32581 + Interview Questions in Mathematics

1.	Standard deviation about mean ¯x for a given discrete frequency distribution x1, x2, x3, ....xn with frequencies f1, f2, f3, .... fn is.
Answer» Standard deviation about mean $¯ x$ for a given discrete frequency distribution x₁, x₂, x₃, ....x_n with frequencies f₁, f₂, f₃, .... f_n is.

Discussion

2.	AB = 4 cm. FInd the length of OA and the length of the tangent PA. .
Answer» AB = 4 cm. FInd the length of OA and the length of the tangent PA. .

2.

AB = 4 cm. FInd the length of OA and the length of the tangent PA. .

Answer»

AB = 4 cm. FInd the length of OA and the length of the tangent PA.

.

Discussion

3.	Given ΔABC∼ΔPQR And ABPQ=13 Find the ratio of their area.
Answer» Given $Δ A B C \sim Δ P Q R$ And $\frac{A B}{P Q} = \frac{1}{3}$ Find the ratio of their area.

Discussion

4.	Which of the following is true about [x], greatest integer function ?
Answer» Which of the following is true about [x], greatest integer function ?

Discussion

5.	The sum of infinite terms of the following series 1+45+752+1053+....... will be [MP PET 1981; RPET 1997; Roorkee 1992; DCE 1996, 2000]
Answer» The sum of infinite terms of the following series $1 + \frac{4}{5} + \frac{7}{5^{2}} + \frac{10}{5^{3}} + . . . . . . .$ will be [MP PET 1981; RPET 1997; Roorkee 1992; DCE 1996, 2000]

Discussion

6.	Write the value of (cot2θ−1sin2θ)
Answer» Write the value of $(c o t^{2} θ - \frac{1}{s i n^{2} θ})$

Discussion

7.	If A (1, 3), B(-1, 2), C(2, 5) and D(x, 4) are the vertices of a \|\|gm ABCD then the value of x is (a) 3 (b) 4 (c) 0 (d) 32
Answer» If A (1, 3), B(-1, 2), C(2, 5) and D(x, 4) are the vertices of a \|\|gm ABCD then the value of x is (a) 3 (b) 4 (c) 0 (d) $\frac{3}{2}$

7.

If A (1, 3), B(-1, 2), C(2, 5) and D(x, 4) are the vertices of a ||gm ABCD then the value of x is (a) 3 (b) 4 (c) 0 (d) 32

Answer»

If A (1, 3), B(-1, 2), C(2, 5) and D(x, 4) are the vertices of a ||gm ABCD then the value of x is

(a) 3 (b) 4 (c) 0 (d) $\frac{3}{2}$

Discussion

8.	The sum of the squares of two consecutive positive even numbers is 452. Find the numbers.
Answer» The sum of the squares of two consecutive positive even numbers is 452. Find the numbers.

Discussion

9.	If A(4, 2), B(6, 5) and C(1, 4) be the vertices of △ABC and AD is a median, then the coordinates of D are (a) (52,3) (b) (5,72) (c) (72,92) (d) none of these
Answer» If A(4, 2), B(6, 5) and C(1, 4) be the vertices of $△ A B C$ and AD is a median, then the coordinates of D are (a) $(\frac{5}{2}, 3)$ (b) $(5, \frac{7}{2})$ (c) $(\frac{7}{2}, \frac{9}{2})$ (d) none of these

9.

If A(4, 2), B(6, 5) and C(1, 4) be the vertices of △ABC and AD is a median, then the coordinates of D are (a) (52,3) (b) (5,72) (c) (72,92) (d) none of these

Answer»

If A(4, 2), B(6, 5) and C(1, 4) be the vertices of $△ A B C$ and AD is a median, then the coordinates of D are

(a) $(\frac{5}{2}, 3)$ (b) $(5, \frac{7}{2})$ (c) $(\frac{7}{2}, \frac{9}{2})$ (d) none of these

Discussion

10.	Prove the following identities: (1+cot A+tan A)(sin A−cos A)=sec Acosec2A−cosec Asec2A=sin A tan A−cot A cos A
Answer» Prove the following identities: $(1 + c o t A + t a n A) (s i n A - c o s A) = \frac{s e c A}{c o s e c^{2} A} - \frac{c o s e c A}{s e c^{2} A} = s i n A t a n A - c o t A c o s A$

10.

