24740 + Interview Questions in Mathematics Page 110 InterviewSolution

5451.	What is the formula for adjusted frequency?
Answer» What is the formula for adjusted frequency?

Discussion

5452.	3. A vector n is inclined to x axis at 45^°, to y axis at 60^°and at an acute angle to z axis. If n is a normal to a plane passing through the point(root2, -1,1)then the equation of the plane is
Answer» 3. A vector n is inclined to x axis at 45^°, to y axis at 60^°and at an acute angle to z axis. If n is a normal to a plane passing through the point(root2, -1,1)then the equation of the plane is

Discussion

5453.	Volume occupied by one molecules of wateris
Answer» Volume occupied by one molecules of wateris

Discussion

5454.	The following table shows the number of illiterate persons in the age group (10-58 years) in a town: Age group (in years)10−1617−2324−3031−3738−4445−5152−58Number of175325100150250400525illiterate persons Draw a histogram to represent the above data.
Answer» The following table shows the number of illiterate persons in the age group (10-58 years) in a town: $\begin{matrix} Age group (in years) & 10 - 16 & 17 - 23 & 24 - 30 & 31 - 37 & 38 - 44 & 45 - 51 & 52 - 58 Number of & 175 & 325 & 100 & 150 & 250 & 400 & 525 illiterate persons \end{matrix}$ Draw a histogram to represent the above data.

Discussion

5455.	In a ∆ABC, D is the mid-point of AC such that BD = 12 AC. Show that ∠ABC is a right angle.
Answer» In a ∆ABC, D is the mid-point of AC such that BD = $\frac{1}{2}$ AC. Show that ∠ABC is a right angle.

Discussion

5456.	How to find the root of a number?
Answer» How to find the root of a number?

Discussion

5457.	Question 1(iii)Evaluate: (12)−5
Answer» Question 1(iii) Evaluate: ${(\frac{1}{2})}^{- 5}$

5457.

Question 1(iii)Evaluate: (12)−5

Answer»

Question 1(iii)

Evaluate:

${(\frac{1}{2})}^{- 5}$

Discussion

5458.	The cost of painting the inner curved surface area of a cylindrical container of depth 20 m is ₹ 8800. If the painter charges ₹ 40 per metre square to paint the cylindrical container, then find its radius. [ Take π=227 ]
Answer» The cost of painting the inner curved surface area of a cylindrical container of depth 20 m is ₹ 8800. If the painter charges ₹ 40 per metre square to paint the cylindrical container, then find its radius. [ $Take π = \frac{22}{7}$ ]

Discussion

5459.	Assertion : ABCD and PQRC are rectangles and Q is mid - point of AC. Then DP = PC. Reason : The line segment joining the mid - points of any two sides of a triangle is parallel to the third side and equal to half of it. Which of the following is correct?
Answer» Assertion : ABCD and PQRC are rectangles and Q is mid - point of AC. Then DP = PC. Reason : The line segment joining the mid - points of any two sides of a triangle is parallel to the third side and equal to half of it. Which of the following is correct?

Discussion

5460.	How the HCF of two numbers is expressed in the form xa+xy?
Answer» How the HCF of two numbers is expressed in the form xa+xy?

Discussion

5461.	If x + a is a factor of x2 + px + q and x2 + mx + n then the value of a in terms of n, q, m and p is?
Answer» If x + a is a factor of x² + px + q and x² + mx + n then the value of a in terms of n, q, m and p is?

Discussion

5462.	The variance of first 50 even natural numbers is
Answer» The variance of first 50 even natural numbers is

Discussion

5463.	Pass Journal entries in the following cases?(a) Expenses of realisation ₹ 1,500.(b) Expenses of realisation ₹ 600 but paid by Mohan, a partner.(c) Mohan, one of the partners of the firm, was asked to look into the dissolution of the firm for which he was allowed a commission of ₹ 2,000.(d) Motor car of book value ₹ 50,000 taken over by creditors of the book value of ₹ 40,000 in full settlement.
Answer» Pass Journal entries in the following cases? (a) Expenses of realisation ₹ 1,500. (b) Expenses of realisation ₹ 600 but paid by Mohan, a partner. (c) Mohan, one of the partners of the firm, was asked to look into the dissolution of the firm for which he was allowed a commission of ₹ 2,000. (d) Motor car of book value ₹ 50,000 taken over by creditors of the book value of ₹ 40,000 in full settlement.

