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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.
| 78901. |
(((text*(0*(f*(o*r))))*((sqrt(-sin(x) %2B 1) %2B sqrt(sin(x) %2B 1))/(sqrt(-sin(x) %2B 1) - sqrt(sin(x) %2B 1))))/t < x) < pi/2 |
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| 78902. |
1=Integral(cos(x)/(((sin(x) %2B 1)*(sin(x) %2B 2))), (x, 0, pi/2)) |
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| 78903. |
(((tan((3*pi)/2 - x)*cot(2*pi - x))*cos(pi/2 %2B x))*sin(pi %2B x))/((((cosec(-x)*sin((3*pi)/2 %2B x))*cos(2*pi %2B x))*sin(2*pi - x))) |
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| 78904. |
\frac 155 \times 155 %2B 155 \times 55 %2B 55 \times 55 155 \times 155 \times 155 - 55 \times 55 \times 55 |
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Answer» 155×155+155×55+55×55/155×155×155-55×55×55=(155×155)+(155×55)+(55×55)/(155×155×155)-(55×55×55)=24025+8525+3025/(3723875)-(166375)=35,575/3557500=0.01 |
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| 78905. |
18. In a group of 500 women, 120 have played golf at least once. Suppose one of these500 women is randomly selected. What is the probability that she has played golfat least once? |
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Answer» among 500,120 have played golf at least once. so probability of getting a woman who has played golf at least once 120/500 = 12/50 = 6/25 = 0.24 |
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| 78906. |
(2) Any day of a week is to be selected randomlyf 52 curds. |
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Answer» Probability of any day to be selected will be 1/7as there are 7 days and one is favourable |
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| 78907. |
2.If ι, β are the roots of the quadratic equation x2-2x-1-0 find the value oiP al1ots of the quadratic equation xx L0,2 |
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Answer» please like if you find it useful |
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| 78908. |
Three coins are tossed simultaneously. Find the probability of getting:(0) no heads(ii) two heads |
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Answer» wrong wrong❌❎❎❎❎❎❎❎❎❌❌❌❌❌🚫🚫🚫🚫🚫🚫 |
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| 78909. |
2. Two coins are tossed 400 times and we gettwo heads : 112 times; one head 160 times; 0 head: 128 tinmesWhen two coins are tossed'at random, what is the probability of getting(iii) 0 head ?(i) 2 heads?(ii) 1 head ? |
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| 78910. |
79 \times \frac { 9 I } { L } \cdot 9 |
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Answer» (7/16)*64=7*4=28is the value |
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| 78911. |
The discriminant of the quadratic equation2--41+3-0 isa. 34c) 8b) 8d 12 |
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Answer» For equation of the form ax^2 + bx + c = 0Discriminant = b^2 - 4ac Then,For equation 2x^2 - 4x + 3 = 0Discriminant = (-4)^2 - 4*2*3= 16 - 24= - 8 (b) is correct option |
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| 78912. |
6. If - 4 is a root of the quadratic equation x + px -4 = 0 and the quadratic equationx + px + k = 0 has equal roots, find the value of k. |
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| 78913. |
Q3 Give reason:-(a) We can get the smell of perfume sitting several metres away(b) Water at room temperature is liquid |
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Answer» 2)Atroom temperature(anywhere from zero degree centigrade to 100 degrees centigrade),wateris found ina liquidstate. This is because of the tiny, weak hydrogen bonds which, in their billions, holdwatermolecules together for small fractions ofasecond.Watermolecules are constantly on the move 1)The perfume molecules spread out or 'diffuse' through the air. The smell becomes less concentrated but it reaches a great distance - meaning you can smell it from relatively far away. When a perfume issprayedseveral metres away from the source, the particles of the perfumediffuseswith the particles of the gas. please like the solution 👍 ✔️👍 |
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| 78914. |
18.A lane 180 m long and 5 m wide is to be pavedwith bricks, of length 20 cm and brcadth 15cm. Find the cost of the bricks that are required,at the rate of 750 per thousand. |
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| 78915. |
