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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.
| 21801. |
Roots of the equation `(x^2-4x+3)+lamda(x^2-6x+8)=0` , `lamda in R` will beA. always realB. real only when `lambda` is positiveC. real only when `lambda` is negativeD. always is magnary |
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Answer» Correct Answer - A Roots of the quadratic ………….. `(x^(2)-4x+3)+lambda(x^(2)-6x+8)=0` `x^(2)(1+lambda)-2x(2+3lambda)+(3+8lambda) = 0` Discriminant. `D = 4(2+3lambda)^(2)-4(1+lambda)(3+8lambda)` `D = 4(lambda^(2)+lambda+1)` If `lambda epsilon R` then `D gt 0` so root of given quadratic always real |
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| 21802. |
If `|x+1|+|x^(2)-3x+2|=|x^(2)-4x+1|`, then sum of the natural number solutions of equation is |
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Answer» Correct Answer - 3 If `|x +1|+|x^(2)-3x+2|=` ………….. `|x+1|+|x^(2)-3x+2|=|x^(2)-4x+1|` `implies |a|+|b|=|a-b|` `implies (x+1)(x-1)(x-2)le 0` `implies x epsilon (-oo, -1)uu[1,2]` |
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| 21803. |
Complete solution set of the inequality `|x^(2)-x-2|+|x+1|le0` isA. `(-oo, -1)`B. `(-1,0)`C. `{-1, 0}`D. `{-1}` |
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Answer» Correct Answer - D Complete solution ………….. `|x^(2)-x-2|+|x+1|le0` `implies |x^(2)-x-2|+|x+1|=0` It is possible only when `x^(2)-x-2=0` and `x+1=0` |
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| 21804. |
If `(x^(2)-x+p)(11y^(2)-4y+2)=(9)/(2)` have exactly one ordered pair of `(x, y)` then find `p`. |
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Answer» Correct Answer - 3 If `(x^(2)-x+p)(11y^(2)-4y+2)`…………… `((4p-1)/(4)) ((88-16)/(44)) = (9)/(2)` `((4p-1)72)/(2xx88) = (9)/(2) implies 4p - 1 = 11 implies p =3` |
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| 21805. |
A moving particle is acted upon by several forces `F_(1),F_(2),F_(3)`….etc. One of the force is chosen sat `F_(2)` the which of the following statement about `F_(2)` will be true.A. Work done by `F_(2)` will be negative if speed of the particle decreasesB. Work done by `F_(2)` will be positive if speed of the particle increasesC. Work done by `F_(2)` will be equal to the work done by other forces if speed of the particle does not changeD. If `F_(2)` is a conservative force, then work done by all other forces will be equal to change in potential energy due to force `F_(2)` when speed remains constant. |
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Answer» Correct Answer - D By work energy theorem `W_(F_(2))+W_("other") = Delta K` `rArr W_(F_(2)) = Delta K - W_("other")` So A & B are wrong If speed do not change `Delta K =0` then `W_(F2)=-W_("other")`...(1) So `W_(F_(2))ne W_("other")` If `F_(2)` is conservative force then `Delta U = -W_(F_(2)) = W_("other") ("from" (1)` |
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| 21806. |
Let relation `R` defined on set of natural number is given by `R = {(a,b) : a^(2)+b^(2)-4bsqrt(3)-2a sqrt(3)+15=0}` then relation `R` isA. only symmetricB. only reflexiveC. only transitiveD. Symmetric and transitive |
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Answer» Correct Answer - A Let relation `R` defined ………….. `(a-sqrt(3))^(2)+(b-2sqrt(3))^(2)=0` `a,b epsilon N` `implies R = { } or phi` an empty relation on non empty set is transitive and Symmetric. |
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| 21807. |
If(2a²+3b² ) proportional to ( ab) Then prove that (9a⁴+4b⁴ ) is proportional to ( a²b²). |
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Answer» (2a²+3b² ) α ( ab) =>(2a²+3b² ) = k ( ab) [ k is constant] =>(2a²+3b² )^2 = k^2 ( ab)^2............(1) =>(2a²+3b² )^2-4*2a^2*3b^2 = k^2 ( ab)^2-24(ab)^2 =>(2a²-3b² )^2 =( k^2 -24)(ab)^2........(2) Dividing (1) by (2) we get (2a²+3b² )^2/(2a²-3b² )^2=k^2/(k^2-24) = a constant = m ^2 (say) So (2a²+3b² )/(2a²-3b² ) = m By componendo and dividendedo we get (2*2a²)/(2*3b² ) = (m+1)/(m-1) =>a^2/b^2=3/2*(m+1)/(m-1) =a constant =n (say) Now (9a⁴+4b⁴ )/ ( a²b²) = 9*a^2/b^2+4*b^2/a^2 = 9n+4/n = a constant So we can say (9a⁴+4b⁴ ) α ( a²b²) |