Discussion

5464.	Factorise -(x+1)(x+3)(x+5)(x+7)+15
Answer» Factorise - (x+1)(x+3)(x+5)(x+7)+15

Discussion

5465.	Sketch the graph of the following curve [\|y\|]=4-[\|x\|]
Answer» Sketch the graph of the following curve [\|y\|]=4-[\|x\|]

Discussion

5466.	Question 2 Calculate the mean of the scores of 20 students in a mathematics test Marks10−2020−3030−4040−5050−60Number of students24761
Answer» Question 2 Calculate the mean of the scores of 20 students in a mathematics test $\begin{matrix} Marks & 10 - 20 & 20 - 30 & 30 - 40 & 40 - 50 & 50 - 60 Number of students & 2 & 4 & 7 & 6 & 1 \end{matrix}$

Discussion

5467.	D is the mid-point of side BC of Δ ABC and E is the mid-point of BD. If O is the mid-point of AE, prove that ar (Δ BOE) = 18 ar (Δ ABC).
Answer» D is the mid-point of side BC of Δ ABC and E is the mid-point of BD. If O is the mid-point of AE, prove that ar (Δ BOE) = $\frac{1}{8}$ ar (Δ ABC).

Discussion

5468.	40×12+3-6÷60
Answer» 40×12+3-6÷60

Discussion

5469.	Given two events A and B. If odds against A are as 2:1 and those in favour of A∪B are as 3:1, then
Answer» Given two events $A$ and $B .$ If odds against $A$ are as $2 : 1$ and those in favour of $A \cup B$ are as $3 : 1,$ then

Discussion

5470.	If a < 0 and b > 0, then the point (a, b) lies in quadrant(a) IV(b) II(c) III(d) none of these
Answer» If a < 0 and b > 0, then the point (a, b) lies in quadrant (a) IV (b) II (c) III (d) none of these

Discussion

5471.	Sets A and B have 3 and 6 elements respectively. What can be the minimum number of elements in (A∪B)?
Answer» Sets A and B have 3 and 6 elements respectively. What can be the minimum number of elements in $(A \cup B)$ ?

5471.

Sets A and B have 3 and 6 elements respectively. What can be the minimum number of elements in (A∪B)?

Answer»

Sets A and B have 3 and 6 elements respectively. What can be the minimum number of elements in $(A \cup B)$ ?

Discussion

5472.	Two equal chords AB and CD intersect at a point P inside the circle. If AP = 12 cm, PC = 4 cm, then find the length of chord CD.
Answer» Two equal chords AB and CD intersect at a point P inside the circle. If AP = 12 cm, PC = 4 cm, then find the length of chord CD.

5472.

Two equal chords AB and CD intersect at a point P inside the circle. If AP = 12 cm, PC = 4 cm, then find the length of chord CD.

Answer»

Two equal chords AB and CD intersect at a point P inside the circle. If AP = 12 cm, PC = 4 cm, then find the length of chord CD.

