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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.
| 12401. |
Find the product of the perpendicular drawn from the point(1 , 2)to the pair of lines x^(2)+4xy+y^(2)=0 |
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| 12402. |
A line L passes through the point (1, 1) and (2,0). Another line M which is perpendicular to L passes through the point[(1)/(2), 0]. Then the area of the triangle formed by the lines L, M and y-axis is |
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Answer» `25//8` |
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| 12403. |
Find the derivative of the following functions (it is to be understand that a,b,c,d,p,q,r and s are fixed non-zero constants and m and n are integers): (x)/(sin^(n)x) |
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Answer» Solution :Let `y=(X)/(sin^(n)x)` `RARR (DY)/(dx)=(d)/(dx)((x)/(sin^(n)x))` `=(sin^(n)XX(d)/(dx)x-x(d)/(dx)(sin^(n)x))/((sin^(n)x)^(2))` `=(sin^(n)x.1-x.n sin^(n-1)x.(d)/(Dx)sinx)/(sin^(2n)x)` `=(sin^(n-1)x[sinx-nxcosx))/(sin^(n+1)x)` |
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| 12404. |
Which of the following is/are true |
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Answer» `2TAN^(-1)x=sin^(-1)((2X)/(1+x^(2)))," when "abs(x) le 1` |
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| 12405. |
In a certain college 4% of the boys and 1 % of the girls are taller than 1.8 meter. Further 60% of the students are girls. If a student is selected at random and is taller than 1.8 meters, then the probability that the student is a girl is |
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Answer» `2/11` |
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| 12406. |
If Delta_( r)= |(2r-1, ""^(m)C_(r ), 1),(m^(2)-1, 2^(m), m+1), ("sin"^(2)(m^(2)), "sin"^(2)(m), "sin"^(2)(m+1))|then sum_(r =0)^(m)Delta_(r )= |
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Answer» 0 |
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| 12407. |
If tanx=-(4)/(3),(pi)/(2)ltxltpi then sin((x)/(2))= ………… |
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Answer» `-(2)/(sqrt(5))` |
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| 12409. |
theta=tan^(-1)(2tan^(2)theta)-tan^(-1)(1/3tantheta) if |
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Answer» `TAN theta=-2` |
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| 12410. |
Find the angle between the planes 2x-y+z-6=0, x+y+2z-7=0. |
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| 12411. |
If 2x+3y+4=0 is the perpenedicular bisector of the segment joining the points A(1,2) and B(alpha, beta) then the value of alpha+beta is |
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Answer» `-81/13` |
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| 12412. |
If sintheta sin(2alpha+theta)sin(4alpha + theta)...sin(2(n-1)alpha+theta)=(sinntheta)/(2^(n-1)) where 2nalpha=pi then cot(theta)+cot(2alpha+theta)+cot(4alpha+theta)+.......+cot(2n-1)alpha+theta)= |
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Answer» `-ncot ntheta` |
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| 12413. |
Find the sum to n terms of each of the series in 5^2 + 6^2 + 7^2 + ... + 20^(2) |
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| 12414. |
When a right handed rectangular cartesian system oxyz is rotated about the z-axis through an angle pi/4 in the counter clockwise direction. It is found that a vector bar(a) has the components 2sqrt(2), 3sqrt(2), 4. The components of bar(a) in the oxyz coordinate system are |
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Answer» 1, -5, 4 |
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| 12415. |
The set S_(1) and S_(2) are solution sets of (1+a)cos theta cos (2 thetacos (2 theta-b)=(1+a cos 2 theta)cos (theta-b) |
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Answer» `{n PI , n in Z}` and `1/2 {n pi +(-1)^(n)SIN^(-1)(a sin b)=b , n in Z}` |
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| 12416. |
Find all points on the line x+y=4 that lie at a unit distance from the line 4x+3y=10. |
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| 12417. |
If the area of the triangle whose vertices are A(1, 2, 3), B(2, -1, 1)and C(1, 2, -4) is lambda sq unit then (2lambda)/(sqrt(10)) must be |
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| 12418. |
Find the multiplicative inverse of each of the following complex numbers when it exists. 2 + 2i |
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| 12420. |
Find the corrdinates of the foci and the vertices, the eccentricity, the length of the latus rectum of the hyperbolas : (i) (x^(2))/(9)-(y^(2))/(16)=1 (ii) y^(2)-16x^(2)=16 |
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| 12421. |
A tetrahedron has vertices O(0,0,0), A(1,2,1), B(2,1,3) and C(-1,1,2). Then the angle between the faces OAB and ABC is |
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Answer» `COS ^(-1) ((17)/(31)) ` |
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| 12422. |
Find the value of lambda for which the equation lambdax^(2) - 10xy + 12y ^(2)+5x – 16y - 3 = 0 represents a pair of striaght lines. |
