Explore topic-wise InterviewSolutions in .

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.

1.

If in `DeltaABC, a = 5, b = 4 and cos (A - B) = 31/32`, thenA. 6B. 7C. 9D. none of these

Answer» Correct Answer - A
Discussion
2.

If a `DeltaABC, b=2, C=60^(@), c=sqrt(6)`, then a =A. `sqrt(3)-1`B. `sqrt(3)`C. `sqrt(3)+1`D. none of these

Answer» Correct Answer - C
Discussion
3.

In a `DeltaABC`, if `b=sqrt(3)+1, c=sqrt(3)-1 and A=60^(@)`, then the value of `tan.(B-C)/(2)` isA. `-1`B. `1//2`C. 1D. none of these

Answer» Correct Answer - C
We have,
`tan.(B-C)/(2)=(b-c)/(b+c)cot.(A)/(2)`
`implies tan.(B-C)/(2)=(2)/(2sqrt(3))cot30^(@)=1`.
Discussion
4.

In a `DeltaABC` if a = 2, `b=sqrt(6),c=sqrt(3)+1`, then cos A=A. `30^(@)`B. `45^(@)`C. `60^(@)`D. none of these

Answer» Correct Answer - B
Discussion
5.

In a `DeltaABC`, if a = 4, b = 3 and `angleA=60^(@)`, then c is a root of the equationA. `c^(2)-3c-7=0`B. `c^(2)+3c+7=0`C. `c^(2)-3c+7=0`D. `c^(2)+3c-7=0`

Answer» Correct Answer - A
We have,
`a=4, b=3 and A=60^(@)`
`therefore cosA=(b^(2)+c^(2)-a^(2))/(2bc)`
`impliescos60^(@)=(9+c^(2)-16)/(6c)impliesc^(2)-3c-7=0`
Discussion
6.

In a `DeltaABC`, if a = 5, `B=45^(@)` and `c=2sqrt(2)`, then b=A. `sqrt(3)`B. 6C. `2sqrt(13)`D. `sqrt(13)`

Answer» Correct Answer - D
We have,
`cosB=(a^(2)+c^(2)-b^(2))/(2ac)`
`implies cos45^(@)=(25+8-b^(2))/(20sqrt(2))implies(1)/(2)=(33-b^(2))/(20sqrt(2))impliesb=sqrt(13)`
Discussion
7.

If the data given to construct a triangle ABC are a = 5, b= 7, sin `A=3//4`, then it is possible to constructA. only one triangleB. two trianglesC. infinitely many trianglesD. no triangles

Answer» Correct Answer - D
Discussion
8.

In a right triangle ABC, right angled at C, if a = 7 cm and b = `7 sqrt(3)` cm, then `angleA`=A. `30^(@)`B. `60^(@)`C. `45^(@)`D. none of these

Answer» Correct Answer - A
We have,
`tan A=(a)/(b)=(7)/(7sqrt(3))=(1)/(sqrt(3))=tan30^(@)impliesangleA=30^(@)`
Discussion
9.

In `Delta ABC , If b/(c^2-a^2)+a/(c^2-b^2)=0` thenA. `(pi)/(2)`B. `(pi)/(4)`C. `(2pi)/(3)`D. `(pi)/(3)`

Answer» Correct Answer - D
We have,
`(a)/(sinA)=(b)/(sinB)=(c)/(sinC)=k("say")`
`therefore (a)/(b^(2)-c^(2))+(c)/(b^(2)-a^(2))=0`
`implies (k sinA)/(k^(2)(sin^(2)B-sin^(2)c))+(k sinC)/(k^(2)(sin^(2)B-sin^(2)A))=0`
`implies (sinA)/(sin(B+C)sin(B-C))+(sinC)/(sin(B+A)sin(B-A))=0`
`implies(sinA)/(sin(B+C)sin(B-C))+(sinC)/(sin(B+A)sin(B-A))=0`
`implies(1)/(sin(B-C))+(1)/(sin(B-A))=0`
`impliessin(B-A)+sin(B-C)=0`
`impliessin(A-B)=sin(B-C)`
`impliesA-B=B-CimpliesA+C=2BimpliesB=60^(@)`
Discussion
10.

In the ambiguous case, if `a, b and A` are given and `c_1, c_2` are the two values of the third `(c_1-c_2)^2 + (c_1+c_2)^2 tan^2 A` is equal toA. 4B. `4a^(2)`C. `4b^(2)`D. `4c^(2)`

Answer» Correct Answer - B
We have,
`cosA=(b^(2)+c^(2)-a^(2))/(2bc)`
`impliesc^(2)-(2bcosA)c+(b^(2)-a^(2))=0`
Since `c_(1)` and `c_(2)` are the roots of this equation.
`therefore c_(1)+c_(2)=2b cosA and c_(1)c_(2)=b^(2)-a^(2)`
Now,
`(c_(1)-c_(2))^(2)+(c_(1)+c_(2))^(2)tan^(2)A`
`=(c_(1)+c_(2))^(2)-4c_(1)c_(2)+(c_(1)+c_(2))^(2)tan^(2)A`
`=(c_(1)+c_(2))^(2)sec^(2)A-4c_(1)c_(2)`
`=4b^(2)cos^(2)Axxsec^(2)A-4(b^(2)-a^(2))=4a^(2)`
Discussion
11.

The smallest angle of the triangle whose sides are `6 + sqrt(12)`, `sqrt(48), sqrt(24)` isA. `pi//3`B. `pi//4`C. `pi//6`D. none of these

Answer» Correct Answer - C
Discussion
12.

In the ambiguous case, if `a, b and A` are given and `c_1, c_2` are the two values of the third `(c_1-c_2)^2 + (c_1+c_2)^2 tan^2 A` is equal toA. `4a^(2) cos^(2)A`B. `4a^(2) cos A`C. `4a cos^(2)A`D. none of these

Answer» Correct Answer - A
Discussion
13.

In a triangle, the lengths of the two larger sides are 10 and 9,respectively. If the angles are in A.P., then the length of the third sidecan be`5-sqrt(6)`(b) `3sqrt(3)`(c)`5`(d) `5+sqrt(6)`A. `5 pm sqrt(6)`B. 0.7C. `sqrt(5)+6`D. none of these

Answer» Correct Answer - A
Discussion
14.

If the angles of a triangle are `30^0a n d45^0`and the included side is `(sqrt(3)+1)c m`then the area of the triangle is______.A. `(sqrt(3)-1)/(2)cm^(2)`B. `(sqrt(3)+1)/(2)cm^(2)`C. `(sqrt(3)-1)cm^(2)`D. none of these

Answer» Correct Answer - B
Let ABC be the triangle in which `a=sqrt(3)+1` cm, `angleB=30^(@) and angleC=45^(@)."Then "angleC=180^(@)-angleA-angleB=105^(@)`.
`therefore b=(asinB)/(sinA) and c=(asinC)/(sinA)`
`implies b=((sqrt(3)+1)sin30^(@))/(sin 105^(@)) and c=((sqrt(3)+1)sin45^(@))/(sin105^(@))`
`implies b = sqrt(2) and c = 2`
`therefore " Area of "DeltaABC = (1)/(2) bc sin A = (sqrt(3)+1)/(2)cm^(2)`
Discussion