Discussion

5473.	If x=2 and y=3, what is the value of xx+yy ?
Answer» If x=2 and y=3, what is the value of $x^{x}$ + $y^{y}$ ?

Discussion

5474.	X takes 3 hours more than Y to walk 30 km. But if X doubles his pace, he is ahead of Y by 1.5 hours. The speed of X is:
Answer» X takes 3 hours more than Y to walk 30 km. But if X doubles his pace, he is ahead of Y by 1.5 hours. The speed of X is:

Discussion

5475.	In the given figure, AB = AC, BC = CD and ∠A=40°, find ∠ACD
Answer» In the given figure, AB = AC, BC = CD and ∠A=40°, find ∠ACD

Discussion

5476.	Find the value of λ, if x=−λ and y=52 is a solution of the equation x+4y−7=0.
Answer» Find the value of $λ, i f x = - λ a n d y = \frac{5}{2} is a solution of the equation x + 4 y - 7 = 0.$

Discussion

5477.	A parrallelogram ABCD has an area 72 cm sq. With AC=9 and BD=16. Find AB and CD
Answer» A parrallelogram ABCD has an area 72 cm sq. With AC=9 and BD=16. Find AB and CD

Discussion

5478.	Choose the correct answer in each of the following: Which of the following is not a criterion for congruence of triangles? (a) SSA (b) SAS (c) ASA (d) SSS
Answer» Choose the correct answer in each of the following: Which of the following is not a criterion for congruence of triangles? (a) SSA (b) SAS (c) ASA (d) SSS

5478.

Choose the correct answer in each of the following: Which of the following is not a criterion for congruence of triangles? (a) SSA (b) SAS (c) ASA (d) SSS

Answer»

Choose the correct answer in each of the following:

Which of the following is not a criterion for congruence of triangles?

(a) SSA (b) SAS (c) ASA (d) SSS

Discussion

5479.	Find the value of: 1−tan230∘1+tan230∘
Answer» Find the value of: $\frac{1 - t a n^{2} 30^{\circ}}{1 + t a n^{2} 30^{\circ}}$

5479.

Find the value of: 1−tan230∘1+tan230∘

Answer»

Find the value of:

$\frac{1 - t a n^{2} 30^{\circ}}{1 + t a n^{2} 30^{\circ}}$

Discussion

5480.	Question 5 (iii)D, E and F are respectively the mid-points of the sides BC, CA and AB of triangle ABC Show that:(iii)area(BDEF)=12area(ABC)
Answer» Question 5 (iii) D, E and F are respectively the mid-points of the sides BC, CA and AB of triangle ABC Show that: $(i i i) a r e a (B D E F) = \frac{1}{2} a r e a (A B C)$

Discussion

5481.	Find the measure of each angle of a parallelogram, if one of its angles is 30∘ less than twice the smallest angle.
Answer» Find the measure of each angle of a parallelogram, if one of its angles is $30^{\circ}$ less than twice the smallest angle.

Discussion

5482.	If the system of linear equationsx+y+3z=0x+3y+k2z=03x+y+3z=0has a non-zero solution (x,y,z) for some k∈R, then x+(yz) is equal to:
Answer» If the system of linear equations $x + y + 3 z = 0$ $x + 3 y + k^{2} z = 0$ $3 x + y + 3 z = 0$ has a non-zero solution $(x, y, z)$ for some $k \in R,$ then $x + (\frac{y}{z})$ is equal to:

Discussion

5483.	In the given figure, line l is the bisector of an angle ∠A and B is any point on l. If BP and BQ are perpendiculars from B to the arms of ∠A, show that(i) ΔAPB ≅ ΔAQB(ii) BP = BQ, i.e., B is equidistant from the arms of ∠A.
Answer» In the given figure, line l is the bisector of an angle ∠A and B is any point on l. If BP and BQ are perpendiculars from B to the arms of ∠A, show that (i) ΔAPB ≅ ΔAQB (ii) BP = BQ, i.e., B is equidistant from the arms of ∠A.

Discussion

5484.	The antecedent of the conditional statement "If all sides of a triangle are congruent then its all angles are congruent" is :
Answer» The antecedent of the conditional statement "If all sides of a triangle are congruent then its all angles are congruent" is :

Discussion

5485.	The side of a rhombus is 10 cm and one of its diagonals is 16 cm. Find its area.
Answer» The side of a rhombus is 10 cm and one of its diagonals is 16 cm. Find its area.

