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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.
| 4501. |
Find the distance between each of pair of point: (0,3,0) and (6,0,2) |
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| 4502. |
A real valued function f(x) satisfies the functional equation f(x-y) = f(x)f(y)-f(a - x)f(a + y) where a is a given constant and f(0)=1, f(2a-x) is equal to: |
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Answer» `F(a)+f(a-X)` |
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| 4503. |
Find n in the Binomial (root3(2)+1/(root3(3)))^(n) , if the ratio of 7th term from the beginning to the 7th term from the end is 1/6. |
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| 4504. |
State whether each of the following set is finite or infinite: The set of lines which are parallel to the x-axis |
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| 4505. |
Find the distance from the origin to each of the point: (4, -1, 2) |
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| 4506. |
Let the statement m^(2) gt 100, the statement P(k+1) will be true if |
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Answer» `P(1)` is TRUE |
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| 4507. |
Alamp post is situated at the middle point M of the side AC of triangular plot ABC with BC = 7m , CA = 8m and AB = 9m. Lamp post subtends an angle15 ^(@)at the point. Find the height of the lamp post |
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| 4508. |
For the proposition P(n), given by, 1+3+5+ldots+(2n-1)=n^(2)+2prove that P(k) is true implies P(k + 1) is true. But, P(n) is not true for all n in N |
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| 4509. |
A point Q is at a distance 3 from the point P (1,1,1) lying on the line joining the points A(0,-1,3) and P, has the coordinates |
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Answer» (2,3,-1) |
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| 4510. |
Let f(x) = {{:("sin"("cos"^(-1) x) + "cos"("sin"^(-1)x),x le 0),("sin"("cos"^(-1)x) -"cos"("sin"^(-1)x),x gt 0):} and g(x) = f(|x|) + |f(x)| g'(1/2) = |
| Answer» ANSWER :A | |
| 4511. |
What are the cartesian co-ordinates of the points1+i, 2+i, 2+3i, 1+3i? |
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| 4512. |
Draw a quadrilateral in the Cartesian plane, whose vertices are (- 4, 5), (0, 7), (5, - 5) and (- 4, -2). Also, find its area. |
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| 4513. |
Pis any point inside a Delta^("le")ABC. lines are drawn through P parallel to the sides and the area of new triangle formed are Delta_(1),Delta_(2),Delta_(3), then sqrt(Delta_(1))+sqrt(Delta_(2))+ sqrt(Delta_(3))= |
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Answer» `SQRT(DELTA)` |
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| 4515. |
Variance of first n natural number is………… |
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Answer» `(n^2 -1)/(12)` |
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| 4516. |
The value of tan""(pi)/16+2tan""(pi)/8+4 is equal to |
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Answer» `COT""(PI)/2` |
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| 4517. |
Which of the following sentences are statements? Give reasons for your answer The sum of 5 and 7 is greater than 10. |
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| 4518. |
(x^(2)cos(pi)/(4))/(sinx) |
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| 4519. |
If Tan22^(@) + Tan38^(@) - sqrt(3) = k Tan22^(@) Tan38^(@) then k = |
| Answer» Answer :B | |
| 4520. |
List all the elements of the following sets : A= {x : x^(2) lt 10, x in Z} |
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| 4521. |
P=(0,1,0),Q=(0,0,1) then projection of bar(PQ) on the plane x+y+z=3 is |
| Answer» ANSWER :B | |
| 4522. |
Given Delta^("le")ABC with AB=20,AC=22(1)/(2),BC=27, Points x and y are taken on AB and AC respectively so thatAX = AY. If Area of Delta^("le") AXY=(1)/(2) area of Delta^("le")ABC find AX. |
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Answer» 15 |
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| 4523. |
A(3, 1, 5), B(-1, -1, 9) and C(0, -5, 1) are the vertices of a triangle. Then find the position vector of the centroid of DeltaABC. |
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| 4524. |
Find the derivative of e ^(- ax ^(2)) .sin (x log x )w.r.t.x |
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| 4525. |
Assertion (A) : sin^(-1)(sin3)=3 Reason (R) : For principal values sin^(-1)(Sinx)=x |
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Answer» Both A and R are TRUE and R is correct EXPLANATION of A |
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| 4526. |
Express (8 cos^2 x + 11 sin x)/(cos x) as the sum of function and hence differentiate it w.r.t.x |
| Answer» SOLUTION :-8 SIN X +`11 sec^2 x` | |
| 4528. |
