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MCQOPTIONS
This section includes 1900 Mcqs, each offering curated multiple-choice questions to sharpen your 9th Class knowledge and support exam preparation. Choose a topic below to get started.
| 401. |
Over a 70 days period David records the number of phone calls he receives. The graph of his data is shown alongside. The Possibility that on any day David will receive at least 3 phone calls. |
| A. | 0.453 |
| B. | 0.534 |
| C. | 0.543 |
| D. | 0.435 |
| Answer» C. 0.543 | |
| 402. |
The probability that a red marble selected at random from a jar containing \[x\]red, y blue and z green marbles is ____. |
| A. | \[\frac{y}{x+y+z}\] |
| B. | \[\frac{x+z}{x+y+z}\] |
| C. | \[\frac{x}{x+y+z}\] |
| D. | \[\frac{y+z}{x+y+z}\] |
| Answer» D. \[\frac{y+z}{x+y+z}\] | |
| 403. |
In a throw of a die, what is the probability of getting a prime number? |
| A. | 2 |
| B. | \[\frac{1}{2}\] |
| C. | \[\frac{3}{2}\] |
| D. | 6 |
| Answer» C. \[\frac{3}{2}\] | |
| 404. |
A coloured cube is cut into 64 equal cubes as shown alongside. What is the probability that a cube selected randomly has one face painted? |
| A. | \[\frac{9}{16}\] |
| B. | \[\frac{3}{16}\] |
| C. | \[\frac{3}{8}\] |
| D. | \[\frac{2}{5}\] |
| Answer» D. \[\frac{2}{5}\] | |
| 405. |
Krish went to play a lucky draw contest. 70 tickets of a lucky draw were sold. If the probability of Krish winning the draw is\[\frac{1}{14},\]then the number of tickets bought by Krish is ___. |
| A. | 5 |
| B. | 10 |
| C. | 15 |
| D. | 20 |
| Answer» B. 10 | |
| 406. |
Find the probability that in a family of 3 children, there will be at least one boy. |
| A. | \[\frac{3}{4}\] |
| B. | \[\frac{1}{8}\] |
| C. | \[\frac{3}{8}\] |
| D. | \[\frac{5}{8}\] |
| Answer» B. \[\frac{1}{8}\] | |
| 407. |
1500 families with 2 children were selected randomly and the following data were recorded. What is the possibility of a family chosen at random having at least 1 girl. Number of girls in a family 2 1 0 Number of families 475 825 200 |
| A. | \[\frac{11}{15}\] |
| B. | \[\frac{11}{15}\] |
| C. | \[\frac{2}{15}\] |
| D. | \[\frac{13}{15}\] |
| Answer» E. | |
| 408. |
What is the probability of getting a number greater than 2 or an even number in a single throw of a fair die? |
| A. | \[\frac{1}{3}\] |
| B. | \[\frac{2}{3}\] |
| C. | \[\frac{5}{6}\] |
| D. | \[\frac{1}{6}\] |
| Answer» D. \[\frac{1}{6}\] | |
| 409. |
An organisation selected 2400 families at random and surveyed them to determine a relationship between cities and the number of vehicles in a family. The information collected is listed in the table below. What is the possibility that the family chosen in Delhi has at least 2 cars? Cities Vehicles per family 0 1 2 3 Delhi 0 160 25 0 Mumbai 0 305 27 2 Kolkata 1 535 29 1 Chennai 2 469 59 25 Bengaluru 1 579 82 88 |
| A. | \[\frac{37}{480}\] |
| B. | \[\frac{39}{240}\] |
| C. | \[\frac{37}{120}\] |
| D. | \[\frac{37}{140}\] |