Prove the following identities: (1+cot A+tan A)(sin A−cos A)=sec Acosec2A−cosec Asec2A=sin A tan A−cot A cos A

Answer»

Prove the following identities:

$(1 + c o t A + t a n A) (s i n A - c o s A) = \frac{s e c A}{c o s e c^{2} A} - \frac{c o s e c A}{s e c^{2} A} = s i n A t a n A - c o t A c o s A$

Discussion

11.	Find the radius of a circle whose circumference is equal to the sum of the circumferences of two circles of radii 15 cm and 18 cm.
Answer» Find the radius of a circle whose circumference is equal to the sum of the circumferences of two circles of radii 15 cm and 18 cm.

Discussion

12.	Question 21(ii) Two dice are thrown together. Find the probability that the product of the numbers on the top of the dice is 12?
Answer» Question 21(ii) Two dice are thrown together. Find the probability that the product of the numbers on the top of the dice is 12?

Discussion

13.	Find the LCM and HCF of 6 and 20 by the prime factorisation method.
Answer» Find the LCM and HCF of 6 and 20 by the prime factorisation method.

Discussion

14.	The angles of a quadrilateral are in A. P. with common difference 20∘. Find its angles.
Answer» The angles of a quadrilateral are in A. P. with common difference $20^{\circ}$ . Find its angles.

Discussion

15.	The mid-point of the line segment joining (4a, 2b - 3) and (-4, 3b) is (2, -2a). Find the values of a and b.
Answer» The mid-point of the line segment joining (4a, 2b - 3) and (-4, 3b) is (2, -2a). Find the values of a and b.

Discussion

16.	The triangle ABC, where A is (2, 6), B is (-3, 5) and C is (4, 7), is reflected in the y-axis to triangle A'B'C'. Triangle A'B'C' is then reflected in the origin to triangle A" B" C". (i) Write down the co-ordinates of A", B" and C". (ii) Write down a single transformation that maps triangle ABC onto triangle A" B" C".
Answer» The triangle ABC, where A is (2, 6), B is (-3, 5) and C is (4, 7), is reflected in the y-axis to triangle A'B'C'. Triangle A'B'C' is then reflected in the origin to triangle A" B" C". (i) Write down the co-ordinates of A", B" and C". (ii) Write down a single transformation that maps triangle ABC onto triangle A" B" C".

16.

The triangle ABC, where A is (2, 6), B is (-3, 5) and C is (4, 7), is reflected in the y-axis to triangle A'B'C'. Triangle A'B'C' is then reflected in the origin to triangle A" B" C". (i) Write down the co-ordinates of A", B" and C". (ii) Write down a single transformation that maps triangle ABC onto triangle A" B" C".

Answer»

The triangle ABC, where A is (2, 6), B is (-3, 5) and C is (4, 7), is reflected in the y-axis to triangle A'B'C'. Triangle A'B'C' is then reflected in the origin to triangle A" B" C".

(i) Write down the co-ordinates of A", B" and C".

(ii) Write down a single transformation that maps triangle ABC onto triangle A" B" C".

Discussion

17.	which of the following about remainder is true?
Answer» which of the following about remainder is true?

Discussion

18.	The domain of the function f(x)=loge(x2+x+1)+sin√x−1 is
Answer» $The domain of the function f (x) = l o g_{e} (x^{2} + x + 1) + s i n \sqrt{x - 1} i s$

Discussion

19.	Solve: (a) Find the point on y = 2x + 2 where the ordinate is thrice the abscissa (b) If the point P lies on the line x = 5 and has its ordinate equal to –3, then find its coordinates. [3 MARKS]
Answer» Solve: (a) Find the point on y = 2x + 2 where the ordinate is thrice the abscissa (b) If the point P lies on the line x = 5 and has its ordinate equal to –3, then find its coordinates. [3 MARKS]

Discussion

20.	Two numbers are in the ratio 1:2. If 7 is added to each number, the ratio becomes to 3:5. The bigger number is :
Answer» Two numbers are in the ratio 1:2. If 7 is added to each number, the ratio becomes to 3:5. The bigger number is :

Discussion

21.	If cosθ = (12/13), then the value of tanθ cosecθ + sinθ secθ + cosecθ is ........................
Answer» If cos $θ$ = (12/13), then the value of tan $θ$ cosec $θ$ + sin $θ$ sec $θ$ + cosec $θ$ is ........................