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| 21808. |
If the daigonals of a rhombus are 9cm and 12cm find its side |
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Answer» Square of each side = (9/2)^2+(12/2)^2 =81/4+36=56.25 So length of each side ,=√56.25=7.5cm |
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| 21809. |
6. If \( y=\sin x^{0} \), find \( \frac{d y}{d x} \). |
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Answer» y = sin x° = sin(\(\frac{x\pi}{180}\)) \(\frac{dy}{dx}=cos(\frac{x\pi}{180})\times\frac{\pi}{180}\) Hence, \(\frac{d}{dx}sin x^o\) = \(\frac{\pi}{180}cos x^o\) |
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| 21810. |
The locus of a point which moves such that the line segment having end points(2,0) and (-2,0) subtend a right angle at that point(a) x+y=4 (b) x2+y2=4 (c) x2-y2=4 (d) none of these |
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Answer» Let the point be P (h,k) Hence by the problem We have (k-0)/(h+2)×(k-0)/(h-2)=-1 =>k^2/(h^2-4)=-1 =>h^2+k^2=4 Replacing h by x and k by y the locus becomes x^2+y^2=4 |
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| 21811. |
Keeping the origin constant axes are rotated at an angle 30° in negative direction If then new coordinates of the point are (2,1) then its coordinates are with respect to old axis are:° |
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Answer» The new coordinates (X,Y) are given as: |
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| 21812. |
Keeping the origin constant axes are rotated at an angle 30° in negative direction, if then new coordinates of the point are (2,1) then its coordinate are with respect to old axis are |
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Answer» Let the line segment joining the origin and the new position of the point (2,1) with respect to new axes subtends angle A with the new X-axis and let the length of the segment be r. So rcosA=2 and rsinA=1 With respect to the old position of the axes the line segment will subtend an angle (A-30)° with the X-axis. So x-cordinate of the point w r to old axes will be x=rcos(A-30) =rcosAcos30°+rsinAsin30° =2×(√3/2)+1×1/2 =(2√3+1)/2 And corresponding y-coordinate. y=rsin(A-30) =rsinAcos30°-rcosAsin30° =1×√3/2-2×1/2 =(√3-2)/2 Hence option (B) accepted |
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| 21813. |
The sum of the products of the area of its elements and the squares of the perpendicular distances of the centres of gravity of these elements from the axis is called ___________(a) centrifugal force(b) moment of inertia of areas(c) centripetal force(d) centre of gravity |
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Answer» Right answer is (b) moment of inertia of areas The explanation: It is a measure of an object’s resistance to changes to its rotation. •Also defined as the capacity of a cross-section to resist bending. •It must be specified with respect to a chosen axis of rotation. •It is usually quantified in m4 or kgm^2. |
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| 21814. |
A body consists of numerous particles on which the pull of the earth, i.e. the forces of gravity act. The resultant of these forces acts through point. This point is called the ________ of the body.(a) centroid(b) neutral axis(c) centre of gravity(d) gravity |
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Answer» Right answer is (c) centre of gravity The explanation: A point from which the weight of a body or system may be considered to act. In uniform gravity it is the same as the centre of mass. |
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| 21815. |
What does ‘2’ denotes in the following window diagram?(a) Lintel(b) Sill(c) Header(d) Terrace |
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Answer» Right answer is (a) Lintel Easiest explanation: A lintel or lintol is a structural horizontal block that spans the space or opening between two vertical supports. It can be a decorative architectural element, or a combined ornamented structural item. It is often found over portals, doors, windows and fireplaces. Modern day lintels are made using prestressed concrete and are also referred to as beam in beam and block slabs or ribs in rib and block slabs. These prestressed concrete lintels and blocks are components that are packed together and propped to form a suspended floor concrete slab. |
