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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.
| 10302. |
An aeroplane is flying horizontally at an altitude of 3000 ft directly over an observer.If it is flying with a speed of 300 ft/sec, the rate at which it is moving away from the observe when it is at 5000 ft away from the observer is |
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Answer» 200 ft/sec |
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| 10303. |
A nonzero polnomial with real coefficients has the ptoperty that f(x) =f'(x) f''(x). If a is the leading coefficient of f(x), then the value 1/2a. |
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| 10304. |
Write the converse, inverse and contrapositive for the statement (~p)impliesq. |
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Answer» <P> |
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| 10305. |
List all the elements of the following sets : D = {x : x is a letter in the word “LOYAL”} |
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| 10306. |
Find the centrefoci and the equation of the directrices of the ellipse8x^(2) +9y^(2) - 16x + 18 y - 55 = 0 |
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| 10307. |
The vector equation of the plane passing through the point 2bar(i)+2bar(j)-3bar(k) and parallel to the vectors 3bar(i)+3bar(j)-5bar(k), bar(i)+2bar(j)+bar(k) is |
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Answer» `bar(R)=t(2bar(i)+bar(J)-bar(K))+s(bar(i)+2bar(j)+2bar(k))` |
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| 10308. |
Lines ax+by =c and a'x + b'y=c' are mutually perpendicular then .......... of the following is valid. |
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Answer» `AA'=BB'` |
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| 10309. |
1^(2)+3^(2)+5^(2)+.......+(2n-1)^(2) =(n(2n-1)(2n+1))/(3) |
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Answer» SOLUTION :`"LET "P (N) : 1^(2)+3^(2)+5^(2)+......+(2n-1)^(2)` ` =1/3 n(4n^(2)-1)` for n =1 `L.H.S. =1^(2) =1, R.H.S. =1/3 .1.(4.1^(2)-1)=1` `:. L.H.S. =R.H.S.` `rArr` P(n)is true for n=1 Let P(n) be true for n=K `:. P(k) : 1^(2) +3^(2)+5^(2)+` `.......+(2k-1)^(2)=1/3 k(4k^(2)-1)` for n=K+1 `P(k+1) : 1^(2) +3^(2) +5^(2)+......+(2K-1)^(2)` `+(2K+1)^(2)=1/3 k(4k^(2)-1)+(2k+1)^(2)` `(k(4k^(2)-1)+3(2k+1)^(2))/(3)` `=1/3[4k^(3)-k+12k^(2)+12k+3]` `=1/3[4k^(3)+12k^(2)+11k+3]` `=1/3(k+1)(4k^(2)+8k+3)` `=1/3(k_+1)[4(k^(2)+2k+1)-1]` `=1/3(k+1)[4(k+1)^(2)-1]` `rArr` P (n) is also true for n=K+1 Hence from the principleof mathematical induction P (n) is true for all natural numbers. n |
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| 10310. |
Let f(x)=log_(2)log_(3)log_(4)log_(5)(sin x+a(2)). Find the set of values of n for which the domain of f(x) is R. |
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Answer» `(-OO, - sqrt(626))UU(sqrt(626), oo)` |
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| 10311. |
The point pis moving with uniform velocity v along a straight line AB. O isa point on a perpendicular to AB at A and distance l from it. The angular velocity of pabout O is |
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| 10312. |
Find the vector equation of the plane passing through the intersection of the planes barr.(bari +barj+bark) = 6 and barr. (2bari+3barj+bark) = -5 " and the point " (1,1,1). |
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| 10313. |
Find the approximations of the following cos(60^(@)5') |
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| 10314. |
If y = sec (Tan ^(-1) x), then(dy)/(dx) at x =1 is equal to |
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Answer» `1//2` |
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| 10315. |
18 mice were placed in two experimental groups and one control group with all groups equally large. In how many ways can the mice be placed into three groups ? |
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| 10316. |
Find the multiplicative invers of each of the complex number 4-3i |
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| 10317. |
Which of the following sentences are statements? Give reasons for your answer: All real numbers are complex numbers. |
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| 10318. |
Showthat the circles x^(2) +y^(2) - 2x - 4y - 20 = 0 and x^(2) + y^(2) + 6x +2y- 90=0touch each other . Find the coordinatesof the pointof contactand the equation of the commontangent . |
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| 10319. |
If sin x ( cos ""(x)/( 4) - 2 sin x) + ( 1 + sin "" (x)/( 4) - 2 cos x) cos x = 0then x = |
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Answer» `( 8 K - 6 ) PI, l in Z` |
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| 10320. |
If ("cos"^4 theta)/(x) + ("sin"^4 theta)/(y) = 1/(x + y)(theta is constant) then (dy)/(dx) = |
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Answer» `XY` |
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| 10321. |
A coin is tossed. If the result is head, a coin is tossed again. If the result is tail, a die is thrown. Write the sample space for this experiment. |
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| 10322. |
ABCD is a square whose vertices A(0,0) B (2,0), C(0,2). This square is rotated in the xy-plane with an angle of 30^@ in aniclockwise direction about an axis passing through the vertex A, the equation of the diagonal BD of this rotated square is ……… . If E is the centre of the square, the equation of the cirecumcircle of the triangle ABE is |
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Answer» `(2-sqrt3x+y=2(sqrt3-1)` |
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| 10323. |
Let f: R to Rbe a function satisfyingf(2-x) = f(2+x) and f(20 -x) = f(x) AA x in R . For this functions f. answer the following If f(0) =5 then the minimum possible number of values of x satisfying f(x)= 5 for x in [0,170]is |