Discussion

22.	Prove that 3+2√5 is irrational. [4 MARKS]
Answer» Prove that $3 + 2 \sqrt{5}$ is irrational. [4 MARKS]

Discussion

23.	If the replacement set is a set of integers (I or Z), between -6 and 9, find the solution set of 6x−1≥9+x
Answer» If the replacement set is a set of integers (I or Z), between -6 and 9, find the solution set of $6 x - 1 \geq 9 + x$

Discussion

24.	If x+a is a factor of 2x²+2ax+6x+10 find a
Answer» If x+a is a factor of 2x²+2ax+6x+10 find a

Discussion

25.	What is the probability of getting a 'composite number' when a die is rolled?
Answer» What is the probability of getting a 'composite number' when a die is rolled?

Discussion

26.	A card is chosen from a well-shuffled deck of 52 cards. Calculate the probability that a card randomly picked will not be an ace.
Answer» A card is chosen from a well-shuffled deck of 52 cards. Calculate the probability that a card randomly picked will not be an ace.

Discussion

27.	A two-digit number is 3 more than 4 times the sum of its digits.If 18is added to the number,its digits are reversed.Find the number. (Answer:35)
Answer» A two-digit number is 3 more than 4 times the sum of its digits.If 18is added to the number,its digits are reversed.Find the number. (Answer:35)

27.

A two-digit number is 3 more than 4 times the sum of its digits.If 18is added to the number,its digits are reversed.Find the number. (Answer:35)

Answer»

A two-digit number is 3 more than 4 times the sum of its digits.If 18is added to the number,its digits are reversed.Find the number.

(Answer:35)

Discussion

28.	The prime factorization of 184 is
Answer» The prime factorization of 184 is

Discussion

29.	The radius of the base of a right circular cone is 21 cm and its height is 20 cm. Find its volume.
Answer» The radius of the base of a right circular cone is 21 cm and its height is 20 cm. Find its volume.

Discussion

30.	√(a−b)2+√(b−a)2 is:
Answer» $\sqrt{(a - b)^{2}} + \sqrt{(b - a)^{2}}$ is:

Discussion

31.	A circle C is inscribed in the quadrilateral ABCD. The quadrilateral ABCD can possibly be a
Answer» A circle C is inscribed in the quadrilateral ABCD. The quadrilateral ABCD can possibly be a

Discussion

32.	Fill in the blank. Price100755025Number6080240
Answer» Fill in the blank. $\begin{matrix} P r i c e & 100 & 75 & 50 & 25 N u m b e r & 60 & 80 & 240 \end{matrix}$

32.

Fill in the blank. Price100755025Number6080240

Answer»

Fill in the blank.

$\begin{matrix} P r i c e & 100 & 75 & 50 & 25 N u m b e r & 60 & 80 & 240 \end{matrix}$

Discussion

33.	In the given figure PQ and RS are the perpendicular diameters of the circle whose centre is O and radius = 14 cm. the area of the shaded region is
Answer» In the given figure PQ and RS are the perpendicular diameters of the circle whose centre is O and radius = 14 cm. the area of the shaded region is

33.

In the given figure PQ and RS are the perpendicular diameters of the circle whose centre is O and radius = 14 cm. the area of the shaded region is

Answer»

In the given figure PQ and RS are the perpendicular diameters of the circle whose centre is O and radius = 14 cm. the area of the shaded region is

Discussion

34.	Split the middle term for x2-x-2
Answer» Split the middle term for x²-x-2

Discussion

35.	The order of matrix A=⎡⎢⎢⎢⎢⎢⎢⎢⎢⎣2−243109−3−1000500−200−7−1−100−51−1−2000⎤⎥⎥⎥⎥⎥⎥⎥⎥⎦ is ___
Answer» The order of matrix $A = ⎡ ⎢⎢⎢⎢⎢⎢⎢⎢ ⎣ \begin{matrix} 2 & - 2 & 4 & 3 & 1 0 & 9 & - 3 & - 1 & 0 0 & 0 & 5 & 0 & 0 - 2 & 0 & 0 & - 7 & - 1 - 1 & 0 & 0 & - 5 & 1 - 1 & - 2 & 0 & 0 & 0 \end{matrix} ⎤ ⎥⎥⎥⎥⎥⎥⎥⎥ ⎦$ is ___

Discussion

36.	The quadratic polynomial having product of zeroes −1 and sum of zeroes 12 is ____
Answer» The quadratic polynomial having product of zeroes $- 1$ and sum of zeroes $\frac{1}{2}$ is ____

Discussion

37.	In theoretical probability approach, the outcomes are
Answer» In theoretical probability approach, the outcomes are

Discussion

38.	The HCF of numbers is 11 and their LCM is 12100. If one of the numbers is a perfect of smallest two digit prime number, then find the other number.
Answer» The HCF of numbers is 11 and their LCM is 12100. If one of the numbers is a perfect of smallest two digit prime number, then find the other number.