| Answer» B. \[\frac{39}{240}\] | |
| 410. |
In a lottery, there are 10 prizes and 25 blanks. A lottery is drawn at random. What is the probability of getting a prize? |
| A. | 10/35 |
| B. | 25/35 |
| C. | 15/35 |
| D. | None of these |
| Answer» B. 25/35 | |
| 411. |
If a coin is tossed twice, what is the probability of getting atleast one head? |
| A. | \[\frac{1}{2}\] |
| B. | \[\frac{1}{4}\] |
| C. | \[\frac{3}{4}\] |
| D. | \[\frac{2}{3}\] |
| Answer» D. \[\frac{2}{3}\] | |
| 412. |
To know the opinion of the students about the subject probability a survey of 500 students also was recorded in the following data. What is the possibilities that a student chosen at random has no opinion? Opinion Number of students Like 145 Dislike 230 No opinion 125 |
| A. | \[\frac{5}{9}\] |
| B. | \[\frac{1}{4}\] |
| C. | \[\frac{1}{3}\] |
| D. | \[\frac{1}{2}\] |
| Answer» C. \[\frac{1}{3}\] | |
| 413. |
Ram and Priya are playing a game. Ram's winning probability is \[\frac{1}{3}\]and sum of their winning probabilities is 1. Numerator of Priya's winning probability is ___. |
| A. | 2 |
| B. | 1 |
| C. | 3 |
| D. | None of these |
| Answer» B. 1 | |
| 414. |
A book containing 100 pages is opened at random. Find the probability that a doublet page is found. |
| A. | \[\frac{9}{100}\] |
| B. | \[\frac{9}{10}\] |
| C. | \[\frac{1}{10}\] |
| D. | \[\frac{1}{5}\] |
| Answer» B. \[\frac{9}{10}\] | |
| 415. |
A bag contains 5 red balls and some blue balls. If the probability of drawing a blue ball is double that of a red ball, find the number of blue balls in the bag. |
| A. | 15 |
| B. | 12 |
| C. | 5 |
| D. | 10 |
| Answer» E. | |
| 416. |
Robert recorded the length of TV commercial in seconds. His results are summarized in the table. The possibility that a randomly chosen TV commercial will show between 20 seconds and a minute. Length Frequency \[0\le t |
| A. | 0.137 |
| B. | 0.317 |
| C. | 0.731 |
| D. | 0.371 |
| Answer» D. 0.371 | |
| 417. |
A card is drawn at random from a well shuffled pack of 52 cards. The probability that the card drawn is neither a red card nor a queen is ____. |
| A. | \[\frac{6}{13}\] |
| B. | \[\frac{5}{13}\] |
| C. | \[\frac{4}{13}\] |
| D. | \[\frac{2}{13}\] |
| Answer» B. \[\frac{5}{13}\] | |
| 418. |
Find the probability for a randomly selected number out of 1, 2, 3, 4, .?., 25 to be a prime number. |
| A. | \[\frac{2}{25}\] |
| B. | \[\frac{23}{25}\] |
| C. | \[\frac{2}{5}\] |
| D. | \[\frac{9}{25}\] |
| Answer» E. | |
| 419. |
A box contains 5 green balls and some white balls. If the probability of drawing a white ball is half of the probability of drawing a green ball, then find the number of white balls in the box. |
| A. | 10 |
| B. | 5 |
| C. | 15 |
| D. | 20 |
| Answer» B. 5 | |
| 420. |
A card is drawn from a packet of 100 cards numbered 1 to 100. Find the probability of drawing a number which is a square. |
| A. | \[\frac{1}{10}\] |
| B. | \[\frac{9}{100}\] |
| C. | \[\frac{1}{100}\] |
| D. | \[\frac{1}{50}\] |
