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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.
| 3351. |
Find the direction in which a straight line must be drawn through the point(-1, 2) so that its point of intersection with the line x + y = 4 may be at a distance of 3 units from this point. |
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| 3353. |
LetA = { 1, 2, { 3, 4 }, 5 }. Which of the following statements are incorrect and why? φ ⊂A |
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| 3355. |
Differentiate the following functions w.r.t. x: (tan x)/( 2x +3) |
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| 3357. |
tan[1/2Cos^(-1)(sqrt5/3)]= |
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Answer» `(3+sqrt(5))/2` |
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| 3358. |
A pair of dice is thrown . Findthe probability of getting a sum of 10 or more , if 5 appears on the first die . |
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| 3359. |
The probability that a person visiting a zoo will see the giraffe is 0.72, the probability that he will see the bears is 0.84 and the probability that he will see both is 0.52. |
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| 3360. |
Let f(x)=x^(2) and g(x)=2x+1 be two real functions. Find (f+g) (x), (f-g) (x), (fg) (x), (f/g) (x). |
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| 3361. |
How manystrings are there usingthe letters of the word INTERMEDIATE , if (i) The vowelsand consonants are alternative (ii) All the vowelsare together (iii) Vowelsare nevertogether . (iv)No two vowelsare together . |
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Answer» (II)151200 (III) 19807200 (IV)43200 . |
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| 3362. |
If A(10,4),B(-4,9) and C(-2,-1) are the vertices of a triangle. Find the equation (i) bar(AB) (ii) the media through A (iii) the altitude through B (iv) the perpendicular bisector of the side bar(AB). |
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Answer» (II) `y-4=0` (III) `12x+5y+3=0` (IV) `28x-10y-19=0` |
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| 3363. |
If A=(0,4),B=(0,-4) and |AP-PB|=6, then the locus of P is |
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Answer» `7x^(2)-9Y^(2)+63=0` |
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| 3364. |
Find the values of theta between 0^(@) and 360^(@) which satisfy the equations cos2theta=(1)/(2). |
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| 3365. |
If vec(a)= 2vec(i) + vec(j)-3vec(k), vec(b)=vec(i) -2vec(j) + vec(k), then a vector of length and perpendicular to both vec(a) and vec(b) is |
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Answer» `+- (5)/(sqrt3) (VEC(i) + vec(j) + vec(k))` |
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| 3366. |
If the sum of two + venumbers is 18 then maximum value of their product is |
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Answer» 81 |
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| 3368. |
Observe the following lists : {:(,ul"List-I",ul"List-II"),(,"(Plane)","(sum of the lengths of the intercepts on axes)"),("A)",3x+4y-5z=0,"1) "-77//30),("B)",2x-3y+5z+7=0,"2)13"),("C)",2x+3y+4z-12=0,"3)0"),(,,"4) 217/30"):} Match List-I to List-II : |
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Answer» `{:(UL"A",ul"B",ul"C"),(3,1,2):}` |
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| 3370. |
If A=Tan^(-1)((1)/(7)), B=Cot^(-1)(3) then |
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Answer» `COS2A=sin4B` |
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| 3371. |
A card is drawn from a pack of cards . Findthe probability that it is a king or a queen. |
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| 3373. |
To remove the x and y terms of the equation14x^(2) - 4xy + 11y^(2) - 36+ 48 y + 41 = 0 the shifted origin is |
| Answer» ANSWER :D | |
| 3374. |
A box contains 100 bolts and 50 nuts. It is given that 50% bolts and 50% nuts are rusted. Two objects are selected from the box at random. Find the probability that either both are bolts or both are rusted. |
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Answer» SOLUTION :Total NUMBER of objects = (100 + 50) = 150. Let S be the sample space. Then, n(S) = number of ways of selecting 2 objects out of 150 `= ""^(150)C_(2).` Number of rusted objects `= (50% " of " 100) + (50% " of " 50) = (50 + 25) = 75.` Let `E_(1) =` event of selecting 2 bolts out of 100 bolts, and `E_(2) =` event of selecting 2 rusted objects out of 75 rusted objects. `therefore (E_(1) nn E_(2)) =` event of selecting 2 rusted bolts out of the 50 rusted bolts `therefore n(E_(1)) =` number of ways of selecting 2 bolts out of 100 `= ""^(100)C_(2).` `therefore n(E_(2)) =` number of ways of selecting 2 rusted objects out of 75 `= ""^(75)C_(2).` `therefore n(E_(1) nn E_(2)) =` number of ways of selecting 2 rusted bolts out of 50 `= ""^(50)C_(2).` `therefore P(E_(1)) = (n(E_(1)))/(n(S)) = (""^(100)C_(2))/(""^(150)C_(2)), P(E_(2)) = (n(E_(2)))/(n(S)) = (""^(75)C_(2))/(""^(150)C_(2))` and `P(E_(1) nn E_(2)) = (n(E_(1) nn E_(2)))/(n(S)) = (""^(50)C_(2))/(""^(150)C_(2)).` P(selecting both bolts or both rusted objects) `= P(E_(1) " or " E_(2)) = P(E_(1) UU E_(2))` `= P(E_(1)) + P(E_(2)) - P(E_(1) nn E_(2))` `= (""^(100)C_(2))/(""^(150)C_(2)) + (""^(75)C_(2))/(""^(150)C_(2)) - (""^(50)C_(2))/(""^(150)C_(2)) = ((""^(100)C_(2) + ""^(75)C_(2) - ""^(50)C_(2)))/(""^(150)C_(2))` `= ((4950 + 2775 - 1225))/(11175) = (6500)/(11175) = 260/447 = 0.58.` HENCE, the required probability is 0.58. |