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Answer» 21 |
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| 10324. |
Let f: R to Rbe a function satisfyingf(2-x) = f(2+x) and f(20 -x) = f(x) AA x in R . For this functions f. answer the following If f(2)nef(6)then the |
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Answer» fundamental PERIOD of `F(X)` is 1 |
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| 10325. |
Let f: R to Rbe a function satisfyingf(2-x) = f(2+x) and f(20 -x) = f(x) AA x in R . For this functions f. answer the following The graph of y = f(x)is not symmetrical about |
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Answer» SYMMETRICAL about `x=2` |
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| 10326. |
If f(x)=x^(2)+x,x=10,deltax=0.1 abserve the following Statement-I deltaf=2.11 Statement-II : df=2.1 Statement-III : Relative error in x is 1 The true statements are |
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Answer» only I, III |
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| 10327. |
If 4-digit numbers greater than 5,000 are randomly formed from the digits 0,1, 3, 5, and 7, what is the probability of forming a number divided by 5 when,(i) the digits are repeated? (ii) the repeition of digits is not allowed? |
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| 10328. |
ABCD is a square whose vertices A(0,0) B (2,0), C(0,2). This square is rotated in the xy-plane with an angle of 30^@ in aniclockwise direction about an axis passing through the vertex A, the equation of the diagonal BD of this rotated square is |
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Answer» `SQRT3X+(1-sqrt3)y=sqrt3` |
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| 10329. |
Solution of 7 sin ^(2)x+3 cos^(2)x=4 is |
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Answer» `N PI +-pi//2` |
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| 10330. |
Prove that for any natural number n, a ^(n) - b ^(n) is divisible by a-b, where a gt b. |
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| 10331. |
If the three plane x = y sin psi+ z sin phi, y = z sin theta + x sin psi, z = x sin phi + y sin theta, intersect in a line, then where theta, phi in (0, (pi)/(2)) Equation of their common line is |
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Answer» `(X)/( sin theta) = (y)/(sin theta) = (Z)/( sin psi )` |
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| 10332. |
If the three plane x = y sin psi+ z sin phi, y = z sin theta + x sin psi, z = x sin phi + y sin theta, intersect in a line, then where theta, phi in (0, (pi)/(2)) theta + phi + psi = |
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Answer» `90^(@)` |
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| 10333. |
If the three plane x = y sin psi+ z sin phi, y = z sin theta + x sin psi, z = x sin phi + y sin theta, intersect in a line, then where theta, phi in (0, (pi)/(2)) theta , phi & psi satisfy |
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Answer» `sin ^(2) theta + sin ^(2) PHI + sin ^(2) psi =1` |
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| 10334. |
Using Heron's formula, show that equilateral triangle has the maximum area for any fixed perimeter. [Hint : In "xyz le k,maximum occurs when x=y=z"]. |
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| 10335. |
Which of the following sentences are statements? Justify A triangle has three sides. |
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| 10336. |
Identify the quantifier in the following statements and write the negation of the statements: For every real number x,x is less than x+1 |
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Answer» There EXISTS a REAL NUMBER x such that x is not less than x + 1. |
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| 10337. |
How many 5-digit telephone numbers can be constructed using the digits 0 to 9 if each number starts with 67 and no digit appears more than once? |
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| 10339. |
Express the following as functions of angles less than 45^(@) : sin194^(@) |
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| 10340. |
State whether each of the following statement is true or false. Justify your answer. { a, e, i, o, u } and { a, b, c, d } are disjoint sets. |
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| 10341. |
Consider the points A, B, C and D with P.V.'s 7bar(i)-4bar(j)+7bar(k), bar(i)-6bar(j)+10bar(k), -bar(i)-3bar(j)+4bar(k) and 5bar(i)-bar(j)+bar(k) respectively. Then ABCD is a |
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Answer» PARALLELOGRAM but not a Rhombus |
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| 10342. |
Find the derivative of the function e ^(2x) log x ( x gt 0) |
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| 10343. |
Answer the equation: int(9dx)/((x-1)(x+2)^(2))dx. |
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| 10344. |
Insert 6 arithmetic means between 3 and 24. |
| Answer» SOLUTION :6,9,12,15,18,21] | |
| 10345. |
If sin theta =a and sin 2 theta = b, find an expression forcos thetain terms of a and b. Hence find a relation between a and b not involving theta. |
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| 10347. |
Prove that the line through the point (x_1, y_1) and parallel to the line Ax + By + C=0 is A(x-x_1) + B(y-y_1)=0. |
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Answer» Which is REQUIRED LINE. |
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| 10349. |
Find the degree measure of the angle subtended at the centre of a circle of radius 100 cm by an arc of length 22 cm (Use pi = (22)/(7)). |
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