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| 21816. |
Figure below shows isometric view of the object having____________(a) irregular curve(b) circular curve(c) inclined curve(d) isometric curve |
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Answer» Right option is (a) irregular curve Easiest explanation: Figure showing isometric view of the object having Irregular curve |
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| 21817. |
When a line is parallel to one plane and inclined to the other, the projection of the line on the plane to which it is parallel will show its __________ length.(a) shortened(b) true(c) enlarged(d) false |
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Answer» The correct choice is (b) true The best I can explain: The projected length on the plane to which it is inclined will always be shorter than the true length. In figure 2, the line AB is parallel to VP and is inclined to HP. The angle of inclination of AB with HP is being θ degrees. Projection of line AB on VP is a’b’ and is the true length of AB. The projection of line AB on HP is indicated as line ab. Length ab is shorter than the true length AB of the line. Refer the figure below. |
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| 21818. |
Find angle BDC shown in the figure below.(a) 30(b) 65(c) 60(d) 45 |
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Answer» Correct option is (d) 45 Easiest explanation: Given both the perpendiculars are equal so according to postulate, equal side has equal angle opposite to it. So, angle ADB = angle BDC, on equating both angles as 7x+17 = 3(4x – 1) x=4, and angle BDC = 45. |
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| 21819. |
Given 2 points A and B, what is the locus of points P so that angle APB is a right angle?(a) A square with points A and B(b) The circle with diameter AB(c) A rectangle with side A and B(d) A semi-circle with diameter AB |
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Answer» The correct answer is (b) The circle with diameter AB Best explanation: The circle with diameter AB, excluding points A and B will be the locus of point AB. This point P will always make 90° angle with the circumference when the lines from two points of radius meet at P, also from circle postulate it is proved. |
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| 21820. |
Let `E = [(1)/(3) + (1)/(50)]+[(1)/(3)+(2)/(50)]+[(1)/(3)+(3)/(50)]+……..` upto `50` terms where `[.]` denotes the greatest integer terms thenA. `E` is divisible by exactly `2` primesB. `E` is primeC. `E ge 30`D. `E le 35` |
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Answer» Correct Answer - B::D For `1 le x le 33` `(1)/(3) lt (1)/(3) + (x)/(50) lt 1 rArr [(1)/(3) + (x)/(50)] = 0` for `34 le x le 50` `1 lt 1/3 + x/50 lt 4/3` `1 lt [(1)/(3) + (x)/(50)] = 1` `:. E = 17` |
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| 21821. |
`(.^(50)C_(1))^(2)+2(.^(50)C_(2))^(2)+3(.^(50)C_(3))^(2)+.....+50(.^(50)C_(50))^(2)=`A. `.^(100)C_(50)`B. `50.(.^(100)C_(50))`C. `25(.^(100)C_(50))`D. `(2^(49))/(49!)(1.3.35…..99)` |
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Answer» Correct Answer - C::D `S = 0.(.^(50)C_(50))^(2) + 1.(.^(50)C_(1))^(2) + ….. + 50(.^(50)C_(50))^(2) …..(1)` `S = 50(.^(50)C_(50))^(2) + 49(.^(50)C_(49))^(2) + ……. + U(.^(60)C_(0))^(2) …..(2)` `(1) + (2)` `S = 25[(.^(50)C_(0))^(2) + (.^(50)C_(1))^(2) + ….. + (.^(50)C_(50))]^(2))` `= 25.(.^(100)C_(50))` |
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| 21822. |
If `sum_(t=1)^(1003) (r^(2) + 1)r! = a! - b(c!)` where `a, b, c in N` the least value of `(a + b + c)` is `pqrs` thenA. `p + q+ r + s = 4`B. `(p + q)/(r + s) = 1`C. `(p + q + r)/(s) = 3`D. `p.q.r.s` is even |
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Answer» Correct Answer - A::B::C::D `sum_(f=1)^(1003)(r^(2) + 1) r! = sum_(r=1)^(1003)((r^(2) + r)-(r - 1))rt` `= sum_(f=1)^(1003)(r(r + 1)! - (r - 1)r!)` `= (1.2! - 0) + (2.3! - 1.2!) + (3.4! - 2.3!)+ …….` `= 1005! - 2(1004!) = a! - b(c!)` `:. (a + b + c)_("least") = 1005 + 2 + 1004 = 2011 = pqrs` |