| Answer» B. \[\frac{9}{100}\] | |
| 421. |
Jayesh does a lot of travelling in his car. So he records how often he fills his car with CNG. The table alongside shows the frequencies of the number of days between refills. The possibility that between there is a gap of at least 5 days? Day between refills Frequency 1 36 2 80 3 41 4 17 5 15 6 11 |
| A. | 0.08 |
| B. | 0.18 |
| C. | 0.108 |
| D. | 0.082 |
| Answer» B. 0.18 | |
| 422. |
Three coins are tossed simultaneously 100 times. The following outcomes are recorded- Outcomes 3 tails 2 tails 1 tail no tail Frequency 23 28 23 Find the probability of getting more than one tail. |
| A. | \[\frac{49}{100}\] |
| B. | \[\frac{27}{50}\] |
| C. | \[\frac{51}{100}\] |
| D. | \[\frac{23}{100}\] |
| Answer» D. \[\frac{23}{100}\] | |
| 423. |
This table shows how long Naidu slept each night recently. The probability that tonight he will sleep for between 5 and 7 hours. Hours Slept Frequency \[5\le h |
| A. | 0.248 |
| B. | 0.224 |
| C. | 0.213 |
| D. | 0.220 |
| Answer» E. | |
| 424. |
An urn contains 11 oranges, 8 mangoes and 13 apples. A fruit is drawn at random. What is the probability of not drawing an apple? |
| A. | \[\frac{15}{32}\] |
| B. | \[\frac{19}{32}\] |
| C. | \[\frac{11}{32}\] |
| D. | \[\frac{13}{32}\] |
| Answer» C. \[\frac{11}{32}\] | |
| 425. |
A bag contains 3 white and 5 red balls. If a ball is drawn at random, find the probability that it is red. |
| A. | \[\frac{3}{8}\] |
| B. | \[\frac{5}{8}\] |
| C. | \[\frac{3}{15}\] |
| D. | \[\frac{5}{15}\] |
| Answer» C. \[\frac{3}{15}\] | |
| 426. |
Direction: for question number 14 ? 17. If A and B be two mutually exclusive events in a sample space such that. \[\operatorname{P}(A)\,=\frac{2}{5}\]and \[\operatorname{P}(B)\,=\frac{1}{2}\] then Find \[\operatorname{P}\left( \overline{A}\cap B \right)\]: |
| A. | \[\frac{1}{2}\] |
| B. | \[\frac{3}{5}\] |
| C. | \[\frac{4}{7}\] |
| D. | \[\frac{7}{15}\] |
| E. | None of these |
| Answer» B. \[\frac{3}{5}\] | |
| 427. |
Direction: for question number 14 ? 17. If A and B be two mutually exclusive events in a sample space such that. \[\operatorname{P}(A)\,=\frac{2}{5}\]and \[\operatorname{P}(B)\,=\frac{1}{2}\] then Find \[\operatorname{P}\left( \overline{A}\cap \overline{B} \right)\]: |
| A. | \[\frac{4}{5}\] |
| B. | \[\frac{1}{10}\] |
| C. | \[\frac{8}{9}\] |
| D. | \[\frac{13}{20}\] |
| E. | None of these |
| Answer» C. \[\frac{8}{9}\] | |
| 428. |
The dot plot alongside show how many times Ravindran went jogging in each of last 32 weeks. The possibility that next week Ravindaran will not go jogging. |
| A. | 0.13 |
| B. | 0.156 |
| C. | 0.167 |
| D. | 0.187 |
| Answer» C. 0.167 | |
| 429. |
Alexander records the number of phone calls he receives over a period of consecutive days. What is the probability that on a particular day Alexander will receive 5 or more phone calls? |
| A. | \[0.\overline{5}\] |
| B. | \[0.\overline{4}\] |
| C. | \[0.\overline{3}\] |
