24740 + Interview Questions in Mathematics Page 85 InterviewSolution

4201.	Question 9In the figure, BC is a diameter of the circle and ∠BAO=60∘. Then, ∠ADC is equal to(A) 30∘(B) 45∘(C) 60∘(D) 120∘
Answer» Question 9 In the figure, BC is a diameter of the circle and $∠ B A O = 60^{\circ}$ . Then, $∠ A D C$ is equal to (A) $30^{\circ}$ (B) $45^{\circ}$ (C) $60^{\circ}$ (D) $120^{\circ}$

Discussion

4202.	the domain of f(x)=root under cos^-1x-sin^-1x is [a,b].find 5a^2+b^2
Answer» the domain of f(x)=root under cos^-1x-sin^-1x is [a,b].find 5a^2+b^2

Discussion

4203.	21.What is Pythagoras theorem
Answer» 21.What is Pythagoras theorem

Discussion

4204.	In the figure, PQRS is a Parallelogram, QS is the diagonal, A is the mid-point of SR and D is the mid-point of RQ. If the area of △ ASQ =20 cm2, then find the area of △ARD.
Answer» In the figure, PQRS is a Parallelogram, QS is the diagonal, A is the mid-point of SR and D is the mid-point of RQ. If the area of $△$ ASQ $= 20$ cm $^{2}$ , then find the area of $△ A R D$ .

Discussion

4205.	The side AB of a parallelogram ABCD is produced to any point P. A line through A and parallel to CP meets CB produced at Q and then parallelogram PBQR is completed (see the following figure). Find the relation between area (ABCD) and area (PBQR). [3 MARKS]
Answer» The side AB of a parallelogram ABCD is produced to any point P. A line through A and parallel to CP meets CB produced at Q and then parallelogram PBQR is completed (see the following figure). Find the relation between area (ABCD) and area (PBQR). [3 MARKS]

Discussion

4206.	The value of --14n-3, where n ∈ N, is ____________.
Answer» The value of ${(- \sqrt{- 1})}^{4 n - 3},$ where n ∈ N, is ____________.

Discussion

4207.	Find the angles x,y and z in the given parallelogram. [3 MARKS]
Answer» Find the angles x,y and z in the given parallelogram. [3 MARKS]

4207.

Find the angles x,y and z in the given parallelogram. [3 MARKS]

Answer»

Find the angles x,y and z in the given parallelogram. [3 MARKS]

Discussion

4208.	The number 0.3¯ in the form pq, where p and q are integers and q ≠ 0, is(a) 33100(b) 310(c) 13(d) 3100
Answer» The number $0 . \bar{3}$ in the form $\frac{p}{q}$ , where p and q are integers and q ≠ 0, is (a) $\frac{33}{100}$ (b) $\frac{3}{10}$ (c) $\frac{1}{3}$ (d) $\frac{3}{100}$

Discussion

4209.	40. If the line y = mx+1 meets the circle xx + yy + 3x = 0 in two points equidistant from and on opposite side of x axis, then m=?
Answer» 40. If the line y = mx+1 meets the circle xx + yy + 3x = 0 in two points equidistant from and on opposite side of x axis, then m=?

Discussion

4210.	Each edge of a cube is increased by 50%, then percentage increase in its surface area =.
Answer» Each edge of a cube is increased by $50 %$ , then percentage increase in its surface area =.

Discussion

4211.	How many methods are available for Triangle Construction 1?
Answer» How many methods are available for Triangle Construction 1?

Discussion

4212.	ntUsing properties of triangle, in a triangle prove the following: cosA + cosB + cosC = 1 + r/R n
Answer» ntUsing properties of triangle, in a triangle prove the following: cosA + cosB + cosC = 1 + r/R n

Discussion

4213.	Find the value of 8 - 3.5
Answer» Find the value of 8 - 3. 5

Discussion

4214.	If in a Δ ABC, a2+b2+c2=8R2, where R = circumradius, then the triangle is
Answer» If in a $Δ$ ABC, $a^{2} + b^{2} + c^{2} = 8 R^{2},$ where R = circumradius, then the triangle is

Discussion

4215.	∫dx√2ax−x2 = ansin−1[xa−1] The value of n is:
Answer» $\int \frac{d x}{\sqrt{2 a x - x^{2}}}$ = $a^{n} s i n^{- 1} [\frac{x}{a} - 1]$ The value of n is:

4215.