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| 21823. |
The particle P of mass m is attached to two light, rigid rods AP and BP of length l each. A and B are hings on a fixed vertical axis. The system APB can rotate freely about this axis. The angle ABP = the angle `BAP = theta`. The tensions in AP and BP are `T_(1)` and `T_(2)` respectively. The system is now rotated by `90^(@)` so that must be imparted to P, normal to the plane of the figure, such that it moves in a complete circular path in a vertical plane with AB as the axis?A. `2sqrt(gl sin theta)`B. `2sqrt(gl cos theta)`C. `(5//2)sqrt(gl sin theta)`D. None of these |
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Answer» Correct Answer - A |
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| 21824. |
if A and B are two fixed point and P moves such that angle APB = pi by 4 then shape of locus of P will be |
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Answer» The locus of point P must be a part of ellipse. Explanation: Take any numerical coordinates of point A and B and coordinates of point P as (h,k). Now find the slope of both the line AP and BP (by the formula y2 - y1 /x2 - x1) tan ϴ = m2 - m1/1 + m1m2 Now you will get the locus of P |
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| 21825. |
Four bar mechanism is generally used in ___________________(a) Bicycle(b) Fan(c) Train suspension(d) Rickshaw |
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Answer» The correct choice is (c) Train suspension Easiest explanation: Four-bar linkage, also called a four-bar, is the simplest movable closed chain linkage. It consists of four bodies, called bars or links, connected in a loop by four joints. Generally, the joints are configured so the links move in parallel planes, and the assembly is called a planar four-bar linkage. |
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| 21826. |
The expression `cos^(2)(alpha + beta + gamma) + cos^(2)(beta + gamma) + cos^(2)alpha - 2cos alpha cos(beta + gamma)cos(alpha + beta + gamma)` isA. independent of `alpha`B. independent of `beta`C. dependent on `gamma` onlyD. dependent on `alpha, beta, gamma` |
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Answer» Correct Answer - A::B `E = cos^(2)alpha + cos^(2)(beta + gamma) + cos^(2)(alpha + beta + gamma) - 2cos alpha cos(beta + gamma)cos(alpha + beta + gamma)` `= cos^(2)alpha + cos^(2)(beta + gamma) + cos^(2)(alpha + beta + gamma) - [(cos(alpha + beta + gamma) + cos(alpha - beta - gamma)).cos(alpha + beta + gamma)]` `= cos^(2)alpha + cos^(2)(beta + gamma) - [cos(beta + gamma - alpha) cos (beta + gamma + alpha))` `= cos^(2)alpha + cos^(2)(beta + gamma) - (cos^(2)(beta + gamma) - [cos^(2)(beta + gamma) - sin^(2)alpha ] = 1` |
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| 21827. |
When the projectors are parallel to each other and also perpendicular to the plane, the projection is called ___________ projection.(a) Oblique projection(b) Orthographic projection(c) Isometric projection(d) Perspective projection |
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Answer» The correct option is (b) Orthographic projection Best explanation: Refer to the figure given below which represents the visual ray. These are parallel to each other and perpendicular to the plane of projection. It represents the projection of objects. |
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| 21828. |
The relation between the direction of current and the direction of magnetic field is?(a) Same direction(b) Opposite direction(c) Perpendicular(d) Unrelated |
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Answer» The correct option is (c) Perpendicular The explanation is: When a conductor carries a certain value of current, the force developed in the conductor, the current in the conductor and the magnetic field in the conductor are mutually perpendicular to each other. |
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| 21829. |
When a line is parallel to a plane, the projection of the line on to that plane will be its ______ length.(a) shortened(b) true(c) enlarged(d) point |
