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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.
| 4151. |
The value of 1∫0xdxx3+16 lies in the interval |
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Answer» The value of 1∫0xdxx3+16 lies in the interval |
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| 4152. |
For a particle displacement x at time t is given by x2=at2+b where a and b are constants. Its acceleration at time t is proportional to |
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Answer» For a particle displacement x at time t is given by x2=at2+b where a and b are constants. Its acceleration at time t is proportional to |
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| 4153. |
If z1 and z2 lie on a circle having centre at the origin, then point of intersection of the tangents at z1 and z2 is |
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Answer» If z1 and z2 lie on a circle having centre at the origin, then point of intersection of the tangents at z1 and z2 is |
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| 4154. |
In a △ABC, cos A=35 and cos B=513 The value of cot C can be |
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Answer» In a △ABC, cos A=35 and cos B=513 The value of cot C can be |
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| 4155. |
How to take antilog of 4.616 |
| Answer» How to take antilog of 4.616 | |
| 4156. |
If f(x)=exg(x), g(0)=2 and g′(0)=1, then f′(0) is |
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Answer» If f(x)=exg(x), g(0)=2 and g′(0)=1, then f′(0) is |
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| 4157. |
Sum of coefficients of ˆi,ˆj and ˆk in the cross product (2ˆi+3ˆj+4ˆk) × (ˆi−ˆj+ˆk) will be___. |
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Answer» Sum of coefficients of ˆi,ˆj and ˆk in the cross product (2ˆi+3ˆj+4ˆk) × (ˆi−ˆj+ˆk) will be |
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| 4158. |
Scientific notation and significant figures |
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Answer» Scientific notation and significant figures |
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| 4159. |
Solve the given inequality for real x: 3(2 – x) ≥ 2(1 – x) |
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Answer» Solve the given inequality for real x: 3(2 – x) ≥ 2(1 – x) |
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| 4160. |
Let b,d >0. The locus of all points P(r,x) for which line OP(O is origin) cuts the line r sin(x) =b in Q such that PQ=d is(A) (r+d)sinx=b (B)(r-d)sinx=b(C) (r-d)cosx=b (D)(r+d)cosx=b |
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Answer» Let b,d >0. The locus of all points P(r,x) for which line OP(O is origin) cuts the line r sin(x) =b in Q such that PQ=d is (A) (r+d)sinx=b (B)(r-d)sinx=b (C) (r-d)cosx=b (D)(r+d)cosx=b |
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| 4161. |
If f:R→R defined by f(x)=⎧⎨⎩x,x<1x2,1≤x≤48√x,x>4, then f−1(x) is |
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Answer» If f:R→R defined by f(x)=⎧⎨⎩x,x<1x2,1≤x≤48√x,x>4 |
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| 4162. |
∫2x(x2+1)(x2+2)dx is equal to |
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Answer» ∫2x(x2+1)(x2+2)dx is equal to |
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| 4163. |
What is the value of sin θ/(1 + cos θ) + sin θ/(1 - cos θ), where (0°< θ < 90°)? |
| Answer» What is the value of sin θ/(1 + cos θ) + sin θ/(1 - cos θ), where (0°< θ < 90°)? | |
| 4164. |
Which of the following points are extrema for f(x) = sin(x) ? |
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Answer» Which of the following points are extrema for f(x) = sin(x) ? |
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| 4165. |
Let A be the set of first ten natural numbers and let R be a relation on A×A defined by R={(x,y):x+2y=10;x,y∈A}. Then range of R−1 is |
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Answer» Let A be the set of first ten natural numbers and let R be a relation on A×A defined by R={(x,y):x+2y=10;x,y∈A}. Then range of R−1 is |
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| 4166. |
If x3+y3=sinx+y, then dydx= |
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Answer» If x3+y3=sinx+y, then dydx= |
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| 4167. |
If π3≤arg[(z+1)(z−1)]≤2π3, represented bythen z lies in |
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Answer» If π3≤arg[(z+1)(z−1)]≤2π3, represented by |
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| 4168. |
5^{2x+1}÷25=125 |
| Answer» 5^{2x+1}÷25=125 | |
| 4169. |
23.Find the sum of the first n terms of the series: 3+ 7 +13 +21 +31 + |
| Answer» 23.Find the sum of the first n terms of the series: 3+ 7 +13 +21 +31 + | |
| 4170. |
If tan−1x+tan−1y=π4,xy<1. then write the value of x+y+xy. |
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Answer» If tan−1x+tan−1y=π4,xy<1. then write the value of x+y+xy. |
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| 4171. |
A variable plane moves so that the sum of the reciprocals of its intercepts on the coordinate axis is 12. The plane passes through the point ____________. |
| Answer» A variable plane moves so that the sum of the reciprocals of its intercepts on the coordinate axis is . The plane passes through the point ____________. | |
| 4172. |
A book has pages numbered from 1 to 85. What is the probability that the sum of the digits on the page is 8, if a page is chosen at random? |
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Answer» A book has pages numbered from 1 to 85. What is the probability that the sum of the digits on the page is 8, if a page is chosen at random? |
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| 4173. |
If S=1+83+279+6427+⋯∞, then the value of 8S is |
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Answer» If S=1+83+279+6427+⋯∞, then the value of 8S is |
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| 4174. |
The value of 6+log32⎛⎜⎝13√2⎷4−13√2⎷4−13√2√4−13√2...⎞⎟⎠ is |
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Answer» The value of 6+log32⎛⎜⎝13√2 ⎷4−13√2 ⎷4−13√2√4−13√2...⎞⎟⎠ is |
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| 4175. |
If α,β are the roots of the equation 2x2+5x+6=0, then find the equation whose roots are 1α and 1β. |
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Answer» If α,β are the roots of the equation 2x2+5x+6=0, then find the equation whose roots are 1α and 1β. |
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| 4176. |
In the adjoining figure, ∆ABC is a right-angled at B and ∠A = 45°. If AC = 32 cm,find (i) BC, (ii) AB. |
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Answer» In the adjoining figure, ∆ABC is a right-angled at B and ∠A = 45°. If AC = cm, find (i) BC, (ii) AB. 