∫dx√2ax−x2 = ansin−1[xa−1] The value of n is:

Answer»

$\int \frac{d x}{\sqrt{2 a x - x^{2}}}$ = $a^{n} s i n^{- 1} [\frac{x}{a} - 1]$

The value of n is:

Discussion

4216.	How many possibilities of even numbers are there when a single die is thrown?
Answer» How many possibilities of even numbers are there when a single die is thrown?

Discussion

4217.	Three cubes of metal whose edges are 6 cm, 8 cm and 10 cm respectively are melted to form a single cube. The edge of the new cube is:
Answer» Three cubes of metal whose edges are 6 cm, 8 cm and 10 cm respectively are melted to form a single cube. The edge of the new cube is:

Discussion

4218.	if (2x+5) is a factor of 2x^2 -k,then value of k is
Answer» if (2x+5) is a factor of 2x^2 -k,then value of k is

Discussion

4219.	If a and b are rational numbers, find 'a' and 'b' when √7−2√7+2=a√7+b
Answer» If a and b are rational numbers, find 'a' and 'b' when $\frac{\sqrt{7} - 2}{\sqrt{7} + 2} = a \sqrt{7} + b$

4219.

If a and b are rational numbers, find 'a' and 'b' when √7−2√7+2=a√7+b

Answer»

If a and b are rational numbers, find 'a' and 'b' when

$\frac{\sqrt{7} - 2}{\sqrt{7} + 2} = a \sqrt{7} + b$

Discussion

4220.	In any triangle ABC, if the angle bisector of angle A and perpendicular bisector of BC intersect, prove that they intersect on the circumcircle of the triangle ABC.
Answer» In any triangle ABC, if the angle bisector of angle A and perpendicular bisector of BC intersect, prove that they intersect on the circumcircle of the triangle ABC.

Discussion

4221.	17. define molarity, molality or more fraction
Answer» 17. define molarity, molality or more fraction

Discussion

4222.	The relationship between mean, median and mode for a moderately skewed distribution is(a) Mode = 2 Median − 3 Mean(b) Mode = Median − 2 Mean(c) Mode = 2 Median − Mean(d) Mode = 3 Median −2 Mean
Answer» The relationship between mean, median and mode for a moderately skewed distribution is (a) Mode = 2 Median − 3 Mean (b) Mode = Median − 2 Mean (c) Mode = 2 Median − Mean (d) Mode = 3 Median −2 Mean

Discussion

4223.	ABCD is a parallelogram whose diagonals intersect at O. If P is any point on BO, prove that:(i) ar (Δ ADO) = ar(Δ CDO)(ii) ar (Δ ABP) = ar (Δ CBP).
Answer» ABCD is a parallelogram whose diagonals intersect at O. If P is any point on BO, prove that: (i) ar (Δ ADO) = ar(Δ CDO) (ii) ar (Δ ABP) = ar (Δ CBP).

Discussion

4224.	29. A circular plate of uniform thickness has a diameter of 56 cm. A circular portion of diameter 42 cm is removed from one edge of the plate. Find the center of mass of the remaining portion.�
Answer» 29. A circular plate of uniform thickness has a diameter of 56 cm. A circular portion of diameter 42 cm is removed from one edge of the plate. Find the center of mass of the remaining portion.�

Discussion

4225.	D, E, F are the mid-point of the sides BC, CA and AB respectively of ΔABC. Then ΔDEF is congruent to triangle(a) ABC(b) AEF(c) BFD, CDE(d) AFE, BFD, CDE
Answer» D, E, F are the mid-point of the sides BC, CA and AB respectively of ΔABC. Then ΔDEF is congruent to triangle (a) ABC (b) AEF (c) BFD, CDE (d) AFE, BFD, CDE

