24740 + Interview Questions in Mathematics Page 186 InterviewSolution

9251.	Question 111Pluto is 5913000000 m from the Sun. Express this in the standard form.
Answer» Question 111 Pluto is 5913000000 m from the Sun. Express this in the standard form.

9251.

Question 111Pluto is 5913000000 m from the Sun. Express this in the standard form.

Answer»

Question 111

Pluto is 5913000000 m from the Sun. Express this in the standard form.

9252.	Question 8 1.6=y1.5
Answer» Question 8 $1.6 = \frac{y}{1.5}$

Discussion

9253.	If the radius of a circle is 6 cm and θ is 30∘, then find the length of the arc of the circle.
Answer» If the radius of a circle is 6 cm and $θ$ is $30^{\circ}$ , then find the length of the arc of the circle.

Discussion

9254.	Which of the following is a factor of 2x^4 + 1 + 3 x^2 ? A 1 + 2x^2 B 4+x^2 C 2x^2 -1 D 3+x^2
Answer» Which of the following is a factor of 2x^4 + 1 + 3 x^2 ? A 1 + 2x^2 B 4+x^2 C 2x^2 -1 D 3+x^2

9254.

Which of the following is a factor of 2x^4 + 1 + 3 x^2 ? A 1 + 2x^2 B 4+x^2 C 2x^2 -1 D 3+x^2

Answer»

Which of the following is a factor of 2x^4 + 1 + 3 x^2 ?

A 1 + 2x^2

B 4+x^2

C 2x^2 -1

D 3+x^2

Discussion

9255.	35. Two circles A and B of radius 3 cm and 4cm intersect at the point C and D such thatcAC and BC are tangent to the circle. Find the lenght of common chord CD
Answer» 35. Two circles A and B of radius 3 cm and 4cm intersect at the point C and D such thatcAC and BC are tangent to the circle. Find the lenght of common chord CD

Discussion

9256.	Which of the following is a true statement ? (a) The sum of two irrational numbers is an irrational number. (b) The product of two irrational numbers is an irrational number. (c) Every real number is always rational. (d) Every real number is either rational or irrational.
Answer» Which of the following is a true statement ? (a) The sum of two irrational numbers is an irrational number. (b) The product of two irrational numbers is an irrational number. (c) Every real number is always rational. (d) Every real number is either rational or irrational.

9256.

Which of the following is a true statement ? (a) The sum of two irrational numbers is an irrational number. (b) The product of two irrational numbers is an irrational number. (c) Every real number is always rational. (d) Every real number is either rational or irrational.

Answer»

Which of the following is a true statement ?

(a) The sum of two irrational numbers is an irrational number.

(b) The product of two irrational numbers is an irrational number.

(c) Every real number is always rational.

(d) Every real number is either rational or irrational.

Discussion

9257.	Which is an example of the commutative property of addition?
Answer» Which is an example of the commutative property of addition?

Discussion

9258.	In the given figure, if AB\|\|CD,∠APQ=50∘ and ∠PRD=127∘, the value of y is:
Answer» In the given figure, if $A B \| \| C D, ∠ A P Q = 50^{\circ} a n d ∠ P R D = 127^{\circ}$ , the value of y is:

Discussion

9259.	Find x if 8x3+6x12x2+1=3519
Answer» Find $x$ if $\frac{8 x^{3} + 6 x}{12 x^{2} + 1} = \frac{35}{19}$

Discussion

9260.	Define the following terms: (i) Line segment (ii) Collinear points (iii) Parallel lines (iv) Intersecting lines (v) Concurrent lines (vi) Ray
Answer» Define the following terms: (i) Line segment (ii) Collinear points (iii) Parallel lines (iv) Intersecting lines (v) Concurrent lines (vi) Ray

Discussion

9261.	Find the perimeter (in ft) of the given swimming pool.28
Answer» Find the perimeter (in ft) of the given swimming pool. 28

Discussion

9262.	evaluate: ∫cos(x - ∝)/cos x dx
Answer» evaluate: ∫cos(x - ∝)/cos x dx

Discussion

9263.	ABCD is a kite where AB =AD and BC =CD .P,Q,R and S are the mid -points of the sides AB, BC, CD and AD respectively. Prove that PQRS is a rectangle.
Answer» ABCD is a kite where AB =AD and BC =CD .P,Q,R and S are the mid -points of the sides AB, BC, CD and AD respectively. Prove that PQRS is a rectangle.