Discussion

5486.	Question 23Factorise(i) x2+9x+18(ii) 6x2+7x−3(iii) 2x2−7x−15(iv) 84−2r−2r2
Answer» Question 23 Factorise (i) $x^{2} + 9 x + 18$ (ii) $6 x^{2} + 7 x - 3$ (iii) $2 x^{2} - 7 x - 15$ (iv) $84 - 2 r - 2 r^{2}$

Discussion

5487.	Factorise a2−81(b−c)2
Answer» Factorise $a^{2} - 81 (b - c)^{2}$

Discussion

5488.	If the larger circle of radius 6 cm has four smaller circles of radius 2 cm, then find the area of the shaded portion.
Answer» If the larger circle of radius 6 cm has four smaller circles of radius 2 cm, then find the area of the shaded portion.

Discussion

5489.	Vector 2^i+4^j,3^i+6^j and (λ−2)^i+5^j have same initial point (2,−2), then the value of 2λ for which all three vectors vanishes on a straight line is
Answer» Vector $2^i + 4^j, 3^i + 6^j$ and $(λ - 2)^i + 5^j$ have same initial point $(2, - 2),$ then the value of $2 λ$ for which all three vectors vanishes on a straight line is

Discussion

5490.	If P is a 3×3 matrix such that PT=2P+I, where PT is the transpose of P and I is the 3×3 identity matrix, then there exists a column matrix X=⎡⎢⎣xyz⎤⎥⎦≠⎡⎢⎣000⎤⎥⎦ such that
Answer» If $P$ is a $3 \times 3$ matrix such that $P^{T} = 2 P + I$ , where $P^{T}$ is the transpose of $P$ and $I$ is the $3 \times 3$ identity matrix, then there exists a column matrix $X = ⎡ ⎢ ⎣ \begin{matrix} x y z \end{matrix} ⎤ ⎥ ⎦ \neq ⎡ ⎢ ⎣ \begin{matrix} 000 \end{matrix} ⎤ ⎥ ⎦$ such that

Discussion

5491.	Arrange these division statements in a manner so that the highest number as the answer is on the top.
Answer» Arrange these division statements in a manner so that the highest number as the answer is on the top.

Discussion

5492.	Find the zeros of the quadratic polynomial x2−8x+12.
Answer» $Find the zeros of the quadratic polynomial x^{2} - 8 x + 12.$

Discussion

5493.	Examine whether the following statements are true or false:(i) {a,b}⊄{b,c,a}(ii) {a,e}⊂{x:x is a vowel in the English alphabet}(iii){1,2,3}⊂{1,3,5}(iv) {a}⊂{a,b,c}(v) {a}∈{a,b,c}(vi) {x:x is an even natural number less than 6}⊂{x:x is a natural number which divides 36}
Answer» Examine whether the following statements are true or false: $(i) {a, b} \subset̸ {b, c, a}$ $(i i) {a, e} \subset {x : x$ is a vowel in the English alphabet $}$ $(i i i) {1, 2, 3} \subset {1, 3, 5}$ $(i v) {a} \subset {a, b, c}$ $(v) {a} \in {a, b, c}$ $(v i) {x : x$ is an even natural number less than $6} \subset {x : x$ is a natural number which divides $36}$

Discussion

5494.	In the given figure, line 𝑙 \|\| line 𝑚 and 𝑀 is the mid-point of the line segment 𝐴𝐵. Then, which of the following options is correct?
Answer» In the given figure, line 𝑙 \|\| line 𝑚 and 𝑀 is the mid-point of the line segment 𝐴𝐵. Then, which of the following options is correct?