MPLE9Simplify each of the the following:\sin ^{-1}\left(\frac{\sin x+\cos x}{\sqrt{2}}\right), \frac{\pi}{4}<x<\frac{5 \pi}{4}\sin ^{-1}\left(\frac{\sin x+\cos x}{\sqrt{2}}\right), \frac{\pi}{4}<x<\frac{5 \pi}{4} |
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| 78916. |
atan((-sqrt(x) %2B 1)/(sqrt(x) %2B 1))=pi/4 - atan(sqrt(x)) |
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| 78917. |
\left. \begin{array} { r } { \operatorname { sin } ( - \frac { 3 \pi } { 4 } ) + \operatorname { cos } ( - \frac { \pi } { 4 } ) + \operatorname { sin } \frac { \pi } { 4 } \times \operatorname { cos } \frac { \pi } { 2 } } \\ { + \operatorname { cos } \frac { \pi } { 2 } \times \operatorname { sin } \frac { \pi } { 2 } } \end{array} \right. |
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Answer» sin(-3π/4) + cos(-π/4) + sin(π/4)cos(π/2) + cos(π/2)sin(π/2)= -1/√2 + 1/√2 + 1/√2×0 +0×1= -1/√2 +1/√2 = 0 |
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| 78918. |
OSWAAL CBSE Sample Question Papers, MAl12426 Find the middle terms of the sequence formed by all numbers between 9 and 95, whichremainder 1 when divided by 3. Also, find the sum of the numbers on both sides of theseparatelyrimMaand nf circle with centre O. At B, a tangent PB is drawn such ththe cherd AB is 16 cm, find its distance from the centre.at its length is 24 cm. The |
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Answer» The sequence are formed by all the numbers between 9 and 95 , which leaves remainder 1 when it is divided by 3 : 10, 13, 16, .........94 Here you can see 10, 13 , 16 , .....94 are in AP where first term , a = 10 and common difference , d = 94 . From AP nth term formula , Tn = a + (n -1)d 94 = 10 + (n -1)3 84/3 = n -1 ⇒n = 29 Hence, there are 29 terms between 10 and 94 It means middle term is (n + 1)/2 th term e.g., middle term = (29+1)/2 = 15th term So, T₁₅ = a + (15 - 1)d = 10 + 14 ×3 = 52 Hence, 15th term is 52 here middle is 15th , it means 14 terms are in left side of it and 14 terms are in right side of it. So, sum of first 14 term {left side } = 14/2 [ 2 × 10 + (14 -1)×3 ] [∵Sn = n/2[2a + (n-1)d]= 7[20 + 39] = 7 × 59 = 413 Now, sum of last 14 term { right side of middle term } = S₂₉ -[ S₁₄ + T₁₅ ]= 29/2[2 × 10 + (29-1) × 3 ] - 413 - 52 = 29/2[20 + 84 ] - 465 = 1508 - 465 = 1043 |
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| 78919. |
1x2 .ex3 dx =26, |
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| 78920. |
(v) A coin showing either head or tall.(v) Petrol prices may rise to 100 per litre by the end of 202042 A coin is tossed two times, what is the probability of getting same the outcome onty that a randomly selected card wouldbear a prime number?hilitt of an event? |
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Answer» 2) tossing 2 coins possibilities areHH,HT,TH,TTso probability of both same=2/4=1/23)number is 1,2,...,12so probability of prime number=5/12 |
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| 78921. |
A fair coin is tossed three times. Find the probability of getting at most one head and twoconsecutive heads |
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| 78922. |
f x = 3is one root of the quadratic equation x2-2kx-6 = 0, then find the value of k. |
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| 78923. |
8. A coin is tossed 200 times. The head appears 79 times. te9. E and E2 are the only two outcomes of an event and PC)0.32then find the value of P(E) |
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Answer» We know P(E1) + P(E2) = 1So, given P(E1) = 0.32 Therefore, P(E2) = 1 - 0.32 = 0.68 |
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| 78924. |
Q8) Find the values of k such that the quadratic equation2.x2-2kx + (7k-12) 0 has equal roots. |
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| 78925. |
(a) x2-2x +15(c) x2+2x-15(b) x2-2x- 15(d) x2 +2x+ 15 |
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| 78926. |
43. Which of the following is not a quadratic equation ?(a) x2 -55x+ 7500(c) x2+ x +8x2-4(b)x2 +2x +20(d)x2-45x-324 |
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| 78927. |
The population of a town increases at the rate of 50 per thousand. If the estimated population a2 years will be 22,050, find the present population of the town. |
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| 78928. |
1. Thepopulation of a town is increasing at the rate of 8% per annum.What will bethe population of the town after two years if the present population is 12,5007 |
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| 78929. |
atan(-1/sqrt(3)) |
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Answer» Letθ=tan^−1(−1/√3) tanθ=tan(tan^−1(−1/√3))=−(1/√3) |