Discussion

4226.	If trace of the matrix ⎡⎢⎣2x22x0x2−113x−4⎤⎥⎦ is given by Tr(A)=limn→0(2n+4n+8n3)1/n, then possible value(s) of x is(are)
Answer» If trace of the matrix $⎡ ⎢ ⎣ \begin{matrix} 2 x & 2 & 2 x 0 & x^{2} & - 1 1 & 3 x & - 4 \end{matrix} ⎤ ⎥ ⎦$ is given by $T r (A) = lim n \to 0 {(\frac{2^{n} + 4^{n} + 8^{n}}{3})}^{1 / n},$ then possible value(s) of $x$ is(are)

Discussion

4227.	With reference to the figure, ABCD is a parallelogram. AE and CF are angle bisectors of ∠DAC and ∠ACB respectively. What can be said about the lines AE and CF ?
Answer» With reference to the figure, ABCD is a parallelogram. AE and CF are angle bisectors of ∠DAC and ∠ACB respectively. What can be said about the lines AE and CF ?

4227.

With reference to the figure, ABCD is a parallelogram. AE and CF are angle bisectors of ∠DAC and ∠ACB respectively. What can be said about the lines AE and CF ?

Answer»

With reference to the figure, ABCD is a parallelogram. AE and CF are angle bisectors of ∠DAC and ∠ACB respectively. What can be said about the lines AE and CF ?

Discussion

4228.	Question 4Three coins are tossed simultaneously 200 times with the following frequencies of different outcomes:Out come3 heads2 heads1 headNo headFrequency23727728If the three coins are simultaneously tossed again, compute the probability of 2 heads coming up.
Answer» Question 4 Three coins are tossed simultaneously 200 times with the following frequencies of different outcomes: $\begin{matrix} Out come & 3 heads & 2 heads & 1 head & No head Frequency & 23 & 72 & 77 & 28 \end{matrix}$ If the three coins are simultaneously tossed again, compute the probability of 2 heads coming up.

Discussion

4229.	In the given figure, ABCD is a special quadrilateral in which the sum of its opposite internal angles is 180∘. What is the value of ∠FDC, given ∠CBE=130∘?
Answer» In the given figure, ABCD is a special quadrilateral in which the sum of its opposite internal angles is $180^{\circ}$ . What is the value of $∠ F D C$ , given $∠ C B E = 130^{\circ}$ ?

Discussion

4230.	In the given figure, O is the centre of the circle, BO is the bisector of ∠ABC. Show that AB = AC.
Answer» In the given figure, O is the centre of the circle, BO is the bisector of ∠ABC. Show that AB = AC.

Discussion

4231.	1(3+2√2)=? (a)3−2√217 (b)(3−2√2)13 (c)(3−2√2) (d)None of these
Answer» $\frac{1}{(3 + 2 \sqrt{2})} = ?$ (a) $\frac{3 - 2 \sqrt{2}}{17}$ (b) $\frac{(3 - 2 \sqrt{2})}{13}$ (c) $(3 - 2 \sqrt{2})$ (d)None of these

4231.

1(3+2√2)=? (a)3−2√217 (b)(3−2√2)13 (c)(3−2√2) (d)None of these

Answer»

$\frac{1}{(3 + 2 \sqrt{2})} = ?$

(a) $\frac{3 - 2 \sqrt{2}}{17}$

(b) $\frac{(3 - 2 \sqrt{2})}{13}$

(c) $(3 - 2 \sqrt{2})$

(d)None of these

Discussion

4232.	If a quadrilateral sin(A+B/2)cos(A-B/2)+sin(C+D/2)cos(C-D/2)=2.find the value of sin(A/2)sin(B/2)sin(C/2)sin(D/2).
Answer» If a quadrilateral sin(A+B/2)cos(A-B/2)+sin(C+D/2)cos(C-D/2)=2.find the value of sin(A/2)sin(B/2)sin(C/2)sin(D/2).

Discussion

4233.	Find the area of the diagram given below.
Answer» Find the area of the diagram given below.

4233.

Find the area of the diagram given below.

