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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.
| 2701. |
Find the derivatives of the function tan ^(-1) (( cos x )/( 1 + cos x )) |
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| 2702. |
A unit vector in the plane of the vectors 2bari +barj+bark, bari - barj+ bark and orthogonal to 5bari +2barj +6bark is |
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Answer» `(6bari-6bark)/(sqrt(61))` |
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| 2703. |
If the opposite vertices of a square are (-2,3) and (8,5) find the equations of the sides of the square. |
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Answer» `3x-2y+12=0, 3x-2y-14=0` |
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| 2704. |
Find the conjugate of ((3-2i)(2+3i))/((1+2i)(2-i)) |
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| 2705. |
Answer each question by selecting the proper alternative from those given below each question so as to make each statement true : The sum of first n terms of two Aps are in the ratio 5n + 4 , 9n + 6 . Then , the ratio of their 18th term is ....... |
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| 2706. |
If a line makes angles alpha, beta, lambda,delta with the fourdiagonals of a cube, then show that cos^(2) alpha+cos^(2) beta + cos^(2)lambda+cos^(2)delta=(4)/(3). |
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| 2707. |
If lines x+2y-1=0, ax+y+3=0, and bx-y+2=0 are concurrent, and S is the curve denoting the locus of (a,b), then the least distance of S from the origin is |
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Answer» `5//sqrt57` |
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| 2708. |
For the following compoundstatement, first identify the connective word and then break it into component statements. Square of an integer is positive or negative. |
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Answer» <P> p : Square of an integer is positive Q : Square of an integer is NEGATIVE. |
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| 2709. |
For each of the following compoundstatements, first identify the connective words and then break it into component statements. All rational numbers are real and all real numbers are not complex. |
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Answer» <P> p : All rational numbers are REAL. Q : All real numbers are not COMPLEX. |
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| 2710. |
For each of the following compoundstatements, first identify the connective words and then break it into comonent statements. x=2 and x =3 are the roots of the equation3x^(2)-x-10=0. |
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Answer» <P> p : x=2 ISA root of the EQUATION`3x^(2)-x-10=0` Q : x=3 is a root of the equation `3x^(2)-x-10=0` |
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| 2711. |
If the distance from point P (1,1,1) to the line passing through the points Q (0,6,8) and R (-1,4,7) is expressed in the form sqrt ((p)/(q))where p and q are coprime, then the value (( p +1) (p + q -1))/(2) equals |
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Answer» 4950 |
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| 2712. |
There Are Three Events A, B, C One of Which Must and Only One Can Happen, the Odds Are 8 to 3 Against A, 5 to 2 Against B. Find the Odds Against C. |
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| 2713. |
Eccentricity of ellipse (x^(2))/(169) + (y^(2))/(25) = 1 and (x^(2))/(a^(2)) + (y^(2))/(b^(2)) = 1 then (a)/(b) = …….. |
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Answer» `(5)/(13)` |
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| 2714. |
If there is an error of 3/10% in the volume of a sphere then the percentage error in its radius is |
| Answer» Answer :A | |
| 2715. |
Write the equation of the lines for which tan theta = (1)/(2), where theta is the (i) y -intercept is = -(3)/(2) |
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| 2718. |
Co-ordinates of focii of hyperbola 2x^(2) - 3y^(2) = 5 is ………. |
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Answer» `(PM(5)/(sqrt(6)),0)` |
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| 2720. |
If A(1,2), B(-3,2) and C(3,-2) are the vertices of DeltaABC, show that : (i) tanA=2 (ii) tanB=(2)/(3) (iii) tanC=(4)/(7) |
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| 2721. |
Write down the expansion by the binomial theorem of (3x - (y)/(2) )^(4). By giving x and y suitable values, deduce the value of (29.5)^(4) correct to four significant figures. |
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| 2722. |
Calculate an index number for the second year, taking the first year as base, taking into account the prices of the four commodities (in Rs. per kg) and the weights given here under. |
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| 2723. |
A straight line passing through A (-2,1), makes an angle of 30^(@) with the positive direction of the X-axis. Find the points on the straight line whose distance from A is 4 units. |
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| 2724. |
Find the sum of the first n terms of the series: 0.2 + 0.22 + 0.222+ ....n - terms |
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| 2725. |