Discussion

9264.	find the value of x2+y2+z2 if x+y+Z=9 and XY+YZ+ZX=26
Answer» find the value of x2+y2+z2 if x+y+Z=9 and XY+YZ+ZX=26

Discussion

9265.	The area of a triangle is half the product of any of its sides and the corresponding altitude
Answer» The area of a triangle is half the product of any of its sides and the corresponding altitude

Discussion

9266.	If x2 + y2 = 14 and xy=3, find the value of 2(x+y)2−5(x−y)2.
Answer» If $x^{2}$ + $y^{2}$ = 14 and $x y = 3$ , find the value of 2 ${(x + y)}^{2} - 5 {(x - y)}^{2}$ .

Discussion

9267.	If f(x)=∣∣∣∣x2253x37209∣∣∣∣, then the value of f′(1) is:
Answer» If $f (x) = ∣ ∣∣ ∣ \begin{matrix} x^{2} & 2 & 5 3 x & 3 & 7 2 & 0 & 9 \end{matrix} ∣ ∣∣ ∣,$ then the value of $f^{'} (1)$ is:

Discussion

9268.	The number of onto functions (surjective functions) from set X={1,2,3,4} to set Y={a,b,c} is36
Answer» The number of onto functions (surjective functions) from set $X = {1, 2, 3, 4}$ to set $Y = {a, b, c}$ is 36

Discussion

9269.	The matrix form of the linear system dxdt=3x−5y and dydt=4x+8y
Answer» The matrix form of the linear system $\frac{d x}{d t} = 3 x - 5 y$ and $\frac{d y}{d t} = 4 x + 8 y$

Discussion

9270.	If the point (4,5) lies on the graph of the equation 5y=ax+9. Find the value of a.
Answer» If the point (4,5) lies on the graph of the equation 5y=ax+9. Find the value of a.

Discussion

9271.	Find the value of x.
Answer» Find the value of x.

9271.

Find the value of x.

Answer»

Find the value of x.

Discussion

9272.	Through A, B and C lines RQ, PR and QP have been drawn, respectively parallel to sides BC, CA and AB of a ΔABC as shown in figure. Show that BC=12QR.
Answer» Through A, B and C lines RQ, PR and QP have been drawn, respectively parallel to sides BC, CA and AB of a $Δ A B C$ as shown in figure. Show that $B C = \frac{1}{2} Q R$ .

Discussion

9273.	Question 1(iii)Do the following pair of linear equations have no solution? Justify your answer.3x + y – 3 = 0 and 2x + 23 y = 2
Answer» Question 1(iii) Do the following pair of linear equations have no solution? Justify your answer. 3x + y – 3 = 0 and 2x + $\frac{2}{3}$ y = 2

Discussion

9274.	If loga(ab)=x, then logb (ab) is equal to
Answer» If $l o g_{a} (a b) = x$ , then $l o g_{b} (a b)$ is equal to

Discussion

9275.	What is a segment ?
Answer» What is a segment ?

Discussion

9276.	log10x=log10 2^25gives uslog10x=25log10 2how does the 2^25 come in exponential form and be in front as 25log10 2
Answer» log10x=log10 2^25 gives us log10x=25log10 2 how does the 2^25 come in exponential form and be in front as 25log10 2

Discussion

9277.	If x=√p+2q+√p-2q/√p+2q-√p-2q then prove that qx²-px+q=0
Answer» If x=√p+2q+√p-2q/√p+2q-√p-2q then prove that qx²-px+q=0

Discussion

9278.	Prove that the area of a trapezium is equal to half the product of the sum of// sides and the altitude
Answer» Prove that the area of a trapezium is equal to half the product of the sum of// sides and the altitude

Discussion

9279.

