . … any trains at the station? yes… . . . . …. three trains right now. On platforms number one… . . . . . …a passenger train. It is going to Kanpur. . . . . . . . . . . . … not many people in this train. People do not like to travel by passenger train…………a goods train on platform number five. It is quite a big train………… no passengers in this train. Almost all the wagons are locked. On platform number seven……….a mail train. It is a very fast train. It is going to Bombay……..four first-class compartments in the train………… A ladies’ compartment also? Yes……..two. Both the compartments are fully packed…………… a sleeper coach in this train? Yes, a big one……… more than seventy berths in it. I am thirsty. I want to have some tea……….any tea’ stalls on platform number seven? I am sure……..one. Let us see…………five tea stalls on this platform………..many things to eat in one of them. The others sell only tea and biscuits. Let us go to the first one, because………..many eatables in that stall. |
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Answer» Are these any trains at the station? yes, there are three trains right now. On platform number one there is a passenger train. It is going to Kanpur. There are not many people in this train. People do not like to travel by passenger train there is a goods train on platform number five. It is quite a big train there is no passengers in this train. Almost all the wagons are locked. On plaform number seven there is a mail train. It is a very fast train. It is going to Bombay there are four first-class compartments in the train. Is there a ladies’ compartment also? Yes, there are two. Both the compartments are fully packed. Is there a sleeper coach in this train? Yes, a big one there are more than seventy berths in it.I am thirsty. I want to have some tea are there any tea stalls on platform number seven? I am sure there is one. Let us see there are five tea stalls on this platform there are many things to eat in one of them. The others sell only tea and biscuits. Let us go to the first one, because there are many eatables in that stall. |
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| 96772. |
You have been provided with three test tubes. One of them contains distilled water and the other two contain an acidic solution and a basic solution respectively. If you are given only red litmus paper, how will you identify the contents of each test tube? |
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Answer» Three test tube A, B, C (i) A contains distilled water (ii) B contains acidic & C contains basic solution. On adding red litmus paper A → no change B → no change C → Turn to blue |
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| 96773. |
The sky _____ seen because of the pollution. A) can not B) can’t be C) might be D) must be |
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Answer» Correct option is B) can’t be |
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| 96774. |
Robert is a millionaire’s son. He _____ never_____ worry about anything in life. A) is / has to B) had / had to C) has / had to D) doesn’t / have to |
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Answer» Correct option is C) has / had to |
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| 96775. |
Read the following sentences given below carefully.Here is a description of what is happening now in Dr. Misra’s house. Read it carefully. Imagine that all this happened last week. Rewrite the Paragraph by making necessary changes. The car stops infront of Dr. Misra’s house. Vinay gets out of the car and rings the door bell. The door is opened by a maid servant. “Is Dr. Misra at home?” asks Vinay, “I must see him immediately. Tell him Dr. Murthy has sent me.” The maid servant shows him into the sitting room and goes into the house.Dr. Misra appears soon after. Vinay gets up from his chair and say, “I am Vinay, Dr. Murthy’s son. My father is ill. He has sent me to fetch you.” Dr. Misra gets ready in no time and hurries out. Vinay opens the door of the car. Dr. Misra gets into the car. Vinay sits beside him; he is nervous. He is still. Both of them sit quiet. |
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Answer» The car stopped infront of Dr. Misra’s house. Vinay got out of the car and rang the door bell. The door was opened by a maid servant. “Is Dr. Misra athome?” asked Vinay, “I must see him immediately. Tell him Dr. Murthy has sent me.” The maid servant showed him into the sitting room and went into thehouse. Dr. Misra appeared soon after. Vinay got up from his chairand said, “I am Vinay, Dr. Murthy’s son. My father is ill. He has sent me to fetch you. ” Dr. Misra got ready in no time and hurriest out. Vinay opened the door of the car. Dr. Misra got into the car. Vinay sat beside him; he was nervous. He was still. Both of them sat quiet. |
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| 96776. |
Assertion: In Newlands’s octaves, the properties of lithium and sodium were found to be same. Reasons: Sodium is the eighth element after lithium.a) Both A and R are true, and R is correct explanation of the assertion.b) Both A and R are true, but R is not the correct explanation of the assertion.c) A is true, but R is false.d) A is false, but R is true. |
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Answer» (a) Both A and R are true, and R is correct explanation of the assertion |
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| 96777. |
You have been provided with three test tubes. One of them contains distilled water and the other two contain an acidic solution and a basic solution, respectively. It you are given only red litmus paper, how will you identify the contents of each test tube? |
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Answer» Add few drops of solution from all three test tubes on the red litmus paper separately. The solution which turns red litmus to blue contains basic solution. Now, we use this blue litmus paper to test the solutions in other two test tubes. The solution from the test tube which turns blue litmus paper to red will be the acidic solution and solution of the test tube which do not change either red or blue litmus paper contain water. |
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| 96778. |
If only ________ it, none of this would’ve happened. A) I wouldn’t have mentioned B) I hadn’t mentioned C) I haven’t mentioned D) I would’ve mentioned |
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Answer» Correct option is B) I hadn’t mentioned |
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| 96779. |
They _____ rather see a larger apartment. A) had B) have C) would D) will |
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Answer» Correct option is C) would |
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| 96780. |
The importance of carbon seems to be immense, in spite of small amount of carbon available in nature. Comment. |