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Answer» Right choice is (b) true To explain I would say: The projection of line AB lying parallel to the Vertical plane (VP) is shown in figure below as a’b’, representing the true length. |
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| 21830. |
If maximum value of current is 5√2 A, what will be the value of RMS current?(a) 10 A(b) 5 A(c) 15 A(d) 25 A |
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Answer» The correct choice is (b) 5 A Easiest explanation: We know, value of RMS current =value of max current/√2 Substituting the value of max current we get, rms current = 5A. |
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| 21831. |
Average value of current over a half cycle is?(a) 0.67Im(b) 0.33Im(c) 6.7Im(d) 3.3Im |
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Answer» Right answer is (a) 0.67Im The best explanation: Average current = ∫0^πidθ/π = ∫0^πImsinθ dθ/π = 2Im/π =0.67 Im. |
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| 21832. |
When the receding lines are true length, and the projectors are at 45 degrees to the plane of projection, the oblique drawing is called ______________(a) oblique projection(b) isometric projection(c) axonometric projection(d) cavalier projection |
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Answer» Right answer is (d) cavalier projection The best I can explain: Cavalier projection is a form of oblique projection in which the projection lines are presumed to make a 45-degree vertical and a 45-degree horizontal angle with the plane of projection. Assume that in figure below the line XX’ represents a side-edge view of the plane of projection and that the square ABCD represents a side of a cube, placed with its front face parallel to, and its top face perpendicular to, the plane of projection. You can see that the projected lengths of AB and AD are the same as the actual lengths. |
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| 21833. |
When the plane surface is held with its surface parallel to one of the planes of projection, the view of the plane surface projected on it will be in __________(a) apparent shape(b) point shape(c) true shape(d) line shape |
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Answer» Right option is (c) true shape To elaborate: When the plane surface is held with its surface parallel to one of the planes of projection, the view of the plane surface projected on it will be in true shape because all the sides or the edges of the plane surface will be parallel to the plane of projection on which the plane surface is projected. |
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| 21834. |
If `(2tan^(2)theta_(1)tan^(2)theta_(2)tan^(2)theta_(3)+tan^(2)theta_(1)tan^(2)theta_(2)+tan^(2)theta_(2)tan^(2)theta_(3)+tan^(2)theta_(3)tan^(2)theta_(1) = 1` then which of the following relations hold good ?A. `sin^(2)theta_(1) + sin^(2)theta_(2) + sin^(2)theta_(3) = 1`B. `cos2theta_(1) + cos2theta_(2) + cios2theta_(3) = 1`C. `sin^(2)theta_(1) + sin^(2)theta_(2) + sin^(2)theta_(3) = 2`D. `cos2theta_(1) + cos2theta_(2) + cos2theta_(3) = -1` |
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Answer» Correct Answer - A::B divide by `tan^(2)theta_(1)tan^(2)thetatan^(2)theta^(3)` `rArr 2 + cot^(2)theta_(3) + cot^(2)theta_(1) + cot^(2)theta_(2) = cot^(2)theta_(1)cot^(2)theta_(2)cot^(2)theta_(3)` `rArr cosec^(2)theta_(1) + cosec^(2)theta_(2) + cosec^(2)theta_(3)-1` `=(cosec^(2)theta_(1)-1)(cosec^(2)theta_(2)-1)(cosec^(2)theta_(3)-1)` `rArr cosec^(2)theta_(1) cosec^(2)theta_(2)+cosec^(2)theta_(2)cosec^(2)theta_(3)+cosec^(2)theta_(3)cosec^(2)theta_(1)` `= cosec^(2)theta_(1)cosec^(2)theta_(2)cosec^(2)theta_(3)` `sin^(2)theta_(1)+sin^(2)theta_(2)+sin^(2)theta_(3) = 1` (A) of `cos2theta_(1)+cos2theta_(2)+cos2theta_(3) = 1` (B) |
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| 21835. |
If `2010` is a root of `x^(2)(1 - pq) - x(p^(2) + q^(2)) - (1 + pq) = 0` and `2010` harmonic mean are inserted between `p` and `q` then the value of `(h_(1) - h_(2010))/(pq(p - q))` is |