Find the mean from the following frequency distribution of marks at a test in statistics: Marks (x): 5 10 15 20 25 30 35 40 45 50 No. of students (f): 15 50 80 76 72 45 39 9 8 6

Answer» Find the mean from the following frequency distribution of marks at a test in statistics:

Marks (x):	5	10	15	20	25	30	35	40	45	50
No. of students (f):	15	50	80	76	72	45	39	9	8	6

Discussion

9280.	In the given figure, two circles intersect at points M and N. Secants drawn through M and N intersect the circles at points R, S and P, Q respectively. Prove that : seg SQ \|\| seg RP.
Answer» In the given figure, two circles intersect at points M and N. Secants drawn through M and N intersect the circles at points R, S and P, Q respectively. Prove that : seg SQ \|\| seg RP.

Discussion

9281.	If x+15=4, then x+1x=(a) 2(b) 4(c) 8(d) 1
Answer» If $x + \sqrt{15} = 4,$ then $x + \frac{1}{x}$ = (a) 2 (b) 4 (c) 8 (d) 1

Discussion

9282.	Find the area of the shaded pathway.
Answer» Find the area of the shaded pathway.

9282.

Find the area of the shaded pathway.

Answer»

Find the area of the shaded pathway.

Discussion

9283.	Let P(2c-1,c+2) be a variable point. PM and PN are perpendiculars from P on two fixed lines which meet at O,the origin MQ, NQ are drawn parallel to the fixed straight lines to meet at Q Prove that the locus of Q is a straight lin
Answer» Let P(2c-1,c+2) be a variable point. PM and PN are perpendiculars from P on two fixed lines which meet at O,the origin MQ, NQ are drawn parallel to the fixed straight lines to meet at Q Prove that the locus of Q is a straight lin

Discussion

9284.	Question 63 In the following question, fill in the blanks to make the statements true. The expression for 35 with a negative exponent is ___
Answer» Question 63 In the following question, fill in the blanks to make the statements true. The expression for $3^{5}$ with a negative exponent is ___

9284.

Question 63 In the following question, fill in the blanks to make the statements true. The expression for 35 with a negative exponent is ___

Answer»

Question 63

In the following question, fill in the blanks to make the statements true.

The expression for $3^{5}$ with a negative exponent is ___

Discussion

9285.	The expression √5−√3√5+√3 when simplified reduces to a-b√15.Then a + b is __________.
Answer» The expression $\frac{\sqrt{5} - \sqrt{3}}{\sqrt{5} + \sqrt{3}}$ when simplified reduces to a-b $\sqrt{15}$ . Then a + b is __________.

9285.

The expression √5−√3√5+√3 when simplified reduces to a-b√15.Then a + b is __________.

Answer»

The expression $\frac{\sqrt{5} - \sqrt{3}}{\sqrt{5} + \sqrt{3}}$ when simplified reduces to a-b $\sqrt{15}$ .

Then a + b is __________.

Discussion

9286.	If m is the slope of a line and m+ 2 m+3,then the possible angle between line and x-axis is(1) 0^° (2) 90^° (3) 60(4) 45^° H y=mx + c is
Answer» If m is the slope of a line and m+ 2 m+3,then the possible angle between line and x-axis is(1) 0^° (2) 90^° (3) 60(4) 45^° H y=mx + c is

Discussion

9287.	If the volume of two cones are in the ratio 1 : 4 and their diameters are in the ratio 4 : 5, then the ratio of their heights, is(a) 1 : 5(b) 5 : 4(c) 5 : 16(d) 25 : 64
Answer» If the volume of two cones are in the ratio 1 : 4 and their diameters are in the ratio 4 : 5, then the ratio of their heights, is (a) 1 : 5 (b) 5 : 4 (c) 5 : 16 (d) 25 : 64

Discussion

9288.	BD is a perpendicular bisector of AC. Which statement can NOT always be proven?
Answer» BD is a perpendicular bisector of AC. Which statement can NOT always be proven?