Discussion

5495.	Question 2 (iii)Simplify :(√5+√2)2 .
Answer» Question 2 (iii) Simplify : ${(\sqrt{5} + \sqrt{2})}^{2}$ .

Discussion

5496.	the breadth of a rec†an gular sheet is measured as 10.1 cm . the error in the measurment is (1) \pm1% (2) \pm0.5% (3) \pm0.1% (4) \pm5%
Answer» the breadth of a rec†an gular sheet is measured as 10.1 cm . the error in the measurment is (1) \pm1% (2) \pm0.5% (3) \pm0.1% (4) \pm5%

Discussion

5497.	Simplify the following expressions : (i) (√3+√7)2 (ii) (√5−√3)2 (iii) (2√5+3√2)2
Answer» Simplify the following expressions : (i) $(\sqrt{3} + \sqrt{7})^{2}$ (ii) $(\sqrt{5} - \sqrt{3})^{2}$ (iii) $(2 \sqrt{5} + 3 \sqrt{2})^{2}$

5497.

Simplify the following expressions : (i) (√3+√7)2 (ii) (√5−√3)2 (iii) (2√5+3√2)2

Answer»

Simplify the following expressions :

(i) $(\sqrt{3} + \sqrt{7})^{2}$

(ii) $(\sqrt{5} - \sqrt{3})^{2}$

(iii) $(2 \sqrt{5} + 3 \sqrt{2})^{2}$

Discussion

5498.	Three cards are drawn successively with replacement from a well shuffled pack of 52 cards. Find the mean and variance of number of red cards.
Answer» Three cards are drawn successively with replacement from a well shuffled pack of 52 cards. Find the mean and variance of number of red cards.

Discussion

5499.	In the given figure, P is the centre of the circle. chord AB and chord CD intersect on the diameter at the point EIf ∠AEP ≅ ∠DEP then prove that AB = CD.
Answer» In the given figure, P is the centre of the circle. chord AB and chord CD intersect on the diameter at the point E If $∠$ AEP $≅$ $∠$ DEP then prove that AB = CD.

Discussion

5500.	Construct the following angles at the initial point of a given ray and justify the construction.(i) 45° (ii) 90°
Answer» Construct the following angles at the initial point of a given ray and justify the construction. (i) 45° (ii) 90°

Discussion

Explore topic-wise InterviewSolutions in .

What is the formula for adjusted frequency?

3. A vector n is inclined to x axis at 45^°, to y axis at 60^°and at an acute angle to z axis. If n is a normal to a plane passing through the point(root2, -1,1)then the equation of the plane is

Volume occupied by one molecules of wateris

The following table shows the number of illiterate persons in the age group (10-58 years) in a town: Age group (in years)10−1617−2324−3031−3738−4445−5152−58Number of175325100150250400525illiterate persons Draw a histogram to represent the above data.

In a ∆ABC, D is the mid-point of AC such that BD = 12 AC. Show that ∠ABC is a right angle.

How to find the root of a number?

Question 1(iii)Evaluate: (12)−5

The cost of painting the inner curved surface area of a cylindrical container of depth 20 m is ₹ 8800. If the painter charges ₹ 40 per metre square to paint the cylindrical container, then find its radius. [ Take π=227 ]

Assertion : ABCD and PQRC are rectangles and Q is mid - point of AC. Then DP = PC. Reason : The line segment joining the mid - points of any two sides of a triangle is parallel to the third side and equal to half of it. Which of the following is correct?

How the HCF of two numbers is expressed in the form xa+xy?

If x + a is a factor of x2 + px + q and x2 + mx + n then the value of a in terms of n, q, m and p is?

The variance of first 50 even natural numbers is

Factorise -(x+1)(x+3)(x+5)(x+7)+15

Sketch the graph of the following curve [|y|]=4-[|x|]

Question 2 Calculate the mean of the scores of 20 students in a mathematics test Marks10−2020−3030−4040−5050−60Number of students24761

D is the mid-point of side BC of Δ ABC and E is the mid-point of BD. If O is the mid-point of AE, prove that ar (Δ BOE) = 18 ar (Δ ABC).

40×12+3-6÷60

Given two events A and B. If odds against A are as 2:1 and those in favour of A∪B are as 3:1, then

If a < 0 and b > 0, then the point (a, b) lies in quadrant(a) IV(b) II(c) III(d) none of these

Sets A and B have 3 and 6 elements respectively. What can be the minimum number of elements in (A∪B)?