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| 4177. |
1) find the ratio in which (7/3,-1) divides the line joining the points (1,5) and (3,-4).2) if the coordinates of two points A and B are (3,4) and ( 5, -2). find coordinates of P if PA = PB and area of triangle PAB=103) Find the incentre of the triangle formed by the coordinates axes and x+y=4 4) find the incentre of the triangle formed by (0,0),(2,20 and (1-root 3, 1+root 3) |
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Answer» 1) find the ratio in which (7/3,-1) divides the line joining the points (1,5) and (3,-4). 2) if the coordinates of two points A and B are (3,4) and ( 5, -2). find coordinates of P if PA = PB and area of triangle PAB=10 3) Find the incentre of the triangle formed by the coordinates axes and x+y=4 4) find the incentre of the triangle formed by (0,0),(2,20 and (1-root 3, 1+root 3) |
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| 4178. |
Find thedistance between andwhen:(i) PQ is parallel to the y-axis, (ii) PQ is parallel to thex-axis. |
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Answer» Find the |
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| 4179. |
Without expanding, show that the values of each of the following determinants are zero:(i) 82712351643(ii) 6-322-12-1052(iii) 23713175152012(iv) 1/aa2bc1/bb2ac1/cc2ab(v) a+b2a+b3a+b2a+b3a+b4a+b4a+b5a+b6a+b(vi) 1aa2-bc1bb2-ac1cc2-ab(vii) 491639742623(viii) 0xy-x0z-y-z0(ix) 143673543172(x) 12223242223242523242526242526272(xi) abca+2xb+2yc+2zxyz(xii) 2x+2-x22x-2-x213x+3-x23x-3-x214x+4-x24x-4-x21(xiii) sinαcosαcos(α+δ)sinβcosβcos(β+δ)sinγcosγcos(γ+δ)(xiv) sin223°sin267°cos180°-sin267°-sin223°cos2180°cos180°sin223°sin267°(xv) cosx+y-sinx+ycos2ysinxcosxsiny-cosxsinx-cosy(xvi) 23+35515+465103+115155(xvii) sin2AcotA1sin2BcotB1sin2CcotC1, where A, B, C are the angles of ∆ABC. |
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Answer» Without expanding, show that the values of each of the following determinants are zero: (i) (ii) (iii) (iv) (v) (vi) (vii) (viii) (ix) (x) (xi) (xii) (xiii) (xiv) (xv) (xvi) (xvii) |
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| 4180. |
3∫0e[x]dx equals to(where [.] denotes the greatest integer function) |
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Answer» 3∫0e[x]dx equals to (where [.] denotes the greatest integer function) |
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| 4181. |
Mark the correct alternative in the following question:If PB=35, PA|B=12 and PA∪B=45, then PA∪B+PA∪B=a 15 b 45 c 12 d 1 |
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Answer» Mark the correct alternative in the following question: |
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| 4182. |
ntFind The number of values of c such that the straight line 3x+4y=c touches the curve x/2=x+y .n |
| Answer» ntFind The number of values of c such that the straight line 3x+4y=c touches the curve x/2=x+y .n | |
| 4183. |
Question 1Points A(5, 3) B(-2, 3) and D(5, -4) are three vertices of a square ABCD. Plot these points on a graph paper and hence, find the coordinates of the vertex C. |
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Answer» Question 1 |
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| 4184. |
For any two sets A and B if n(A) = 10, n(B) = 8 and n((A ∩ B) = 4, then value of n((A × B) ∩ (B × A)) is equal to |
| Answer» For any two sets A and B if n(A) = 10, n(B) = 8 and n((A ∩ B) = 4, then value of n((A × B) ∩ (B × A)) is equal to | |
| 4185. |
For what value of ‘k’, do the equations 5x –3y + 8 = 0 and 15x + ky = –24 represent coincident lines? |
| Answer» For what value of ‘k’, do the equations 5x –3y + 8 = 0 and 15x + ky = –24 represent coincident lines? | |
| 4186. |
If Δr=∣∣∣∣∣2r−1mCr1m2−12mm+1sin2(m2)sin2(m)sin2(m+1)∣∣∣∣∣,(0≤r≤m),then value of m∑r=0Δr is |
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Answer» If Δr=∣∣ |
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| 4187. |
If A=⎡⎢⎣12−1−1122−11⎤⎥⎦, then the value of det(adj(adjA)) is |
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Answer» If A=⎡⎢⎣12−1−1122−11⎤⎥⎦, then the value of det(adj(adjA)) is |