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| 12423. |
Show that the function f(x) =x sub (1)/(x) , x ne 0 f(0) =0is continuous at x = 0 |
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| 12424. |
Expand (1)/((3+2x)^(2)) in powers of x. Find a condition on x for which the expansion is valid. |
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| 12425. |
If x is real and the expression (x^(2) + 2x - 11)/( x - 3) takes all values which do not lie between a and b, then find a and b |
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| 12428. |
Find the slope of the lines : Making inclination of 60^(@)with the positive direction of x- axis. |
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| 12429. |
Evaluate the following limits : Lim_(x to 0) (3^(x)-1)/(sqrt(1+x)-1) |
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| 12430. |
Solve each of the following equations for real x and y : (x+yi) - (7+4i) =3- 5i |
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| 12431. |
Whenever the terms on the two sides of the equation are differentnature, then equations are known non standard form of an ordinary equation. But cannot be solved by standard procedure, non standard problemsrequire high degree of logic, they also require the use of graphs, inverse properties of functions, inequalities . The number of real solutions of the equation sin (e^(x)) = 5^(x) + 5^(x) is |
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Answer» 0 |
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| 12432. |
Whenever the terms on the two sides of the equation are different nature, then equations are known non standard form of an ordinary equation. But cannot be solved by standard procedure, non standard problems required high degree of logic, they also require the use of graphs, inverse properties of functions, inequalities.The number of solutions of the equation sinx=x^(2)+x+1 is |
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Answer» 0 |
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| 12433. |
Find the eccentricity andthe coordinate of foci of the hyperbola 25 x ^(2) - 9y ^(2) = 225. |
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| 12436. |
Whenever the terms on the two sides of the equation are differentnature, then equations are known non standard form of an ordinary equation. But cannot be solved by standard procedure, non standard problemsrequire high degree of logic, they also require the use of graphs, inverse properties of functions, inequalities . The number of solutions of the equation 2 cos ((x)/(2)) = 3 ^(x) + 3^(-x) is |
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Answer» 1 |
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| 12437. |
The straight lines 4ax+3by+c=0, where a+b+c=0, are concurrent at the point |
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Answer» (4,3) |
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| 12438. |
The maximum and minimum value of f(x)=(x-8)^4(x-9)^5 occurs at x= |
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Answer» `4,3//4` |
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| 12439. |
Match each of the set on the left described in the roster form with the same set on the right described in the set builder form : |
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| 12440. |
y = log^(n)x x where log^(n) means log.log.log ....(repeated n times) then x.logx.log^2x.log^3x-log^(n-1)x,(dy)/(dx)= |
| Answer» Answer :D | |
| 12441. |
sin^(2)((pi)/(8))+sin^(2)((3pi)/(8))+sin^(2)((5pi)/(8))+sin^(2)((7pi)/(8))= ......... |
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Answer» 1 |
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| 12442. |
Find the equation of a line drawn perpendicular to the line x/4 + y/6 = 1 through the point , where it meets the y-axis. |
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| 12443. |
Find the derivative of the following functions: 5sin x-6 cos x+7 |
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| 12445. |
State the equation of the line which has the y-intercept -5 and is equally inclined to the axes |
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| 12446. |
………of the following is logically equivalent statement of ~(~p implies q) |
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Answer» `p^^q` |
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| 12447. |
Event G and C denotes that student is intelligent and fond of chocolate . If P(G) = 0.6 ,P(C) = 0.7 , P(GcapC) = 0.4,then P(G'capC')= ….. |
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| 12448. |
Two medians drawn from the acute acute angles of a right-angled triangle intersect at a angle pi//6. If the length of the hypotenuse of the triangle is 3 unit then area of the triangle (in sp. Units) is |
| Answer» Answer :A | |
| 12449. |
The maximum value of expression |sqrt(sin^(2)x+2a^(2))-sqrt(2a^(2)-1-cos^(2)x)|, where a and x are real numbers, is |
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Answer» `sqrt(3)` |
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| 12450. |
Evaluate the following limits : Lim_(n to oo) (Sigman^(3))/(n^(4)) |
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