| D. | \[0.\overline{2}\] |
| Answer» E. | |
| 430. |
A small child has a collection of shapes. She chooses one of the shapes at random. What is the possibility that it is a rectangle? |
| A. | \[\frac{1}{2}\] |
| B. | \[\frac{4}{13}\] |
| C. | \[\frac{1}{4}\] |
| D. | \[\frac{1}{6}\] |
| Answer» D. \[\frac{1}{6}\] | |
| 431. |
Without looking at any page, a number is chosen at random from the page. What is the probability that the digit at the units place of the number chosen is greater than 6? |
| A. | \[\frac{3}{10}\] |
| B. | \[\frac{6}{10}\] |
| C. | \[\frac{4}{10}\] |
| D. | None of these |
| Answer» B. \[\frac{6}{10}\] | |
| 432. |
Two dice are thrown at a time. What is the probability that the difference of the numbers shown on the dice is 1? |
| A. | \[\frac{5}{18}\] |
| B. | \[\frac{1}{36}\] |
| C. | \[\frac{1}{6}\] |
| D. | \[\frac{7}{36}\] |
| Answer» B. \[\frac{1}{36}\] | |
| 433. |
100 people arriving at the beach are asked their age. The results are shown alongside. Assuming that they give honest replies. What is the possibility that a randomly selected person on the beach will be aged between 30 or more? Age Frequency 0-9 25 10-19 17 20-29 31 30-39 20 40 7 |
| A. | 0.273 |
| B. | 0.270 |
| C. | 0.271 |
| D. | 0.272 |
| Answer» C. 0.271 | |
| 434. |
A shared garden area has 16 patches owned by 16 different people. The patches are separated by fences as shown. If a patch is selected at random, then what is the possibilities that it has three shared fences? |
| A. | \[\frac{1}{3}\] |
| B. | \[\frac{1}{4}\] |
| C. | \[\frac{1}{2}\] |
| D. | \[\frac{1}{6}\] |
| Answer» D. \[\frac{1}{6}\] | |
| 435. |
There are 25 cards numbered from 1 to 25. One card is drawn at random. What is the, probability that the number on this card is not divisible by 3? |
| A. | \[\frac{6}{25}\] |
| B. | \[\frac{17}{25}\] |
| C. | \[\frac{19}{25}\] |
| D. | \[\frac{11}{25}\] |
| Answer» C. \[\frac{19}{25}\] | |
| 436. |
In an experiment, what is the sum of probabilities of all events? |
| A. | 0.5 |
| B. | 1 |
| C. | -2 |
| D. | \[\frac{3}{8}\] |
| Answer» C. -2 | |
| 437. |
The product\[(a+b)(a-b)({{a}^{2}}-ab+{{b}^{2}})\]\[({{a}^{2}}+ab+{{b}^{2}})\] is equal to ___. |
| A. | \[{{a}^{6}}+{{b}^{6}}\] |
| B. | \[{{a}^{6}}-{{b}^{6}}\] |
| C. | \[{{a}^{3}}-{{b}^{3}}\] |
| D. | \[{{a}^{3}}+{{b}^{3}}\] |
| Answer» C. \[{{a}^{3}}-{{b}^{3}}\] | |
| 438. |
If\[({{x}^{2}}+3x+5)({{x}^{2}}-3x+5)={{m}^{2}}-{{n}^{2}}\], find\[m\]. |
| A. | \[{{x}^{2}}-3x\] |
| B. | \[3x+5\] |
| C. | \[{{x}^{2}}+5\] |
| D. | \[{{x}^{2}}-5\] |
| Answer» D. \[{{x}^{2}}-5\] | |
| 439. |
If \[(x+k)\] is a common factor of \[f(x)=({{x}^{2}}+px+q)\]and\[g(x)=({{x}^{2}}+lx+m),\]then the value of k is ____. |
| A. | \[l+p\] |
| B. | \[m-q\] |
| C. | \[\frac{l-p}{m-q}\] |
| D. | \[\frac{m-q}{l-p}\] |
| Answer» E. | |
| 440. |
If the factors of\[{{a}^{2}}+{{b}^{2}}+2(ab+bc+ca)\]are\[(a+b+m)\]and\[(a+b+nc)\], find the value of\[m+n\]. |
| A. | \[0\] |
| B. | \[2\] |
| C. | \[4\] |