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| 78930. |
-atan(1/239) %2B 4*atan(1/5)=pi/4 |
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Answer» let x = arctan Atan x = Atan (x + x) = (tan x + tan x)/(1 - tan x . tan x)tan 2x = (2 tan x) / (1 - tan^2 x)tan 2x = (2A) / (1 - A^2)2x = arctan ((2A) / (1 - A^2))2 arctan A = arctan ((2A) / (1 - A^2))4 arctan A = 2 arctan ((2A) / (1 - A^2))4 arctan (1/5) = 2 arctan ((2.1/5) / (1 - 1/25))= 2 arctan (5/12)= 2 arctan (5/12) - arctan (1/239)= arctan ((2.5/12) / (1 - 25/144)) - arctan (1/239)= arctan (120/119) - arctan (1/239)= arctan ((120/119 - 1/239) / (1 + 120/119 * 1/239)= arctan (1.0042 / 1.0042)= arctan (1)= π/4 |
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| 78931. |
atan(tan((3*pi)/4)) |
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Answer» -π/4is a correct answer 3π/4 is the is correct answer |
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| 78932. |
2. Write the missing numbers in the number sequence:(along the row500 450 400 15 30 451 2 46 12 1822 44 8811 22 339 18 27 |
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Answer» 500 450 400, 350,300,250,20015,30,45,60,75,90,1051,2,4,7,11,16,226,12,18,24,30,36,4222,44,88,176,352,714,142811,22,33,44,55,66,779,18,27,36,45,54,63 |
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| 78933. |
Find the middle term of the sequence formed byall three-digit numbers which leave a remainder3, when divided by 4. Also find the sum of allnumbers on both sides of the middle termsseparatelyForeign Set I, 2015) |
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Answer» The list of 3 digit number that leaves a remainder of 3 when divided by 4 is : 103 , 107 , 111 , 115 , .... 999 The above list is in AP with first term, a = 103 and common difference, d = 4 Let n be the number of terms in the AP. Now, an= 999 103 + ( n - 1 ) 4 = 999 103 + 4n - 4 = 999 4n + 99 = 999 4n = 900 n = 225 Since, the number of terms is odd, so there will be only one middle term. middleterm=(n+12)thterm=113thterm=a+112d=103+112×4=551 Weknowthat,sumoffirstntermsofanAPis,Sn=n2[2a+(n−1)d] Now,Sum=112/2[2×103+111×4]=36400 Sumofalltermsbefore middleterm=36400sum of all numbers= 225/2[2×103+224×4]=123975 Now,sumoftermsafter middleterm=S225−(S112+551)=123975−(36400+551)=87024 |
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| 78934. |
1x2 2x3 3x4 |
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Answer» If you like the solution, Please give it a 👍 |
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| 78935. |
EXERCISE 8(A)I. Find, in each case, the remainder when10. Find the value of a, if the division of ax' +-3+2x+1 is divided by 19+4x-10 by x+3 leaves a remainder 5.i)3- 12x + 4 is divided by x -2. 11Iaxbe+6 hasGin +1 is divided by-2 as a factorand leaves a remainder 3 when divided byx-3, find the values of a and ib.2. Show that[200510) x-2 is a factor of 5x + 15x 50Gii) 3x + 2 is a factor of 3x-x-22 leaveswhen divided by12. The expression 2x +ax bx3. Use the Remainder Theorem to Sad which of2x-3 and x+ 2 respectivelyremainder 7 andvalues of a and b.the follgwing is a factor of 2+3-5x-6(ii) 2x -113. What number should be added to3x,-5x2 + 6x so that when resulting4. 0) If 2x +1 is a factor of 2x +ax-3, findpolynomial is divided by x -3, the remainderis 8 ?the value of aWhat number should be subtracted fromx-2, the remainder is 10 ?G) Find the value of k, if 3x - 4 is a facrof expression 3x2+ 2x -k5. Find the values of constants a and b whenx 2 and x+3 both are the factors of 15, The polynomials 2x3 -x2+ax 6 andexpression x+a+ bx 126. Find the value of k, if 2x+1 is a factor ofx3-8x2+ (2a +1)x 16 leave the sameremainder when divided by x -2. Find thevalue of 'a'(3k +2) + (k - 1)7 Find the value of a, if. If ( 2) is a factor of the expression-2 is a factor ofa2r +ax2 +bx -14 and when the expressionis divided by (x -3), it leaves a remainder 528 End the values of m and n so that x- I and find the values of a and b.12013]x + 2 both are factors ofFind 'a' if the two polynomials a +3x2 -9r (3m+ 1)x2 +nx- 18.and 2x3 + 4x + a, leave the same remainder9Whenx+2.2-Kx+4 is divided by x -2, the when divided by x + 3.(2015)remainder is k. Find the value of constant k8.4 Using the Factor Theorem to factorise the given polynomialFactorising a polynomial completely after obtaining one factor by factor theoremWhen expression fx) is divided by x - a, the remain20-87-28 13:44 |
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Answer» Kindly post one question per post to experience the instant solution feature of scholr at its best. |