Discussion

39.	Find the mid value of the class having highest frequency in the table given below. HeightNumber of students150−1544155−1593160−1642165−1691170−1742
Answer» Find the mid value of the class having highest frequency in the table given below. $\begin{matrix} Height & Number of students 150 - 154 & 4 155 - 159 & 3 160 - 164 & 2 165 - 169 & 1 170 - 174 & 2 \end{matrix}$

39.

Find the mid value of the class having highest frequency in the table given below. HeightNumber of students150−1544155−1593160−1642165−1691170−1742

Answer»

Find the mid value of the class having highest frequency in the table given below.

$\begin{matrix} Height & Number of students 150 - 154 & 4 155 - 159 & 3 160 - 164 & 2 165 - 169 & 1 170 - 174 & 2 \end{matrix}$

Discussion

40.	Mohan has a recurring deposit account in a bank for 2 years at 6% p.a. simple interest. If he gets Rs 1,200 as interest at the time of maturity, find : (i) the monthly instalment (ii) the amount of maturity.
Answer» Mohan has a recurring deposit account in a bank for 2 years at 6% p.a. simple interest. If he gets Rs 1,200 as interest at the time of maturity, find : (i) the monthly instalment (ii) the amount of maturity.

40.

Mohan has a recurring deposit account in a bank for 2 years at 6% p.a. simple interest. If he gets Rs 1,200 as interest at the time of maturity, find : (i) the monthly instalment (ii) the amount of maturity.

Answer»

Mohan has a recurring deposit account in a bank for 2 years at 6% p.a. simple interest. If he gets Rs 1,200 as interest at the time of maturity, find :

(i) the monthly instalment

(ii) the amount of maturity.

Discussion

41.	Solve 6x+3y=6xy, 2x+4y=5xy.
Answer» Solve 6x+3y=6xy, 2x+4y=5xy.

Discussion

42.	Mrs. Jhaluka deposits ₹1000 every month in a recurring deposit account for a time period of 3 years at 8% interest per annum. What is the Maturity Amount?
Answer» Mrs. Jhaluka deposits ₹1000 every month in a recurring deposit account for a time period of 3 years at 8% interest per annum. What is the Maturity Amount?

Discussion

43.	If one zero of the quadratic polynomial x2 +:3x + k is 2, then find the value of k
Answer» If one zero of the quadratic polynomial x²+:3x + k is 2, then find the value of k

Discussion

44.	X is a number selected from a group of numbers -3,-2,-1,0,1,2,3.find probability that \|x\|=<2.in this qustions answer how are there only 3 favourable outcomes.wont-2and -3 be considered as a favourable outcome
Answer» X is a number selected from a group of numbers -3,-2,-1,0,1,2,3.find probability that \|x\|=<2.in this qustions answer how are there only 3 favourable outcomes.wont-2and -3 be considered as a favourable outcome

Discussion

45.	In the following figure, a circle is inscribed in the quadrilateral ABCD. If BC = 38 cm, QB = 27 cm, DC = 25 cm and that AD is perpendicular to DC, find the radius of the circle.
Answer» In the following figure, a circle is inscribed in the quadrilateral ABCD. If BC = 38 cm, QB = 27 cm, DC = 25 cm and that AD is perpendicular to DC, find the radius of the circle.

45.

In the following figure, a circle is inscribed in the quadrilateral ABCD. If BC = 38 cm, QB = 27 cm, DC = 25 cm and that AD is perpendicular to DC, find the radius of the circle.

Answer»

In the following figure, a circle is inscribed in the quadrilateral ABCD.

If BC = 38 cm, QB = 27 cm, DC = 25 cm and that AD is perpendicular to DC, find the radius of the circle.

Discussion

46.	The sum of the digit of two digit number is 12.if the new number formed by reversing the digits is greater than the original number by 54.find the original number.
Answer» The sum of the digit of two digit number is 12.if the new number formed by reversing the digits is greater than the original number by 54.find the original number.