Two equal chords AB and CD intersect at a point P inside the circle. If AP = 12 cm, PC = 4 cm, then find the length of chord CD.

If x=2 and y=3, what is the value of xx+yy ?

X takes 3 hours more than Y to walk 30 km. But if X doubles his pace, he is ahead of Y by 1.5 hours. The speed of X is:

In the given figure, AB = AC, BC = CD and ∠A=40°, find ∠ACD

Find the value of λ, if x=−λ and y=52 is a solution of the equation x+4y−7=0.

A parrallelogram ABCD has an area 72 cm sq. With AC=9 and BD=16. Find AB and CD

Choose the correct answer in each of the following: Which of the following is not a criterion for congruence of triangles? (a) SSA (b) SAS (c) ASA (d) SSS

Find the value of: 1−tan230∘1+tan230∘

Question 5 (iii)D, E and F are respectively the mid-points of the sides BC, CA and AB of triangle ABC Show that:(iii)area(BDEF)=12area(ABC)

Find the measure of each angle of a parallelogram, if one of its angles is 30∘ less than twice the smallest angle.

If the system of linear equationsx+y+3z=0x+3y+k2z=03x+y+3z=0has a non-zero solution (x,y,z) for some k∈R, then x+(yz) is equal to:

In the given figure, line l is the bisector of an angle ∠A and B is any point on l. If BP and BQ are perpendiculars from B to the arms of ∠A, show that(i) ΔAPB ≅ ΔAQB(ii) BP = BQ, i.e., B is equidistant from the arms of ∠A.

The antecedent of the conditional statement "If all sides of a triangle are congruent then its all angles are congruent" is :

The side of a rhombus is 10 cm and one of its diagonals is 16 cm. Find its area.

Question 23Factorise(i) x2+9x+18(ii) 6x2+7x−3(iii) 2x2−7x−15(iv) 84−2r−2r2

Factorise a2−81(b−c)2

If the larger circle of radius 6 cm has four smaller circles of radius 2 cm, then find the area of the shaded portion.

Vector 2^i+4^j,3^i+6^j and (λ−2)^i+5^j have same initial point (2,−2), then the value of 2λ for which all three vectors vanishes on a straight line is

If P is a 3×3 matrix such that PT=2P+I, where PT is the transpose of P and I is the 3×3 identity matrix, then there exists a column matrix X=⎡⎢⎣xyz⎤⎥⎦≠⎡⎢⎣000⎤⎥⎦ such that

Arrange these division statements in a manner so that the highest number as the answer is on the top.

Find the zeros of the quadratic polynomial x2−8x+12.

Examine whether the following statements are true or false:(i) {a,b}⊄{b,c,a}(ii) {a,e}⊂{x:x is a vowel in the English alphabet}(iii){1,2,3}⊂{1,3,5}(iv) {a}⊂{a,b,c}(v) {a}∈{a,b,c}(vi) {x:x is an even natural number less than 6}⊂{x:x is a natural number which divides 36}

In the given figure, line 𝑙 || line 𝑚 and 𝑀 is the mid-point of the line segment 𝐴𝐵. Then, which of the following options is correct?

Question 2 (iii)Simplify :(√5+√2)2 .

the breadth of a rec†an gular sheet is measured as 10.1 cm . the error in the measurment is (1) \pm1% (2) \pm0.5% (3) \pm0.1% (4) \pm5%

Simplify the following expressions : (i) (√3+√7)2 (ii) (√5−√3)2 (iii) (2√5+3√2)2

Three cards are drawn successively with replacement from a well shuffled pack of 52 cards. Find the mean and variance of number of red cards.

In the given figure, P is the centre of the circle. chord AB and chord CD intersect on the diameter at the point EIf ∠AEP ≅ ∠DEP then prove that AB = CD.

Construct the following angles at the initial point of a given ray and justify the construction.(i) 45° (ii) 90°