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Answer» Food, clothes, medicines, books or many of the things are all based on versatile element carbon. In addition, all living structures are carbon based. The amount of carbon present in the earth’s crust and in the atmosphere is quite meagre. The earth’s crust has only 0.02% carbon in the form of minerals (like carbonates, hydrogen-carbonates, coal and petroleum) and the atmosphere has 0.03% of carbon dioxide. In spite of this small amount of carbon available in nature, it is available in the form of hydrocarbon such as fossil fuel, methane gas and crude oil. Carbon fibres have multiple uses since they are strong, yet light weight, durable material. These fibres are used in making tennis rackets, fishing rods, even aeroplane and rockets. The industrial diamonds are used for drilling and cutting rocks. Carbon cycle, carbon dating, greenhouse effect, all are life sustaining processes on earth. |
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| 96781. |
The phone is ringing. _____ I answer it? A) Will B) Would C) Shall D) Won’ t |
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Answer» Correct option is C) Shall |
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| 96782. |
I_____ sorry if she had left. A) will be B) would’ve been C) would be D) had been |
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Answer» Correct option is B) would’ve been |
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| 96783. |
Hardly _____ I_____ the phone down when it started ringing again. A) did / put B) will have / put C) did / to have put D) had / put |
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Answer» Correct option is D) had / put |
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| 96784. |
You ______ pleased to hear that your father______ to the committee. A) have been / selected B) will be / has been selected C) are / is selecting D) have been / was selected |
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Answer» Correct option is B) will be / has been selected |
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| 96785. |
In the years ahead, it seems likely that people ______ even greater control over nature. A) to acquire B) will be acquired C) will acquire D) will have been acquired |
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Answer» Correct option is C) will acquire |
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| 96786. |
The Prime Minister refuses to enter into negotiations with the railway men until they ______ all ______ to work. A) are / return B) have / returned C) had / returned D) will / have I returned |
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Answer» Correct option is B) have / returned |
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| 96787. |
He ______ a cold for the last three days. A) is fighting off B) will have fought off C) has been fighting off D) was fighting off |
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Answer» Correct option is C) has been fighting off |
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| 96788. |
I usually _____ for 6 hours a day, but I _____ for 8 hours yesterday. A) work / worked B) works / worked C) worked / worked D) work / work |
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Answer» A) work / worked |
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| 96789. |
If we compare the mass of hydrogen in a star with the rate at which energy ______, we can estimate its potential life. A) is being emitted B) be emitted C) was emitted D) will be emitted |
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Answer» Correct option is A) is being emitted |
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| 96790. |
Children are forbidden to play with matches ____ they may get burned. A) so that B) for fear that C) if D) when |
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Answer» Correct option is B) for fear that |
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| 96791. |
He ______ from the company for several years before they found him out. A) has been stealing B) had been stealing C) was stealing D) will have been stolen |
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Answer» Correct option is B) had been stealing |
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| 96792. |
Yesterday Stephen studied for five hours ________. A) on end B) at length C) in full D) in time E) at once |
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Answer» Correct option is A) on end |
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| 96793. |
Describe any important object of sculpture made by the Harappan |
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Answer» An important object of sculpture made by the Harappans is the Dancing Girl. Dancing Girl is a sculpture made from bronze, created over 4500 years ago in the city of Mohenjo daro in the Indus Valley Civilisation. |
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| 96794. |
He won’t be able to finish studying those reports at the office. He wants to ____ at home. A) look for themB) look after them C) look them over D) look them up |
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Answer» Correct option is C) look them over |
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| 96795. |
It has been predicted that within the next 50 years, scientists ______ a drug to prolong life up to 150 years or more. A) are producing B) to be produced C) will be produced D) will have produced |
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Answer» Correct option is D) will have produced |
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| 96796. |
By April 2010, he ______ for this organization for fifteen years. A) has been working B) will be working C) will have been working D) had been working |
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Answer» Correct option is C) will have been working |
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| 96797. |
We ______ at the Italian restaurant last night, but it was full, so we ate somewhere else. A) were eating B) were going to eat C) are going to eat D) had eaten |
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Answer» Correct option is B) were going to eat |
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| 96798. |
His parents ______ married for eight years when he was born. A) have been B) will be C) had been D) were |
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Answer» Correct option is C) had been |
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| 96799. |
He won’t be able to drive his car unless he ________ his license. A) remits B) reforms C) revises D) reports E) renews |
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Answer» Correct option is E) renews |
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| 96800. |
What a pretty dress! Turn _____ ! Let me look at it from the back. A) up B) round C) away D) on |
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Answer» Correct option is B) round |
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