9288.

BD is a perpendicular bisector of AC. Which statement can NOT always be proven?

Answer»

BD is a perpendicular bisector of AC. Which statement can NOT always be proven?

Discussion

9289.	If A=[√31−1230] and B=⎡⎢⎣2√51−2312⎤⎥⎦, then the value of A+B is
Answer» If $A = [\begin{matrix} \sqrt{3} & 1 & - 1 2 & 3 & 0 \end{matrix}]$ and $B = ⎡ ⎢ ⎣ \begin{matrix} 2 & \sqrt{5} & 1 - 2 & 3 & \frac{1}{2} \end{matrix} ⎤ ⎥ ⎦$ , then the value of $A + B$ is

Discussion

9290.	Solve the following equations for x: (i) 72x+3=1 (ii) 2x+1=4x−3 (iii)25x+3=8x+3 (iv) 42x=132 (v)4x−1×(0.5)3−2x=(18)x (vi)23x−7=256
Answer» Solve the following equations for x: (i) $7^{2 x + 3} = 1$ (ii) $2^{x + 1} = 4^{x - 3}$ (iii) $2^{5 x + 3} = 8^{x + 3}$ (iv) $4^{2 x} = \frac{1}{32}$ (v) $4^{x - 1} \times (0.5)^{3 - 2 x} = {(\frac{1}{8})}^{x}$ (vi) $2^{3 x - 7} = 256$

9290.

Solve the following equations for x: (i) 72x+3=1 (ii) 2x+1=4x−3 (iii)25x+3=8x+3 (iv) 42x=132 (v)4x−1×(0.5)3−2x=(18)x (vi)23x−7=256

Answer»

Solve the following equations for x:

(i) $7^{2 x + 3} = 1$

(ii) $2^{x + 1} = 4^{x - 3}$

(iii) $2^{5 x + 3} = 8^{x + 3}$

(iv) $4^{2 x} = \frac{1}{32}$

(v) $4^{x - 1} \times (0.5)^{3 - 2 x} = {(\frac{1}{8})}^{x}$

(vi) $2^{3 x - 7} = 256$

Discussion

9291.	A dice was cast 40 times and each score noted is given below. Draw up a frequency table for this data.3, 2, 5, 6, 4, 2, 3, 1, 6, 6, 2, 3, 5, 3, 5, 3, 4, 2, 4, 5, 4, 2, 6, 3, 3, 2 4, 3, 3, 4, 1, 4, 3, 3, 2, 2, 5, 3, 3, 4
Answer» A dice was cast 40 times and each score noted is given below. Draw up a frequency table for this data. 3, 2, 5, 6, 4, 2, 3, 1, 6, 6, 2, 3, 5, 3, 5, 3, 4, 2, 4, 5, 4, 2, 6, 3, 3, 2 4, 3, 3, 4, 1, 4, 3, 3, 2, 2, 5, 3, 3, 4

Discussion

9292.	In quadrilateral ABCD , BM and DN are drawn perpendiculars to diagonal AC such that BM = DN. If BR =18cm ( R is s point of intersection of AC and BD) then BD is
Answer» In quadrilateral ABCD , BM and DN are drawn perpendiculars to diagonal AC such that BM = DN. If BR =18cm ( R is s point of intersection of AC and BD) then BD is

Discussion

9293.	The rato between the curved surface area and the total surface area of a right circular cylinder is 1:2.Find the volume of the cylinder if its total surface area is 616cm2.
Answer» The rato between the curved surface area and the total surface area of a right circular cylinder is 1:2.Find the volume of the cylinder if its total surface area is $616 c m^{2}$ .

Discussion

9294.	79. Find the area of quidrilateral abcd in which ab=3cm bc=4cm cd=4cm da=5cm ac=5cm
Answer» 79. Find the area of quidrilateral abcd in which ab=3cm bc=4cm cd=4cm da=5cm ac=5cm

Discussion

9295.	How many outcomes does the experiment "drawing three balls from a bag" have if the bag contains 5 green balls and 2 black balls? __
Answer» How many outcomes does the experiment "drawing three balls from a bag" have if the bag contains 5 green balls and 2 black balls? __

Discussion

9296.	If the length of a rectangle is 5 cm and its breadth is 2 cm, then the ratio of length to breadth is ________.
Answer» If the length of a rectangle is 5 cm and its breadth is 2 cm, then the ratio of length to breadth is ________.

Discussion

9297.	Question 153In parallelogram LOST, SN⊥OL and SM⊥LT. Find ∠STM,∠SON and ∠NSM.
Answer» Question 153 In parallelogram LOST, $S N ⊥ O L$ and $S M ⊥ L T$ . Find $∠ S T M, ∠ S O N$ and $∠ N S M$ .

Discussion

9298.	A hemispherical bowl made of brass has inner diameter 10.5 cm. Find the cost of tin-plating it on the inside at the rate of Rs 16 per 100 cm2.
Answer» A hemispherical bowl made of brass has inner diameter 10.5 cm. Find the cost of tin-plating it on the inside at the rate of Rs 16 per 100 cm².

Discussion

9299.	The cost of 35 envelops is ₹ 105. How many envelops can be bought for Rs 90?
Answer» The cost of 35 envelops is ₹ 105. How many envelops can be bought for Rs 90?

Discussion

9300.	Given the proportion 45: 75 :: 75: 125, what is the mean proportion? ___
Answer» Given the proportion 45: 75 :: 75: 125, what is the mean proportion? ___

Discussion

Explore topic-wise InterviewSolutions in .

Question 111Pluto is 5913000000 m from the Sun. Express this in the standard form.

Question 8 1.6=y1.5

If the radius of a circle is 6 cm and θ is 30∘, then find the length of the arc of the circle.

Which of the following is a factor of 2x^4 + 1 + 3 x^2 ? A 1 + 2x^2 B 4+x^2 C 2x^2 -1 D 3+x^2

35. Two circles A and B of radius 3 cm and 4cm intersect at the point C and D such thatcAC and BC are tangent to the circle. Find the lenght of common chord CD

Which of the following is a true statement ? (a) The sum of two irrational numbers is an irrational number. (b) The product of two irrational numbers is an irrational number. (c) Every real number is always rational. (d) Every real number is either rational or irrational.

Which is an example of the commutative property of addition?

In the given figure, if AB||CD,∠APQ=50∘ and ∠PRD=127∘, the value of y is:

Find x if 8x3+6x12x2+1=3519

Define the following terms: (i) Line segment (ii) Collinear points (iii) Parallel lines (iv) Intersecting lines (v) Concurrent lines (vi) Ray

Find the perimeter (in ft) of the given swimming pool.28

evaluate: ∫cos(x - ∝)/cos x dx

ABCD is a kite where AB =AD and BC =CD .P,Q,R and S are the mid -points of the sides AB, BC, CD and AD respectively. Prove that PQRS is a rectangle.

find the value of x2+y2+z2 if x+y+Z=9 and XY+YZ+ZX=26

The area of a triangle is half the product of any of its sides and the corresponding altitude

If x2 + y2 = 14 and xy=3, find the value of 2(x+y)2−5(x−y)2.

If f(x)=∣∣∣∣x2253x37209∣∣∣∣, then the value of f′(1) is:

The number of onto functions (surjective functions) from set X={1,2,3,4} to set Y={a,b,c} is36

The matrix form of the linear system dxdt=3x−5y and dydt=4x+8y

If the point (4,5) lies on the graph of the equation 5y=ax+9. Find the value of a.

Find the value of x.

Through A, B and C lines RQ, PR and QP have been drawn, respectively parallel to sides BC, CA and AB of a ΔABC as shown in figure. Show that BC=12QR.

Question 1(iii)Do the following pair of linear equations have no solution? Justify your answer.3x + y – 3 = 0 and 2x + 23 y = 2

If loga(ab)=x, then logb (ab) is equal to

What is a segment ?

log10x=log10 2^25gives uslog10x=25log10 2how does the 2^25 come in exponential form and be in front as 25log10 2

If x=√p+2q+√p-2q/√p+2q-√p-2q then prove that qx²-px+q=0

Prove that the area of a trapezium is equal to half the product of the sum of// sides and the altitude

Find the mean from the following frequency distribution of marks at a test in statistics: Marks (x): 5 10 15 20 25 30 35 40 45 50 No. of students (f): 15 50 80 76 72 45 39 9 8 6

In the given figure, two circles intersect at points M and N. Secants drawn through M and N intersect the circles at points R, S and P, Q respectively. Prove that : seg SQ || seg RP.

If x+15=4, then x+1x=(a) 2(b) 4(c) 8(d) 1

Find the area of the shaded pathway.

Let P(2c-1,c+2) be a variable point. PM and PN are perpendiculars from P on two fixed lines which meet at O,the origin MQ, NQ are drawn parallel to the fixed straight lines to meet at Q Prove that the locus of Q is a straight lin

Question 63 In the following question, fill in the blanks to make the statements true. The expression for 35 with a negative exponent is ___

The expression √5−√3√5+√3 when simplified reduces to a-b√15.Then a + b is __________.

If m is the slope of a line and m+ 2 m+3,then the possible angle between line and x-axis is(1) 0^° (2) 90^° (3) 60(4) 45^° H y=mx + c is

If the volume of two cones are in the ratio 1 : 4 and their diameters are in the ratio 4 : 5, then the ratio of their heights, is(a) 1 : 5(b) 5 : 4(c) 5 : 16(d) 25 : 64

BD is a perpendicular bisector of AC. Which statement can NOT always be proven?

If A=[√31−1230] and B=⎡⎢⎣2√51−2312⎤⎥⎦, then the value of A+B is

Solve the following equations for x: (i) 72x+3=1 (ii) 2x+1=4x−3 (iii)25x+3=8x+3 (iv) 42x=132 (v)4x−1×(0.5)3−2x=(18)x (vi)23x−7=256

A dice was cast 40 times and each score noted is given below. Draw up a frequency table for this data.3, 2, 5, 6, 4, 2, 3, 1, 6, 6, 2, 3, 5, 3, 5, 3, 4, 2, 4, 5, 4, 2, 6, 3, 3, 2 4, 3, 3, 4, 1, 4, 3, 3, 2, 2, 5, 3, 3, 4

In quadrilateral ABCD , BM and DN are drawn perpendiculars to diagonal AC such that BM = DN. If BR =18cm ( R is s point of intersection of AC and BD) then BD is

The rato between the curved surface area and the total surface area of a right circular cylinder is 1:2.Find the volume of the cylinder if its total surface area is 616cm2.

79. Find the area of quidrilateral abcd in which ab=3cm bc=4cm cd=4cm da=5cm ac=5cm

How many outcomes does the experiment "drawing three balls from a bag" have if the bag contains 5 green balls and 2 black balls? __

If the length of a rectangle is 5 cm and its breadth is 2 cm, then the ratio of length to breadth is ________.

Question 153In parallelogram LOST, SN⊥OL and SM⊥LT. Find ∠STM,∠SON and ∠NSM.

A hemispherical bowl made of brass has inner diameter 10.5 cm. Find the cost of tin-plating it on the inside at the rate of Rs 16 per 100 cm2.

The cost of 35 envelops is ₹ 105. How many envelops can be bought for Rs 90?

Given the proportion 45: 75 :: 75: 125, what is the mean proportion? ___