| D. | \[6\] |
| Answer» C. \[4\] | |
| 441. |
if \[~{{a}^{4}}+{{b}^{4}}={{x}^{2}}{{y}^{2}}\], then \[\left( {{\mathbf{a}}^{\mathbf{6}}}+{{\mathbf{b}}^{\mathbf{6}}} \right)\] equals |
| A. | 0 |
| B. | 1 |
| C. | \[{{x}^{2}}+{{y}^{2}}\] |
| D. | \[{{a}^{2}}{{b}^{4}}+{{a}^{2}}{{b}^{2}}\] |
| Answer» B. 1 | |
| 442. |
Given that \[x=2\]is a solution of \[{{x}^{3}}-7x+6=0.\]The other solutions are_____. |
| A. | -1, 3 |
| B. | 1,-3 |
| C. | 1,-2 |
| D. | -1,-2 |
| Answer» C. 1,-2 | |
| 443. |
Identify one of the factors of\[{{x}^{2}}+\frac{1}{{{x}^{2}}}+2-2x-\frac{2}{x}\]from the following. |
| A. | \[x-\frac{1}{x}\] |
| B. | \[x+\frac{1}{x}-1\] |
| C. | \[x+\frac{1}{x}\] |
| D. | \[{{x}^{2}}+\frac{1}{{{x}^{2}}}\] |
| Answer» D. \[{{x}^{2}}+\frac{1}{{{x}^{2}}}\] | |
| 444. |
If\[{{x}^{3}}+{{y}^{3}}+{{z}^{3}}-3xyz=k(x+y+z)\] \[\{{{(x-y)}^{2}}+{{(y-z)}^{2}}+{{(z-x)}^{2}}\}\], find\[k\]. |
| A. | \[1\] |
| B. | \[\frac{1}{4}\] |
| C. | \[\frac{1}{2}\] |
| D. | \[\frac{1}{3}\] |
| Answer» D. \[\frac{1}{3}\] | |
| 445. |
If \[\mathbf{a=}\frac{\sqrt{\mathbf{5}}\mathbf{-}\sqrt{\mathbf{3}}}{\sqrt{\mathbf{5}}\mathbf{+}\sqrt{\mathbf{3}}}\]and \[\mathbf{b=}\frac{\sqrt{\mathbf{5}}\mathbf{+}\sqrt{\mathbf{3}}}{\sqrt{\mathbf{5}}\mathbf{-}\sqrt{\mathbf{3}}}\] then the value of \[\frac{{{\mathbf{a}}^{\mathbf{2}}}\mathbf{-ab+}{{\mathbf{b}}^{\mathbf{2}}}}{{{\mathbf{a}}^{\mathbf{2}}}\mathbf{+ab+}{{\mathbf{b}}^{\mathbf{2}}}}\mathbf{=?}\] |
| A. | \[\frac{63}{61}\] |
| B. | \[\frac{67}{65}\] |
| C. | \[\frac{65}{63}\] |
| D. | \[\frac{69}{67}\] |
| Answer» B. \[\frac{67}{65}\] | |
| 446. |
If \[(x+2)\] and\[(x-1)\]are factors of \[({{x}^{3}}+10{{x}^{2}}+3x+n),\]then the value of m, n respectively are _______. |
| A. | -5, 5 |
| B. | 7, 18 |
| C. | 7,-18 |
| D. | -5,-18 |
| Answer» D. -5,-18 | |
| 447. |
If\[p(x)=4{{x}^{3}}-3{{x}^{2}}+2x+1\],\[q(x)={{x}^{3}}-{{x}^{2}}+x+1\]and\[r(x)={{x}^{2}}-2x+1\]find the value of\[3p(x)+7q(x)+r(x)\] |
| A. | \[19{{x}^{3}}-15{{x}^{2}}+11x+11\] |
| B. | \[-19{{x}^{3}}-15{{x}^{2}}+11x-11\] |
| C. | \[19{{x}^{3}}-15{{x}^{2}}-11x+11\] |
| D. | \[19{{x}^{3}}-15{{x}^{2}}-11x-11\] |
| Answer» B. \[-19{{x}^{3}}-15{{x}^{2}}+11x-11\] | |
| 448. |
Given that\[(1-x)(1+x+{{x}^{2}}+{{x}^{3}}+{{x}^{4}})\]is \[\frac{31}{32}\] and \[x\] is a rational number, what is\[1+x+{{x}^{2}}+{{x}^{3}}+{{x}^{4}}+{{x}^{5}}\]? |
| A. | \[\frac{31}{64}\] |
| B. | \[\frac{63}{32}\] |
| C. | \[\frac{63}{64}\] |
| D. | \[\frac{31}{32}\] |
| Answer» C. \[\frac{63}{64}\] | |
| 449. |
Which of the following are the factors of\[4{{x}^{2}}-{{y}^{2}}+2x-2y-3xy\]? |
| A. | \[(x+y)\]and\[(4x+y-2)\] |
| B. | \[(x-y)\]and\[(4x-y+2)\] |
| C. | \[(x+y)\]and\[(4x-y-2)\] |
| D. | \[(x-y)\]and\[(4x+y+2)\] |
| Answer» E. | |
| 450. |
Resolve into factors: \[1+a+b+c+ab+bc+\]\[ca+abc\] |
| A. | \[(1+a)(1+b)(1+c)\] |
| B. | \[(a+b+c+1)(a-b-c)\] |
| C. | \[(a+b)(b+c)(c+a)\] |
| D. | \[({{a}^{2}}+{{b}^{2}}+{{c}^{2}})(1-a-b-c)\] |
| Answer» B. \[(a+b+c+1)(a-b-c)\] | |