If A and B are two candidates seeking admission in an engineering College. The probability that A is selected is .5 and the probability that both A and B are selected is at most.3. Is it possible that the probability of B getting selected is 0.7? |
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| 2726. |
cos5^(@) + cos 24^(@) + cos 175^(@) + cos 204^(@) + cos 300^(@) = |
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Answer» `1//2` |
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| 2727. |
Period of ( 2 sin 2x -5 cos 2x )/( 7 cos x - 8 sin x) is |
| Answer» Answer :B | |
| 2728. |
Which of the following sentences are statement? Give reason for your answer: All prime numbers are eve numbers. |
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| 2729. |
Delta^("le") ABC is equilateral triangle of side a.P lies on BA such that A is mid point of PB. If r_(1) is inradius of Delta^("le") PAC" and " r_(2)is ex radius of Delta^("le") PBCopposite to P then r_(1)r_(2) = |
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Answer» `a//2` |
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| 2730. |
If |vec(a)|= |vec(b)|=5, (vec(a), vec(b))= 45^(@), then find the area of triangle constructed with the vectors vec(a)- 2vec(b), 3vec(a) + 2vec(b) as adjacent sides |
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| 2732. |
If y = 5^(2(log_(5)(x+1)-log_(5)(3x+1)) then (dy)/(dx) at x = 0 is |
| Answer» ANSWER :D | |
| 2733. |
bari xx [(baraxxbarb)xxbari] +barj xx [(baraxx barb)x barj] + bark xx [(baraxx barb)xx bark] = |
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Answer» `BAR0` |
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| 2734. |
Let h(x)=|kx+5|, the domain of f(x) be [-5, 7], the domain of f(h(x)) be [-6, 1] and the same as the domain of f(x). Then the value of k is |
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Answer» 1 |
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| 2735. |
Find the number of ways in which 4 boys and 4 girls be seated in a row so that, (i) No two girls may sit together. (ii) All the girls sit together and all the boys sit together. |
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| 2736. |
Which of the following lies in the sixth octant? |
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Answer» `(-3,-2,-2)` |
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| 2737. |
18 m ice were placed in two experimental groups and one control group, with all group equally large. In how many ways can the mice be placed into three groups? |
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| 2738. |
If x = phi (t), y = Psi(t) then (d^2y)/(dx^2) is |
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Answer» `(phi^1Psi^(11)-PSI^(1)phi^(11))/((phi^(1))^2)` |
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| 2739. |
alpha, beta, gamma, delta are angles in I, II, III and IV quadrant respectively and no one of them is an integral multiple of pi//2. They form an increasing arithmetic progression.Which of the following holds |
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Answer» `cos(alpha+delta)GT0` |
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| 2740. |
alpha, beta, gamma, delta are angles in I, II, III and IV quadrant respectively and no one of them is an integral multiple of pi//2. They form an increasing arithmetic progression.Which of the following does not hold |
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Answer» `sin(beta+gamma)=sin(alpha+delta)` |
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| 2741. |
Find sin ""(x)/(2), cos "" (x)/(2) and tan "" (x)/(2) in each of the case: sin x = (1)/(4), xin II quadrant. |
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| 2742. |
Find the total number of ways of selecting five different letters of which 3 are alike from the word INDEPENDENT. |
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| 2744. |
Find the slope of the lines : (d) Making inclination of 60° with the positive direction of x-axis. |
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| 2745. |
For 0lexle2pi, Match the equations in List I to no. of solutions in List II {:(ul"List I",ul"List II"),(ul"(Trigonometric equation)",ul"(no. of solution)"),("I) "Tan^(2)x+Cot^(2)x=2,"a) 2"),("II) "Sin^(2)x-Cosx=1//4,"b) 0"),("III) "4Sin^(2)x+6Cos^(2)x=10,"c) 1"),("IV) "Sinx = 1,"d) 4"),(,):} |
| Answer» Answer :A | |
| 2746. |
Find the ratio in which the line joining the points (2, 4, 5), (3,5,-4) is divided by the yz-plane. |
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| 2747. |
Show that two lines a_(1)x + b_(1) y+ c_(1) = 0 " and " a_(2)x + b_(2) y + c_(2) = 0 " where " b_(1) , b_(2) ne 0are : (i) Parallel if a_(1)/b_(1) = a_(2)/b_(2) , and (ii) Perpendicular if a_(1) a_(2) + b_(1) b_(2) = 0 . |
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| 2748. |
Locus of the mid-points of the portion of the line x sin theta +y cos theta = p intercepted between the axes is…...... |
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Answer» <P> |
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| 2749. |
The approximate value of (1)/(root(3)(8.08)) is |
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Answer» 0.49 |
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| 2750. |
InDelta ABC,if a = 6, b=3and cos (A-B) = (4)/(5)" then "angle C = |
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Answer» `(3PI)/4 ` |
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