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| 3375. |
Eighth term of G.P is 128 and common ratio is r = 2 then product of first 5 terms = ......... . |
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| 3376. |
Identify the quantifier in the following statements and write the negation of the statements: There exists a capital for every state in India. |
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| 3377. |
Identify the quantifier in the following statements and write the negation of the statements: There exists a number which is equal to its square. |
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| 3378. |
Calculate the standard deviation for the following distribution. |
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| 3379. |
Domain of the function defined by f(x)= sqrt(5|x|)=x^(2)-6 is……. |
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Answer» `(-3, -2) UU(2, 3)` |
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| 3380. |
If a_(1)=1anda_(n+1)=(4+3a_(n))/(3+2a_(n)),nge1 and if Lt_(ntooo)a_(n)=n then find a. |
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| 3381. |
A plane meets the coordinate axes A, B, C so that the centroid of the triangle ABC is (1,2,4). Then the equation of the plane is |
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Answer» `X + 2y + 4Z =12 ` |
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| 3382. |
Find the approximate value of root(4)(17) |
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| 3383. |
Letf:[0,4pi]to[0,pi] be defined by f(x)=cos^(-1)(cosx). The number of points x in [0,4pi] satisfying the equation f(x)=(10-x)/10 is |
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| 3384. |
Evaluate Lt_(ntooo)(1^(2)+2^(2)+3^(2)+......+n^(2))/n^(3). |
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| 3385. |
If tantheta+sintheta=mandtantheta-sintheta=n, then prove that m^(2)-n^(2)=4sinthetatantheta. |
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| 3389. |
The perimeter of a right angled triangle is 6 times the smaller side, if alpha is the smallest angle then tan alpha= |
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Answer» `(3)/(4)` |
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| 3390. |
Write the following sets in the set builder form : B= {-2, -1, 0, 1, 2, 3, 4} |
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| 3391. |
Find the orthocentre of the triangle whose vertices are (-5,-7),(13,2),(-5,6) |
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| 3392. |
From the following information, find the equation of the hyperbola.Focus (-2,1) , Directrix: 2x - 3y + 1 =0, e = (2)/(sqrt3) |
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| 3393. |
If no solution of 3 sin y + 12 sinx^(3) = a lies on the line y = 3 x , then |
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Answer» `a in (- INFTY, - 9) CUP (9 , infty)` |
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| 3394. |
Evaluate: [i^(18) + ((1)/(i))^(25)]^(3) |
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| 3395. |
Find the angle throughwhich the axes be rotated to remove the xy term from the equations ax^(2) + 2hxy + ay^(2) = 0 |
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| 3396. |
Three coins are tossed . Describe Three events which are mutually exclusive and exhaustive. |
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| 3398. |
Let f:RtoR be a differentiable function AAxinR . If the tangent drawn to the curve at any point xin(a,b) always lies below the curve , then |
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Answer» `f'(x)GT0,f''(x)lt0AAx in(a,B)` |
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| 3399. |
A shopkeeper in a Nuts and Spices shop makes gift packs of cashew Nuts, raisins and almonds.Pack-I coin 100 gm of cashew nuts ,100gm of raisins and 50 gm of almonds.Pack-II contains 200 gm of cashew nuts, 100 gm of raisins and 100 gm of almonds. Pack-III contains 250 gm of cashew nuts, 250 gm of raisins and 150 gm of almonds.The cost of 50 gm of cashew nuts is Rs 50/-, 50 gm of raisins is Rs 10/-, and 50 gm of almonds is Rs60/-, What is the cost of each gift pack? |
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| 3400. |
Let f(x) = max { 1+ sin x, 1.1 -cos x } , x in [0,2pi ]and g(x)= max {1, |x-|}x in RThen |
| Answer» Answer :A::B::D | |