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| 4188. |
The position of the term independent of x in the expansion of x3+32x210 is ___________. |
| Answer» The position of the term independent of x in the expansion of is ___________. | |
| 4189. |
Find the value of limx→π2sinxx |
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Answer» Find the value of limx→π2sinxx |
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| 4190. |
The range of f(x)=tan−1(x2+x+a)∀xϵ is a subset of [0,π2) then range of a is |
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Answer» The range of f(x)=tan−1(x2+x+a)∀xϵ is a subset of [0,π2) then range of a is |
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| 4191. |
The direction cosines of the vector 2i^+2j^-k^ are ______________. |
| Answer» The direction cosines of the vector are ______________. | |
| 4192. |
If one root of the equation px^2-qx+r=0 is the square of the other, then the condition that the coefficients satisfy is (1) 2(p+q+r)=pqr (2) p+q+r=0 (3) 2p+q+r=3pqr (4) pr(p+r+3q)=q^3 |
| Answer» If one root of the equation px^2-qx+r=0 is the square of the other, then the condition that the coefficients satisfy is (1) 2(p+q+r)=pqr (2) p+q+r=0 (3) 2p+q+r=3pqr (4) pr(p+r+3q)=q^3 | |
| 4193. |
Find the area of the region bounded by line x = 2 and parabola y2=8x. |
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Answer» Find the area of the region bounded by line x = 2 and parabola y2=8x. |
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| 4194. |
A straight line L through the point (3,−2) is inclined at an angle 60∘ to the line √3x+y=1. If L also intersects the x-axis, then the equation of line L is |
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Answer» A straight line L through the point (3,−2) is inclined at an angle 60∘ to the line √3x+y=1. If L also intersects the x-axis, then the equation of line L is |
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| 4195. |
A variable plane passes through a fixed point (a,b,c) and cuts the coordinate axes at A,B and C. Then the locus of the centre of the sphere OABC is |
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Answer» A variable plane passes through a fixed point (a,b,c) and cuts the coordinate axes at A,B and C. Then the locus of the centre of the sphere OABC is |
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| 4196. |
61.A unit vector found which is perpendicular to A= i +2j+3k and B =i-2j-3k is ?? |
| Answer» 61.A unit vector found which is perpendicular to A= i +2j+3k and B =i-2j-3k is ?? | |
| 4197. |
On the curve xm+2n.yn=a, m,n ϵ N,a ϵ R+, if the ratio of slopes of tangent at any point P to that of a line segment OP (O being origin) is -4 than value of mn is |
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Answer» On the curve xm+2n.yn=a, m,n ϵ N,a ϵ R+, if the ratio of slopes of tangent at any point P to that of a line segment OP (O being origin) is -4 than value of mn is |
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| 4198. |
Let I=∫sin2x+sinx1+sinx+cosxdx, J=∫cos2x+cosx1+sinx+cosxdx and c is the constant of integration.FunctionIntegral(a) I (p) 12(x−sinx−cosx)+c (b) J (q) 12(x+sinx+cosx)+c (c) I + J (r) x+c (d) I - J (s) c−cosx−sinx (t) c+cosx+sinx (u) −12(x+sinx+cosx+c)Then the value of d(I+J)dx at x=√2 is |
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Answer» Let I=∫sin2x+sinx1+sinx+cosxdx, J=∫cos2x+cosx1+sinx+cosxdx and c is the constant of integration. |
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| 4199. |
If A (α,β)=⎡⎢⎣cos αsinα0−sin αcos α000eβ⎤⎥⎦,then |
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Answer» If A (α,β)=⎡⎢⎣cos αsinα0−sin αcos α000eβ⎤⎥⎦,then |
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| 4200. |
Number of solutions of the equation 2sinx−2√3cosx−√3tanx+3=0 where x∈[0,2π) is |
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Answer» Number of solutions of the equation 2sinx−2√3cosx−√3tanx+3=0 where x∈[0,2π) is |
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and
when: