24740 + Interview Questions in Mathematics Page 3 InterviewSolution

101.	For a cube of side 'a' and a cuboid of length 'l', breadth 'b' and height 'h', match the following.
Answer» For a cube of side 'a' and a cuboid of length 'l', breadth 'b' and height 'h', match the following.

Discussion

102.	i) What is the percentage of people in the height range 149.5 -159.5cm?ii) What is the percentage difference between the number of people in the height range 159.5 - 169.5cm and 169.5 - 179.5cm?
Answer» i) What is the percentage of people in the height range 149.5 -159.5cm? ii) What is the percentage difference between the number of people in the height range 159.5 - 169.5cm and 169.5 - 179.5cm?

102.

i) What is the percentage of people in the height range 149.5 -159.5cm?ii) What is the percentage difference between the number of people in the height range 159.5 - 169.5cm and 169.5 - 179.5cm?

Answer»

i) What is the percentage of people in the height range 149.5 -159.5cm?

ii) What is the percentage difference between the number of people in the height range 159.5 - 169.5cm and 169.5 - 179.5cm?

Discussion

103.	Find the value of k for which x2–4x+k=0 has coincident roots.
Answer» Find the value of k for which $x^{2} - 4 x + k = 0$ has coincident roots.

Discussion

104.	The area of a parallelogram of the given dimensions is:
Answer» The area of a parallelogram of the given dimensions is:

104.

The area of a parallelogram of the given dimensions is:

Answer»

The area of a parallelogram of the given dimensions is:

Discussion

105.	From the options given below, choose the option which has all the measurements you will require to construct a quadrilateral ABCD.
Answer» From the options given below, choose the option which has all the measurements you will require to construct a quadrilateral ABCD.

Discussion

106.	If I pick a red ball 10 times out of 30 times from a bag that contains red and black balls, then the probability of picking a black ball is _________.
Answer» If I pick a red ball 10 times out of 30 times from a bag that contains red and black balls, then the probability of picking a black ball is _________.

Discussion

107.	If a+b+c= 6 and 1/a + 1/b + 1/c = 3/2, then find a/b + a/c + b/a + b/c + c/a + c/b.Kindly show the detailed steps.
Answer» If a+b+c= 6 and 1/a + 1/b + 1/c = 3/2, then find a/b + a/c + b/a + b/c + c/a + c/b. Kindly show the detailed steps.

Discussion

108.	factorize 4096 subtracted from x raise to 12
Answer» factorize 4096 subtracted from x raise to 12

Discussion

109.	If ∠A, ∠B, ∠C and ∠D of a quadrilateral ABCD taken in order, are in the ratio 3 : 7 : 6 : 4 then ABCD is a(a) rhombus(b) kite(c) trapezium(d) parallelogram
Answer» If ∠A, ∠B, ∠C and ∠D of a quadrilateral ABCD taken in order, are in the ratio 3 : 7 : 6 : 4 then ABCD is a (a) rhombus (b) kite (c) trapezium (d) parallelogram

Discussion

110.	If A is non-singular matrix satisfying AB−BA=A, then
Answer» If $A$ is non-singular matrix satisfying $A B - B A = A$ , then

Discussion

111.	How many lead shots, each 3 mm in diameter, can be made from a cuboid with dimensions 12cm×11×9cm?
Answer» How many lead shots, each 3 mm in diameter, can be made from a cuboid with dimensions $12 c m \times 11 \times 9 c m$ ?

Discussion

112.	In the following figure, ABCD is a parallelogram. If E is the mid-point of BC and AE is the bisector of ∠A, then prove that AB = 12 AD.
Answer» In the following figure, ABCD is a parallelogram. If E is the mid-point of BC and AE is the bisector of ∠A, then prove that AB = $\frac{1}{2}$ AD.

Discussion

113.	If a(x)2+bx+c is a monomial in x , what can be said about a, b and c?
Answer» If $a (x)^{2} + b x + c$ is a monomial in $x$ , what can be said about $a$ , $b$ and $c$ ?

Discussion

114.	Prove that if the diagonals of a quadrilateral are equal and are perpendicular bisectors to each other, then it is a square.[4 MARKS]
Answer» Prove that if the diagonals of a quadrilateral are equal and are perpendicular bisectors to each other, then it is a square.[4 MARKS]

Discussion

115.	The surface area of a sphere of radius 5 cm is five times the area of the curved surface of a cone of radius 4 cm. Find the height of the cone.
Answer» The surface area of a sphere of radius 5 cm is five times the area of the curved surface of a cone of radius 4 cm. Find the height of the cone.

Discussion

116.	If the area of an isosceles right triangle is 8 cm2, what is the perimeter of the triangle?(a) 8 + 2 cm2(b) 8 + 42 cm2(c) 4 + 82 cm2(d) 122 cm2
Answer» If the area of an isosceles right triangle is 8 cm², what is the perimeter of the triangle? (a) 8 + $\sqrt{2}$ cm² (b) 8 + 4 $\sqrt{2}$ cm² (c) 4 + 8 $\sqrt{2}$ cm² (d) 12 $\sqrt{2}$ cm²

Discussion

117.	Find x in the following figure:
Answer» Find $x$ in the following figure:

117.

Find x in the following figure:

Answer»

Find $x$ in the following figure:

Discussion

118.	Question 5 In ΔPQR and ΔMST,∠P=55∘,∠Q=25∘,∠M=100∘ and ∠S=25∘.Is ΔQPR∼ΔTSM? Why?
Answer» Question 5 $I n Δ P Q R a n d Δ M S T, ∠ P = 55^{\circ}, ∠ Q = 25^{\circ}, ∠ M = 100^{\circ} a n d ∠ S = 25^{\circ} . I s Δ Q P R \sim Δ T S M ? W h y ?$

Discussion

119.	Consider the functions f(x)={x+1, x≤12x+1, 1<x≤2g(x)={x2, −1≤x<2x+2, 2≤x≤3Range of the function f(g(x)) is
Answer» Consider the functions $f (x) = {\begin{matrix} x + 1, x \leq 1 2 x + 1, 1 < x \leq 2 \end{matrix}$ $g (x) = {\begin{matrix} x^{2}, - 1 \leq x < 2 x + 2, 2 \leq x \leq 3 \end{matrix}$ Range of the function $f (g (x))$ is

Discussion

120.	Draw the graph of y=2x+1,y=2x and y=2x-1/2 are these parallel
Answer» Draw the graph of y=2x+1,y=2x and y=2x-1/2 are these parallel

Discussion

121.	On a number line, co-ordinates of P, Q, R are 3,- 5 and 6 respectively. State with reason whether the following statements are true or false.(i) d(P,Q) + d(Q,R) = d(P,R) (ii) d(P,R) + d(R,Q) = d(P,Q)(iii) d(R,P) + d(P,Q) = d(R,Q) (iv) d(P,Q) - d(P,R) = d(Q,R)
Answer» On a number line, co-ordinates of P, Q, R are 3, $-$ 5 and 6 respectively. State with reason whether the following statements are true or false. (i) d(P,Q) + d(Q,R) = d(P,R) (ii) d(P,R) + d(R,Q) = d(P,Q) (iii) d(R,P) + d(P,Q) = d(R,Q) (iv) d(P,Q) $-$ d(P,R) = d(Q,R)

Discussion

122.	In △ABC,∠B=90∘ and sin A=513, then sec2A−tan2A= __________________
Answer» In $△ A B C, ∠ B = 90^{\circ}$ and $s i n A = \frac{5}{13}$ , then $s e c^{2} A - t a n^{2} A =$ __________________

Discussion

123.	What is the total surface area of a closed hemisphere?
Answer» What is the total surface area of a closed hemisphere?

Discussion

124.	Insert 3 irrational numbers between 2 root 2 and 5. ( root 2 = 1.414 )
Answer» Insert 3 irrational numbers between 2 root 2 and 5. ( root 2 = 1.414 )

Discussion

125.	In a ∆ABC, if AB = 8 cm, AC = 10 cm and BC = 14 cm, then the length of median AD drawn from point ‘A’ on BC is equal to
Answer» In a ∆ABC, if AB = 8 cm, AC = 10 cm and BC = 14 cm, then the length of median AD drawn from point ‘A’ on BC is equal to

Discussion

126.	Question 1In the given figure, E is any point on the median AD of a ΔABC. Show that ar(ABE) = ar(ACE).
Answer» Question 1 In the given figure, E is any point on the median AD of a $Δ A B C$ . Show that ar(ABE) = ar(ACE).

Discussion

127.	Of which of the binomials given below is m2n2 + 14mnpq + 49p2q2 the expansion? (i) (m + n) (p + q) (ii) (mn- pq) (iii) (7mn + pq) (iv) (mn + 7pq)
Answer» Of which of the binomials given below is m²n²+ 14mnpq + 49p²q²the expansion? (i) (m + n) (p + q) (ii) (mn- pq) (iii) (7mn + pq) (iv) (mn + 7pq)

Discussion

128.	14. the wavelength of the series limit for the paschen's series of H spectra
Answer» 14. the wavelength of the series limit for the paschen's series of H spectra

Discussion

129.	In the given figure an equilateral triangle has been cut into two equal parts. What is the area of the 1st part ?
Answer» In the given figure an equilateral triangle has been cut into two equal parts. What is the area of the 1st part ?

129.

In the given figure an equilateral triangle has been cut into two equal parts. What is the area of the 1st part ?

Answer»

In the given figure an equilateral triangle has been cut into two equal parts.

What is the area of the 1st part ?

Discussion

130.	Rectify the following errors:(a) Bought Radio for ₹ 1,000 for the proprietor was debited to General Expenses A/c.(b) Bought goods from Mohan ₹ 2,000 was passed through the Sales Book, however, the account of Mohan was credited correctly.(c) Wages due ₹ 1,500 has not been taken into account.(d) Goods Returned by Kamal ₹ 240 has been debited to his account ₹ 420.
Answer» Rectify the following errors: (a) Bought Radio for ₹ 1,000 for the proprietor was debited to General Expenses A/c. (b) Bought goods from Mohan ₹ 2,000 was passed through the Sales Book, however, the account of Mohan was credited correctly. (c) Wages due ₹ 1,500 has not been taken into account. (d) Goods Returned by Kamal ₹ 240 has been debited to his account ₹ 420.

Discussion

131.	IF ABC and BDE are two equlateral triangles such that D is the mid point of BC, then find ar (△ABC):ar(△BDE).
Answer» IF ABC and BDE are two equlateral triangles such that D is the mid point of BC, then find ar $(△ A B C) : a r (△ B D E) .$

Discussion

132.	54 is divided into 2 parts such that the sum of 10 times the first part and 22 times the second part is 780. The bigger number is ----
Answer» 54 is divided into 2 parts such that the sum of 10 times the first part and 22 times the second part is 780. The bigger number is ----

Discussion

133.	If cotθ = 78, the value of cot2θ is
Answer» $I f c o t θ = \frac{7}{8}, t h e v a l u e o f c o t^{2} θ i s$

Discussion

134.	Sum of two numbers is 20 and their difference is 5. Find the difference in their squares.100
Answer» Sum of two numbers is 20 and their difference is 5. Find the difference in their squares. 100

134.

Sum of two numbers is 20 and their difference is 5. Find the difference in their squares.100

Answer»

Sum of two numbers is 20 and their difference is 5. Find the difference in their squares.

100

Discussion

135.	In a parallelogram ABCD, the line drawn through a point P on AB; parallel to BC, meets AC at Q. The line through Q, parallel to AB meets AD at R. Then, prove that APPB= AQQC= ARRD.
Answer» In a parallelogram ABCD, the line drawn through a point P on AB; parallel to BC, meets AC at Q. The line through Q, parallel to AB meets AD at R. Then, prove that $\frac{A P}{P B} =$ $\frac{A Q}{Q C} =$ $\frac{A R}{R D}$ .

Discussion

136.	Question 7 (iii) ABC is a triangle right angled at C. A line through the mid-point M of hypotenuse AB and parallel to BC intersects AC at D. Show that CM=MA=12AB
Answer» Question 7 (iii) $A B C$ is a triangle right angled at $C$ . A line through the mid-point $M$ of hypotenuse $A B$ and parallel to $B C$ intersects AC at D. Show that $C M = M A = \frac{1}{2} A B$

Discussion

137.	Prove that two angle of a triangle must be acute angle .
Answer» Prove that two angle of a triangle must be acute angle .

Discussion

138.	If BC is a diameter of a circle with centre O and OD is perpendicular to the chord AB of a circle, then CA = ____ OD. ___
Answer» If BC is a diameter of a circle with centre O and OD is perpendicular to the chord AB of a circle, then CA = ____ OD. ___

138.

If BC is a diameter of a circle with centre O and OD is perpendicular to the chord AB of a circle, then CA = __ OD. _

Answer»

If BC is a diameter of a circle with centre O and OD is perpendicular to the chord AB of a circle, then CA = ____ OD.

___

Discussion

139.	31, 38, 27, 28, 36, 25, 35, 40
Answer» 31, 38, 27, 28, 36, 25, 35, 40

Discussion

140.	If a and b are rational numbers and √11−√7√11+√7=a−b√77, find a−b.4
Answer» If a and b are rational numbers and $\frac{\sqrt{11} - \sqrt{7}}{\sqrt{11} + \sqrt{7}} = a - b \sqrt{77},$ find $a - b$ . 4

Discussion

141.	if (x-1) and (x+2) are two factors of the polynomial 2x^3 + mx^2 -x-n, then find the vaue of (m^2-n^2)
Answer» if (x-1) and (x+2) are two factors of the polynomial 2x^3 + mx^2 -x-n, then find the vaue of (m^2-n^2)

Discussion

142.	Rationalize the denominator of 5√3−√5
Answer» Rationalize the denominator of $\frac{5}{\sqrt{3} - \sqrt{5}}$

Discussion

143.	A box contains cards with numbers marked from 1 to 100. Find the probability of getting a card (a) with a perfect square (b) Divisible by both 25 and 50
Answer» A box contains cards with numbers marked from 1 to 100. Find the probability of getting a card (a) with a perfect square (b) Divisible by both 25 and 50

143.

A box contains cards with numbers marked from 1 to 100. Find the probability of getting a card (a) with a perfect square (b) Divisible by both 25 and 50

Answer»

A box contains cards with numbers marked from 1 to 100. Find the probability of getting a card

(a) with a perfect square (b) Divisible by both 25 and 50

Discussion

144.	Write any three rational numbers between the two numbers given below.(i) 0.3 and -0.5 (ii) -2.3 and -2.33(iii) 5.2 and 5.3 (iv) -4.5 and -4.6
Answer» Write any three rational numbers between the two numbers given below. (i) 0.3 and -0.5 (ii) -2.3 and -2.33 (iii) 5.2 and 5.3 (iv) -4.5 and -4.6

Discussion

145.	For the diagram shown above, the points with their x− coordinate 0 are , while the points with their y− coordinate 0 are .
Answer» For the diagram shown above, the points with their $x -$ coordinate $0$ are , while the points with their $y -$ coordinate $0$ are .

Discussion

146.	Question 1 (ii)Solve the following pairs of equations by reducing them to a pair of linear equations:2√x+3√y=24√x−9√y=−1
Answer» Question 1 (ii) Solve the following pairs of equations by reducing them to a pair of linear equations: $\frac{2}{\sqrt{x}} + \frac{3}{\sqrt{y}} = 2 \frac{4}{\sqrt{x}} - \frac{9}{\sqrt{y}} = - 1$

Discussion

147.	Find the polar form of the complex number -5.
Answer» Find the polar form of the complex number -5.

Discussion

148.	1+tan2theta/1+cot2theta is equal to tan2 theta. Prove it.
Answer» 1+tan2theta/1+cot2theta is equal to tan2 theta. Prove it.

Discussion

149.	Q 1. ABC is a triangle in which ab= bc point d is produced on bc such that angle bad=30 also e is produced on ac such that ae= ad find angle edc Q 2. a set of n numbers has sum s . each no. of set is increased by 20 then multiply by 5 and then decreased by 20. the sum of no. in new set thus obtained is ? Q 3. circles with centre p, q and s are touching each other externally at a, b and can. if radii of circle p,q and s are 1,2 and 3 respectively then find the length of cord ABC.
Answer» Q 1. ABC is a triangle in which ab= bc point d is produced on bc such that angle bad=30 also e is produced on ac such that ae= ad find angle edc Q 2. a set of n numbers has sum s . each no. of set is increased by 20 then multiply by 5 and then decreased by 20. the sum of no. in new set thus obtained is ? Q 3. circles with centre p, q and s are touching each other externally at a, b and can. if radii of circle p,q and s are 1,2 and 3 respectively then find the length of cord ABC.

Discussion

150.	Write the relation r={(x,x3):x is a prime number less than 10} in roster form.
Answer» Write the relation $r = {(x, x^{3}) : x$ is a prime number less than 10} in roster form.

Discussion

Explore topic-wise InterviewSolutions in .

For a cube of side 'a' and a cuboid of length 'l', breadth 'b' and height 'h', match the following.

i) What is the percentage of people in the height range 149.5 -159.5cm?ii) What is the percentage difference between the number of people in the height range 159.5 - 169.5cm and 169.5 - 179.5cm?

Find the value of k for which x2–4x+k=0 has coincident roots.

The area of a parallelogram of the given dimensions is:

From the options given below, choose the option which has all the measurements you will require to construct a quadrilateral ABCD.

If I pick a red ball 10 times out of 30 times from a bag that contains red and black balls, then the probability of picking a black ball is _________.

If a+b+c= 6 and 1/a + 1/b + 1/c = 3/2, then find a/b + a/c + b/a + b/c + c/a + c/b.Kindly show the detailed steps.

factorize 4096 subtracted from x raise to 12

If ∠A, ∠B, ∠C and ∠D of a quadrilateral ABCD taken in order, are in the ratio 3 : 7 : 6 : 4 then ABCD is a(a) rhombus(b) kite(c) trapezium(d) parallelogram

If A is non-singular matrix satisfying AB−BA=A, then

How many lead shots, each 3 mm in diameter, can be made from a cuboid with dimensions 12cm×11×9cm?

In the following figure, ABCD is a parallelogram. If E is the mid-point of BC and AE is the bisector of ∠A, then prove that AB = 12 AD.

If a(x)2+bx+c is a monomial in x , what can be said about a, b and c?

Prove that if the diagonals of a quadrilateral are equal and are perpendicular bisectors to each other, then it is a square.[4 MARKS]

The surface area of a sphere of radius 5 cm is five times the area of the curved surface of a cone of radius 4 cm. Find the height of the cone.

If the area of an isosceles right triangle is 8 cm2, what is the perimeter of the triangle?(a) 8 + 2 cm2(b) 8 + 42 cm2(c) 4 + 82 cm2(d) 122 cm2

Find x in the following figure:

Question 5 In ΔPQR and ΔMST,∠P=55∘,∠Q=25∘,∠M=100∘ and ∠S=25∘.Is ΔQPR∼ΔTSM? Why?