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Answer» Correct Answer - 1 Let `2010 = n` `:. n^(2)(1-pq)-n(p^(2)-q^(2))-(1+pq) = 0` `(n^(2)-1)=pq(n^(2)+1)+n(p^(2)-q^(2))….(1)` `d=(p-q)/(pq(n+1)):.(1)/(h_(1))=(1)/(p)+d,(1)/(h_(2))=(1)/(q)-d` `h_(1)-h_(n)=(1)/((1)/(p)+d)-(1)/((1)/(q)-d)=(P)/(1+pd)-(q)/(1-qd)` `(p)/(1+(p(p-q))/(pq(n+1)))-(q)/(1+(q(p-q))/(pq(n+1)))` `= (pq(p-q)(n^(2)-1))/((qn+p)(pn+q))` `=(pq(p-q)[pq(n^(2)+1)+n(p^(2)+q^(2))])/((qn+p)(pn+q))` `:. (h_(1) - h_(n))/(pq(p-q)) = 1` |
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| 21836. |
When the Projection of a line is parallel to both HP and VP its length will be _______(a) shortened(b) false(c) enlarged(d) true |
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Answer» The correct answer is (d) true For explanation: Since the line is parallel to both HP and VP, both the front view a’b’ and the top view ab are in true lengths. Since the line is perpendicular to the right PP, the left side view of the line will be a point a΄΄(b΄΄). After projection on to the projection planes, the planes are rotated such that all the three projection planes lie in the same planes. The multi-view drawing of line AB is shown in figure b. |
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| 21837. |
In a case when a line is perpendicular to HP & parallel to VP then what figure will be projected on HP?(a) Point(b) Line(c) Square(d) Inclined line |
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Answer» The correct choice is (a) Point For explanation: Draw the horizontal projector through a(b) to cut the 45 degree line at m. Draw the horizontal projectors through a’ and b’ to intersect the vertical projector drawn through m at a΄΄ and b΄΄. a΄΄b΄΄ is the left view of the line AB. |
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| 21838. |
If `a, b, c` are distinct positive real numbers such that the quadratic expression `Q_(1)(x) = ax^(2) + bx + c`, `Q_(2)(x) = bx^(2) + cx + a, Q_(3)(x) = cx^(2) + x + b` are always non-negative, then possible integer in the range of the expression `y = (a^(2)+ b^(2) + c^(2))/(ab + bc + ca)` isA. `1`B. `2`C. `3`D. `4` |
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Answer» Correct Answer - B::C For `a ne b ne c a, b, c in R^(+)` if `ax^(2) + bx + c ge 0` then `a gt 0` and `b^(2) - 4ac le 0` `bx^(2) + cx + a ge 0` then `b gt 0` and `c^(2) - 4ab le 0` `cx^(2) + ax + b ge 0` then `c gt 0` and `a^(2) - 4bc le 0` `rArr a^(2)+b^(2)+c^(2)-4(ab+bc+ac)le0 rArr (a^(2)+b^(2)+c^(2))/(ab+bc+ca)lt4` Also we know that `(a-b)^(2) + (b-c)^(2) + (c-a)^(2) gt 0` `a^(2) + b^(2) + c^(2) - ab - bc- ac gt 0 rArr (a^(2) + b^(2) + c^(2))/(ab + bc + ca) gt 1` `:.` range is `(1, 4)` |
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| 21839. |
Let `f_(n)(theta) = sum_(n=0)^(n) (1)/(4^(n))sin^(4)(2^(n)theta)`. Then which of the following alternative(s) is/are correct ?A. `f_(2)((pi)/(4))=(pi)/(sqrt(2))`B. `f_(3)((pi)/(8)) = (2 + sqrt(2))/(4)`C. `f_(4)((3pi)/(2)) = 1`D. `f_(5)(pi) = 0` |
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Answer» Correct Answer - C::D `f_(n)(theta)=overset(n)underset(n=0)(sum)(1)/(4^(n))sin^(4)(2^(n)theta)= overset(n)underset(n=0)sum(1)/(4^(n))(sin^(2)(2^(n)0))(1-cos^(2)2^(n)theta)` `=overset(n)underset(n=0)(sum)[sin^(2)(2^(n)theta)-(1)/(4)sin^(2)(2^(n-1)theta)](1)/(4^(n))` `rArrf_(n)(theta)overset(n)underset(n=0)(sum)[(1)/(4^(n))sin^(2)2^(n)theta-(1)/(4^(n+1))sin^(2)(2^(n+1)theta)]` `:. f_(n)(theta) = (sin^(2) 2theta- (1)/(4)sin^(2)2theta)` `+((1)/(4)sin^(2)2theta-(1)/(4^(2))sin^(2)2^(2)theta)+.......(n)` term `f_(n)(theta) = sin^(2)theta - (1)/(4^(n-1))sin^(2)(2^(n+1)theta)` |
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| 21840. |
If `S_(n) = sum_(n=1)^(n) (2n + 1)/(n^(4) + 2n^(3) + n^(2))` then `S_(10)` is less thenA. `0`B. `1`C. `2`D. `3` |
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Answer» Correct Answer - B::C::D `S_(n)=sum_(n=1)^(n)(2n+1)/(n^(2)(n+1)^(2)) = sum_(n=1)^(n)((1)/(n^(2))-(1)/((n+1)^(2)))` `S_(10) = 1-(1)/(121)=(120)/(121)` |
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| 21841. |
Auxiliary planes are of _______ types.(a) two(b) one(c) three(d) six |