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| 78936. |
A girl throws a dice. If she gets a 5 or 6, she toses a coin three times and nothe number of heads. If she gets 1, 2, 3 or 4, she tosses a coin two timesnotes the number of heads obtained. If she obtained exactly two heads, whathe probability that she throws 1, 2, 3 or 4 with the dice? |
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| 78937. |
4. For what value of k, will the equation 2kx? - 2(1 + 2k)x + (3 + 2k) = 0 have real butdistinct roots? When will the roots be[CBSE 2010] |
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Answer» for real and distinct root we must have D>0 I.e. b^2-4ac>0so use -2(1+2k) as b , 2k as a and 3+2k as c condition for equal root b^2-4ac= 0{2(1+2k)^2-4(2k)(3+2k=04(1+4k+4k^2)= 4(6k+ 4k^2)1+4k+4k^2= 6k+4k^211= 6k-4k1= 2k1/2=k equal root b^2-4ac; [2(1+2k)^2-4(2k)(3+2k)=0; 4(1+4k+4k^2]=4[6k+4k^2); 1+4k+4k^2=6k+4k^2; 1+ 4k=6k; 1=6k-4k=2k; k=1/2 |
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| 78938. |
For what value of k, will the equation2k^2-2(1 + 2k)x + (3k + 2) = 0 have real but distinct roots? |
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| 78939. |
(viii)x2-2(5 + 2k) x + 3 (7 + 10k) = 0 |
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| 78940. |
In a town, where the population is 90,000, the male population is two-thirds the female population. Findthe male and female population of the town. |
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| 78941. |
152×4578÷152 |
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Answer» 152×4578÷152=152×30.1184210526=4577.99999999999 |
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| 78942. |
population of a town has increased by 5% in a year. Last year its population was00320. What is the present population of the town?The population of |
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Answer» 20320 -5% = 19304 is the last year populatin |
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| 78943. |
3.Cross out the wrongly written RomanBly written Roman numerals:a. wwb. XId. XMe. CCCL |
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Answer» Xl is the correct answer option A,D,E is cross out roman numeral the correct answer is options B A,D,E are right answers xm is wrongly written vvv xm cccl is the answer of the following |
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| 78944. |
2*asin(3/5)=atan(24/7) |
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| 78945. |
atan((3*sin(2*x))/(3*cos(2*x) %2B 5)) |
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| 78946. |
25, Find the sum of the infinite seri sTratanta25. Find the sum of the infinite series\frac{1}{9}+\frac{1}{18}+\frac{1}{30}+\frac{1}{45}+\frac{1}{63}+\ldots+4 |
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Answer» 1 2 3 |
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| 78947. |
0.28 Find the middle term of the sequence formed by all three-digit numberswhich leave a remainder 5 when divided by 7. Also find the sum of allnumber on both sides of the middle term separately |
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Answer» A.P: 103, 110, 117, ...., 999 a = 103 d = 7 n be the number of terms an= 999 103 + (n - 1)7 = 999 103 + 7n - 7 = 999 7n + 96 = 999 7n = 903 n = 129 Middle term term = (n+1)/2=65th= a + 64d = 103 + 64 x 7 = 551 Sn =n/2 [2a + (n - 1)d] =64/2 [2 x 103 + 63 x 7] = 20704 = 129/2[2 x 103 + 128 x 7] = 71079 S129 - ( S64+ 551) = 71079 - (20704 + 551) = 49824 Like if you find it useful |
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| 78948. |
Give cxamples of polynomialspé), g(o,ge) andr(x), which satisfy the division algorithmand) degp(x) deg qr)(ii) deg q(x) degr(t) ii) deg r(x) 0 |
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Answer» ty |
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| 78949. |
The polynomials 2x3 + ax2+ 3x-5 and x3 + x2-4x+ a leave the same remainder whendivided by x - 2, find 'a |
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| 78950. |
12. A coimis tossed three times. Find the probability of the following events:( 1 ) A : getting at least two heads(2)B: getting exactly two heads(3 )C: getting at most one head |
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Answer» There are 8possible outcomes, thepossible outcomesare HHH, HHT, HTH, HTT, THH, THT, TTH and TTT.1) at least two HEAD= 4/8= 1/22) exactly two heads = 3/83)4/8= 1/2 |
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