Consider the functions f(x)={x+1, x≤12x+1, 1&lt;x≤2g(x)={x2, −1≤x&lt;2x+2, 2≤x≤3Range of the function f(g(x)) is

Draw the graph of y=2x+1,y=2x and y=2x-1/2 are these parallel

On a number line, co-ordinates of P, Q, R are 3,- 5 and 6 respectively. State with reason whether the following statements are true or false.(i) d(P,Q) + d(Q,R) = d(P,R) (ii) d(P,R) + d(R,Q) = d(P,Q)(iii) d(R,P) + d(P,Q) = d(R,Q) (iv) d(P,Q) - d(P,R) = d(Q,R)

In △ABC,∠B=90∘ and sin A=513, then sec2A−tan2A= __________________

What is the total surface area of a closed hemisphere?

Insert 3 irrational numbers between 2 root 2 and 5. ( root 2 = 1.414 )

In a ∆ABC, if AB = 8 cm, AC = 10 cm and BC = 14 cm, then the length of median AD drawn from point ‘A’ on BC is equal to

Question 1In the given figure, E is any point on the median AD of a ΔABC. Show that ar(ABE) = ar(ACE).

Of which of the binomials given below is m2n2 + 14mnpq + 49p2q2 the expansion? (i) (m + n) (p + q) (ii) (mn- pq) (iii) (7mn + pq) (iv) (mn + 7pq)

14. the wavelength of the series limit for the paschen's series of H spectra

In the given figure an equilateral triangle has been cut into two equal parts. What is the area of the 1st part ?

IF ABC and BDE are two equlateral triangles such that D is the mid point of BC, then find ar (△ABC):ar(△BDE).

54 is divided into 2 parts such that the sum of 10 times the first part and 22 times the second part is 780. The bigger number is ----

If cotθ = 78, the value of cot2θ is

Sum of two numbers is 20 and their difference is 5. Find the difference in their squares.100

In a parallelogram ABCD, the line drawn through a point P on AB; parallel to BC, meets AC at Q. The line through Q, parallel to AB meets AD at R. Then, prove that APPB= AQQC= ARRD.

Question 7 (iii) ABC is a triangle right angled at C. A line through the mid-point M of hypotenuse AB and parallel to BC intersects AC at D. Show that CM=MA=12AB

Prove that two angle of a triangle must be acute angle .

If BC is a diameter of a circle with centre O and OD is perpendicular to the chord AB of a circle, then CA = ____ OD. ___

31, 38, 27, 28, 36, 25, 35, 40

If a and b are rational numbers and √11−√7√11+√7=a−b√77, find a−b.4

if (x-1) and (x+2) are two factors of the polynomial 2x^3 + mx^2 -x-n, then find the vaue of (m^2-n^2)

Rationalize the denominator of 5√3−√5

A box contains cards with numbers marked from 1 to 100. Find the probability of getting a card (a) with a perfect square (b) Divisible by both 25 and 50

Write any three rational numbers between the two numbers given below.(i) 0.3 and -0.5 (ii) -2.3 and -2.33(iii) 5.2 and 5.3 (iv) -4.5 and -4.6

For the diagram shown above, the points with their x− coordinate 0 are , while the points with their y− coordinate 0 are .

Question 1 (ii)Solve the following pairs of equations by reducing them to a pair of linear equations:2√x+3√y=24√x−9√y=−1

Find the polar form of the complex number -5.

1+tan2theta/1+cot2theta is equal to tan2 theta. Prove it.

Write the relation r={(x,x3):x is a prime number less than 10} in roster form.

Consider the functions f(x)={x+1, x≤12x+1, 1<x≤2g(x)={x2, −1≤x<2x+2, 2≤x≤3Range of the function f(g(x)) is

If BC is a diameter of a circle with centre O and OD is perpendicular to the chord AB of a circle, then CA = __ OD. _