Answer»

Find the area of the diagram given below.

Discussion

4234.	Question 14In a right triangle, prove that the line-segment joining the mid-point of the hypotenuse to the opposite vertex is half the hypotenuse.
Answer» Question 14 In a right triangle, prove that the line-segment joining the mid-point of the hypotenuse to the opposite vertex is half the hypotenuse.

Discussion

4235.	Question 1(i)Represent these numbers on the number line:74
Answer» Question 1(i) Represent these numbers on the number line: $\frac{7}{4}$

Discussion

4236.	In the given figure, △ABC is right-angled at B, in which AB = 15 cm and BC = 8 cm. A circle with center O has been inscribed in △ABC. Calculate the value of x, the radius of the inscribed circle. [4 MARKS]
Answer» In the given figure, $△ A B C$ is right-angled at B, in which AB = 15 cm and BC = 8 cm. A circle with center O has been inscribed in $△ A B C$ . Calculate the value of x, the radius of the inscribed circle. [4 MARKS]

4236.

In the given figure, △ABC is right-angled at B, in which AB = 15 cm and BC = 8 cm. A circle with center O has been inscribed in △ABC. Calculate the value of x, the radius of the inscribed circle. [4 MARKS]

Answer»

In the given figure, $△ A B C$ is right-angled at B, in which AB = 15 cm and BC = 8 cm. A circle with center O has been inscribed in $△ A B C$ . Calculate the value of x, the radius of the inscribed circle. [4 MARKS]

Discussion

4237.	A three-wheeler scooter charges Rs 15 for first kilometer and Rs 8 each for every subsequent kilometer. For a distance of x km, an amount of Rs y is paid. Write the linear equation representing the above information.
Answer» A three-wheeler scooter charges Rs 15 for first kilometer and Rs 8 each for every subsequent kilometer. For a distance of x km, an amount of Rs y is paid. Write the linear equation representing the above information.

Discussion

4238.	Mode of data 3, 2, 5, 2, 3, 5, 6, 6, 5, 3, 5, 2, 5 is:
Answer» Mode of data 3, 2, 5, 2, 3, 5, 6, 6, 5, 3, 5, 2, 5 is:

Discussion

4239.	Factorise the following polynomial.2axy2+10x+3ay2+15
Answer» Factorise the following polynomial. $2 a x y^{2} + 10 x + 3 a y^{2} + 15$

Discussion

4240.	The sides NM and PO of the parallelogram MNOP are produced as shown in the figure given below. Which of the following statements is correct?
Answer» The sides NM and PO of the parallelogram MNOP are produced as shown in the figure given below. Which of the following statements is correct?

Discussion

4241.	If the sides of a triangle are produced in order, then the sum of the three exterior angles so formed is(a) 90°(b) 180°(c) 270°(d) 360°
Answer» If the sides of a triangle are produced in order, then the sum of the three exterior angles so formed is (a) 90° (b) 180° (c) 270° (d) 360°

Discussion

4242.	The midpoint of 5 and 8 is:
Answer» The midpoint of 5 and 8 is:

Discussion

4243.	ABC is an isoceles trainagle whose sides AB and AC are 10 cms and base BC MEASURES 8 cm. AD is drawn perpendicular from A to D and P is a point on AD such that angle BPC equals 90 degree. FInd the area of the shaded region
Answer» ABC is an isoceles trainagle whose sides AB and AC are 10 cms and base BC MEASURES 8 cm. AD is drawn perpendicular from A to D and P is a point on AD such that angle BPC equals 90 degree. FInd the area of the shaded region

Discussion

4244.	Which is the equivalent fraction of 23?
Answer» Which is the equivalent fraction of $\frac{2}{3}$ ?

Discussion

4245.	Which of the following options is equal to the given expresssion?cot(90∘−θ)cosec2θ × secθ.cot3θsin2(90∘−θ)
Answer» Which of the following options is equal to the given expresssion? $\frac{c o t (90^{\circ} - θ)}{c o s e c^{2} θ}$ $\times$ $\frac{s e c θ . c o t^{3} θ}{s i n^{2} (90^{\circ} - θ)}$

4245.