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Answer» Correct answer is (a) two The explanation is: These are A.V.P (Auxiliary vertical plane) and A.I.P. (Auxiliary inclined plane). Auxiliary vertical plane is perpendicular to the H.P. and inclined to the V.P. projection on an A.V.P. is called auxiliary front plane. Auxiliary inclined plane is perpendicular to the V.P. and inclined to the H.P. projection on an A.I.P. is called auxiliary top view. |
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| 21842. |
Anti-siphonage pipe is connected to __________(a) top of P trap W.C(b) main soil pipe(c) bottom of P trap W.C(d) side of water closet |
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Answer» Right option is (c) bottom of P trap W.C Best explanation: A vent is open at top and bottom, to facilitate exit of foul gases. It is carried at least one meter higher than the roof level. Rain water pipe: it is a pipe which carries only the rain water. Anti-siphonage pipe: it is pipe which is installed in the house drainage to preserve the water seal of traps. |
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| 21843. |
To save space on the drawing or to save time only ___________ view may be drawn.(a) Half auxiliary(b) Full auxiliary(c) Front(d) Top |
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Answer» The correct answer is (a) Half auxiliary For explanation: If an auxiliary view is symmetrical, and if it is necessary to save space on the drawing or to save time, only half of the auxiliary view may be drawn, as shown below. In this case, half of a regular view is also shown since the bottom flange is also symmetrical as shown in the figure below. |
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| 21844. |
Parabolic curves is not used in ________(a) Arches(b) Bridges(c) Sound reflectors(d) Boring |
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Answer» Right answer is (d) Boring For explanation I would say: Mostly used in construction and also for converging or diverging light since radiation often needs to be concentrated at one point (e.g. radio telescopes, pay TV dishes, solar radiation collectors) also to be transmitted from a single point into a wide parallel beam (e.g. headlight reflectors). Boring uses single point cutting tools which are straight vertical shaped. |
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| 21845. |
_________ pointing is made by making a projection in the form of V-shape.(a) V-pointing(b) Struck pointing(c) Weathered pointing(d) Surface pointing |
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Answer» Correct answer is (a) V-pointing To explain I would say: This type of pointing is made similar to keyed or grooved pointing by suitably shaping the end of the steel rod to be used for forming the groove. V pointing pointing is formed by forming v-groove in the flush finishing face. |
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| 21846. |
The point at which the line intersects the VP, extended if necessary, is known as ____________(a) profile trace(b) horizontal trace(c) vertical trace(d) auxiliary trace |
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Answer» Right choice is (c) vertical trace Best explanation: If a line is parallel to any of the plane, it has no trace upon that plane. For example: If the line is parallel to horizontal plane then that line will not meet H.P and hence there will be no Horizontal Trace and only Vertical Trace. |
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| 21847. |
Hens-Eggs, Cow-______? |
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Answer» Correct answer is Milk |
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| 21848. |
Oven-Kitchen, End table-______? |
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Answer» Correct answer is Living room |
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| 21849. |
Elbow-Arm, Knee-______? |
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Answer» Correct answer is Leg |
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| 21850. |
Pure-Purify, Soft-______? |
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Answer» Correct answer is Soften |
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