The sum and sum of square corresponding to length x (in cm) and weight y (in gm) of 50 plant products are given below: sum_(i=1)^(50)x_(i)=212, sum_(i=1)^(50)x_(i)^(2)=902.8, sum_(i=1)^(50)y_(i)=261 sum_(i=1)^(50)y_(i)^(2)=1457.6 Which is more varying , the length or weight? |
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Answer» SOLUTION :For length, `sumx_(i)=212, sumx_(i)^(2)=902.8,N=50` `:.` MEAN `barx=(sumx_(i))/N=212/50=4.24cm` Variance `=(sumx_(i)^(2))/N-((sumx_(i))/N)^(2)=902.8/50-(212/50)^(2)` `=(45140-44944)/(50^(2))=196/2500` `implies` Standard deviation `SIGMA=14/50=0.28cm` Coefficient of variation of length `=(sigma)/x XX 100` `=0.28/4.24xx 100=6.6` For weight, `sumy_(i)=261,sumy_(i)^(2)=1457.6, N=50` `:.` Mean `=(sumy_(i))/N=261/N=5.22` Variance `sigma^(2)=(sumy_(i)^(2))/N-((sumy_(i))/N)^(2)=1457.6/50-(261/60)^(2)` `=(72880-68121)/((50)^(2))=4759/25500` `implies` Standard deviation `sigma=sqrt(4759/2500)=68.98/50=1.38` Now coefficient of variation of weight `=(sigma)/x xx100=1.38/5.22xx 100=26.43` Therefore, the weight of products are more varying. |
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| 4529. |
Fill in the blanks to make each of the following a true statement : φ′ ∩ A = . . . |
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| 4530. |
For the function f(x) = |x^2 - 5x +6| , the right hand derivation f'(2+) is equal to |
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| 4533. |
If P(-2,4,-5) and Q(1,2,3) are two points. Find the direction cosines of bar(PQ) |
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| 4534. |
Let theta, phi in [0,2pi] be such that 2cos theta(1-sin phi)=sin^(2)theta("tan"(theta)/2+"cot"(theta)/2)cos phi-1, tan (2pi-theta)gt0 and -1lt sin theta lt -(sqrt(3))/2. Then phi can not saitsfy |
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Answer» `0 lt philt(PI)/2` |
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| 4535. |
If sin h^(-1) 2 alpha= 2 coh h^(-1) beta then |
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Answer» `ALPHA^(2)+beta^(2)=alpha^(4)` |
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| 4536. |
sin((7pi)/(12))cos(pi/4)-cos((7pi)/(12))sin(pi/4)=........... |
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| 4537. |
If 0lexlt2pi then the number of real values of x, which satisy the equation |
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Answer» 5 |
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| 4538. |
Let A = {x : x is a natural number}, B = {x : x is an even natural number}, C = {x : x is an odd natural number} and D = {x : x is a prime number}. Find |
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| 4539. |
A point P(x, y) moves so that the sum of its distances from the points S(4, 2) and S^(') (-2, 2) is 8. Find the equation of its locus and show that it is an ellipse. |
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| 4540. |
Observe the following, choose correct answer : Assertion(A): The lines barr =(2bari + barj)+s(bari + barj -bark) and barr =(bari +bark)+t(7bari - barj +bark) are coplanar. Reason (R) : Condition for the lines barr = bara + sbarb and barr = barc + tbard to be coplanar is [bara-barc barb -bard]=0 |
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Answer» A is TRUE, R is false |
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| 4541. |
Rolle's theorem can not applicable for |
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Answer» `f(X) = SIN x ` |
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| 4542. |
(5,2) and (3,4) are end points of latus rectums then its focii is .......... . |
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| 4543. |
The vectors of bar(AB)=3bar(i)+4bar(k) and bar(AC)=5bar(i)-2bar(j)+4bar(k) are the sides of a triangle ABC. The length of the median through A is |
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Answer» `SQRT(72)` |
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| 4545. |
Given the complex number z= (-1 + sqrt3i)/(2) and w= (-1- sqrt3i)/(2) (where i= sqrt-1) Calculate the modulus and argument of w and z |
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| 4546. |
Given the complex number z= (-1 + sqrt3i)/(2) and w= (-1- sqrt3i)/(2) (where i= sqrt-1) Calculate the modulus and argument of (w)/(z) |
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| 4547. |
lim_(xtoa)(f(x)-f(a))/(x^(3)-a^(3))=…………… |
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Answer» `F'(a)(1)/(3A^(2))` |
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| 4548. |
The tangents from P to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 are mutually perpendicular show that the locus of P is the circle x^(2)+y^(2)=a^(2)-b^(2) |
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| 4549. |
Fourcards are drawn at random from a pack of 52 playing cards , Find the probability of getting all cards of the same colour , |
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