Which of the following options is equal to the given expresssion?cot(90∘−θ)cosec2θ × secθ.cot3θsin2(90∘−θ)

Answer»

Which of the following options is equal to the given expresssion?

$\frac{c o t (90^{\circ} - θ)}{c o s e c^{2} θ}$ $\times$ $\frac{s e c θ . c o t^{3} θ}{s i n^{2} (90^{\circ} - θ)}$

Discussion

4246.	What are the all possible outcomes when a dice is thrown?
Answer» What are the all possible outcomes when a dice is thrown?

Discussion

4247.	If two circles intersect at two points, then prove that their centres lie on the perpendicular bisector of the common chord.
Answer» If two circles intersect at two points, then prove that their centres lie on the perpendicular bisector of the common chord.

4247.

If two circles intersect at two points, then prove that their centres lie on the perpendicular bisector of the common chord.

Answer»

If two circles intersect at two points, then prove that their centres lie on the perpendicular bisector of the common chord.

Discussion

4248.	What is 'F' in 'F(x)'
Answer» What is 'F' in 'F(x)'

Discussion

4249.	If 2n=1024, then 32n4-4=(a) 3(b) 9(c) 27(d) 81
Answer» If $\sqrt{2^{n}} = 1024,$ then ${3^{2}}^{(\frac{n}{4} - 4)} =$ (a) 3 (b) 9 (c) 27 (d) 81

Discussion

4250.	Question 83Find the area of shaded portion.
Answer» Question 83 Find the area of shaded portion.

4250.

Question 83Find the area of shaded portion.

Answer»

Question 83

Find the area of shaded portion.

Discussion

Explore topic-wise InterviewSolutions in .

Question 9In the figure, BC is a diameter of the circle and ∠BAO=60∘. Then, ∠ADC is equal to(A) 30∘(B) 45∘(C) 60∘(D) 120∘

the domain of f(x)=root under cos^-1x-sin^-1x is [a,b].find 5a^2+b^2

21.What is Pythagoras theorem

In the figure, PQRS is a Parallelogram, QS is the diagonal, A is the mid-point of SR and D is the mid-point of RQ. If the area of △ ASQ =20 cm2, then find the area of △ARD.

The side AB of a parallelogram ABCD is produced to any point P. A line through A and parallel to CP meets CB produced at Q and then parallelogram PBQR is completed (see the following figure). Find the relation between area (ABCD) and area (PBQR). [3 MARKS]​

The value of --14n-3, where n ∈ N, is ____________.

Find the angles x,y and z in the given parallelogram. [3 MARKS]

The number 0.3¯ in the form pq, where p and q are integers and q ≠ 0, is(a) 33100(b) 310(c) 13(d) 3100

40. If the line y = mx+1 meets the circle x*x + y*y + 3x = 0 in two points equidistant from and on opposite side of x axis, then m=?

Each edge of a cube is increased by 50%, then percentage increase in its surface area =.

How many methods are available for Triangle Construction 1?

ntUsing properties of triangle, in a triangle prove the following: cosA + cosB + cosC = 1 + r/R n

Find the value of 8 - 3.5

If in a Δ ABC, a2+b2+c2=8R2, where R = circumradius, then the triangle is

∫dx√2ax−x2 = ansin−1[xa−1] The value of n is:

How many possibilities of even numbers are there when a single die is thrown?

Three cubes of metal whose edges are 6 cm, 8 cm and 10 cm respectively are melted to form a single cube. The edge of the new cube is:

if (2x+5) is a factor of 2x^2 -k,then value of k is

If a and b are rational numbers, find 'a' and 'b' when √7−2√7+2=a√7+b

In any triangle ABC, if the angle bisector of angle A and perpendicular bisector of BC intersect, prove that they intersect on the circumcircle of the triangle ABC.

17. define molarity, molality or more fraction

The relationship between mean, median and mode for a moderately skewed distribution is(a) Mode = 2 Median − 3 Mean(b) Mode = Median − 2 Mean(c) Mode = 2 Median − Mean(d) Mode = 3 Median −2 Mean

ABCD is a parallelogram whose diagonals intersect at O. If P is any point on BO, prove that:(i) ar (Δ ADO) = ar(Δ CDO)(ii) ar (Δ ABP) = ar (Δ CBP).

29. A circular plate of uniform thickness has a diameter of 56 cm. A circular portion of diameter 42 cm is removed from one edge of the plate. Find the center of mass of the remaining portion.�

D, E, F are the mid-point of the sides BC, CA and AB respectively of ΔABC. Then ΔDEF is congruent to triangle(a) ABC(b) AEF(c) BFD, CDE(d) AFE, BFD, CDE

If trace of the matrix ⎡⎢⎣2x22x0x2−113x−4⎤⎥⎦ is given by Tr(A)=limn→0(2n+4n+8n3)1/n, then possible value(s) of x is(are)

With reference to the figure, ABCD is a parallelogram. AE and CF are angle bisectors of ∠DAC and ∠ACB respectively. What can be said about the lines AE and CF ?

Question 4Three coins are tossed simultaneously 200 times with the following frequencies of different outcomes:Out come3 heads2 heads1 headNo headFrequency23727728If the three coins are simultaneously tossed again, compute the probability of 2 heads coming up.

In the given figure, ABCD is a special quadrilateral in which the sum of its opposite internal angles is 180∘. What is the value of ∠FDC, given ∠CBE=130∘?

In the given figure, O is the centre of the circle, BO is the bisector of ∠ABC. Show that AB = AC.

1(3+2√2)=? (a)3−2√217 (b)(3−2√2)13 (c)(3−2√2) (d)None of these

If a quadrilateral sin(A+B/2)cos(A-B/2)+sin(C+D/2)cos(C-D/2)=2.find the value of sin(A/2)sin(B/2)sin(C/2)sin(D/2).

Find the area of the diagram given below.

Question 14In a right triangle, prove that the line-segment joining the mid-point of the hypotenuse to the opposite vertex is half the hypotenuse.

Question 1(i)Represent these numbers on the number line:74

In the given figure, △ABC is right-angled at B, in which AB = 15 cm and BC = 8 cm. A circle with center O has been inscribed in △ABC. Calculate the value of x, the radius of the inscribed circle. [4 MARKS]

A three-wheeler scooter charges Rs 15 for first kilometer and Rs 8 each for every subsequent kilometer. For a distance of x km, an amount of Rs y is paid. Write the linear equation representing the above information.

Mode of data 3, 2, 5, 2, 3, 5, 6, 6, 5, 3, 5, 2, 5 is:

Factorise the following polynomial.2axy2+10x+3ay2+15

The sides NM and PO of the parallelogram MNOP are produced as shown in the figure given below. Which of the following statements is correct?

If the sides of a triangle are produced in order, then the sum of the three exterior angles so formed is(a) 90°(b) 180°(c) 270°(d) 360°

The midpoint of 5 and 8 is:

ABC is an isoceles trainagle whose sides AB and AC are 10 cms and base BC MEASURES 8 cm. AD is drawn perpendicular from A to D and P is a point on AD such that angle BPC equals 90 degree. FInd the area of the shaded region

Which is the equivalent fraction of 23?

Which of the following options is equal to the given expresssion?cot(90∘−θ)cosec2θ × secθ.cot3θsin2(90∘−θ)

What are the all possible outcomes when a dice is thrown?

If two circles intersect at two points, then prove that their centres lie on the perpendicular bisector of the common chord.

What is 'F' in 'F(x)'

If 2n=1024, then 32n4-4=(a) 3(b) 9(c) 27(d) 81

Question 83Find the area of shaded portion.

The side AB of a parallelogram ABCD is produced to any point P. A line through A and parallel to CP meets CB produced at Q and then parallelogram PBQR is completed (see the following figure). Find the relation between area (ABCD) and area (PBQR). [3 MARKS]

40. If the line y = mx+1 meets the circle xx + yy + 3x = 0 in two points equidistant from and on opposite side of x axis, then m=?