Discussion

47.	Select the correct order for solving a pair of linear equations in two variables by elimination method. i) Add or subtract one equation from the other so that one variable gets eliminated. ii) Multiply both the equations by any non-zero constant to make the coefficients of any one of the variables numerically equal. iii) Substitute the obtained value in either of the original equations to get the value of the other variable. iv) Solve the equation in one variable thus obtained to get its value.
Answer» Select the correct order for solving a pair of linear equations in two variables by elimination method. i) Add or subtract one equation from the other so that one variable gets eliminated. ii) Multiply both the equations by any non-zero constant to make the coefficients of any one of the variables numerically equal. iii) Substitute the obtained value in either of the original equations to get the value of the other variable. iv) Solve the equation in one variable thus obtained to get its value.

47.

Select the correct order for solving a pair of linear equations in two variables by elimination method. i) Add or subtract one equation from the other so that one variable gets eliminated. ii) Multiply both the equations by any non-zero constant to make the coefficients of any one of the variables numerically equal. iii) Substitute the obtained value in either of the original equations to get the value of the other variable. iv) Solve the equation in one variable thus obtained to get its value.

Answer»

Select the correct order for solving a pair of linear equations in two variables by elimination method.

i) Add or subtract one equation from the other so that one variable gets eliminated.

ii) Multiply both the equations by any non-zero constant to make the coefficients of any one of the variables numerically equal.

iii) Substitute the obtained value in either of the original equations to get the value of the other variable.

iv) Solve the equation in one variable thus obtained to get its value.

Discussion

48.	Using euclids division algorithm find whether 847 and 2160 are co prime or not.
Answer» Using euclids division algorithm find whether 847 and 2160 are co prime or not.

Discussion

49.	A dice is thrown four times and its four different positions are shown below. Find the number on the face opposite the face showing 2.
Answer» A dice is thrown four times and its four different positions are shown below. Find the number on the face opposite the face showing 2.

49.

A dice is thrown four times and its four different positions are shown below. Find the number on the face opposite the face showing 2.

Answer»

A dice is thrown four times and its four different positions are shown below. Find the number on the face opposite the face showing 2.

Discussion

50.	The distance between points (a + b, b + c) and (a – b, c – b) is ____ units.
Answer» The distance between points (a + b, b + c) and (a – b, c – b) is ____ units.

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Standard deviation about mean ¯x for a given discrete frequency distribution x1, x2, x3, ....xn with frequencies f1, f2, f3, .... fn is.

AB = 4 cm. FInd the length of OA and the length of the tangent PA. .

Given ΔABC∼ΔPQR And ABPQ=13 Find the ratio of their area.

Which of the following is true about [x], greatest integer function ?

The sum of infinite terms of the following series 1+45+752+1053+....... will be [MP PET 1981; RPET 1997; Roorkee 1992; DCE 1996, 2000]

Write the value of (cot2θ−1sin2θ)

If A (1, 3), B(-1, 2), C(2, 5) and D(x, 4) are the vertices of a ||gm ABCD then the value of x is (a) 3 (b) 4 (c) 0 (d) 32

The sum of the squares of two consecutive positive even numbers is 452. Find the numbers.

If A(4, 2), B(6, 5) and C(1, 4) be the vertices of △ABC and AD is a median, then the coordinates of D are (a) (52,3) (b) (5,72) (c) (72,92) (d) none of these

Prove the following identities: (1+cot A+tan A)(sin A−cos A)=sec Acosec2A−cosec Asec2A=sin A tan A−cot A cos A

Find the radius of a circle whose circumference is equal to the sum of the circumferences of two circles of radii 15 cm and 18 cm.

Question 21(ii) Two dice are thrown together. Find the probability that the product of the numbers on the top of the dice is 12?

Find the LCM and HCF of 6 and 20 by the prime factorisation method.

The angles of a quadrilateral are in A. P. with common difference 20∘. Find its angles.

The mid-point of the line segment joining (4a, 2b - 3) and (-4, 3b) is (2, -2a). Find the values of a and b.

which of the following about remainder is true?

The domain of the function f(x)=loge(x2+x+1)+sin√x−1 is

Solve: (a) Find the point on y = 2x + 2 where the ordinate is thrice the abscissa (b) If the point P lies on the line x = 5 and has its ordinate equal to –3, then find its coordinates. [3 MARKS]

Two numbers are in the ratio 1:2. If 7 is added to each number, the ratio becomes to 3:5. The bigger number is :

If cosθ = (12/13), then the value of tanθ cosecθ + sinθ secθ + cosecθ is ........................

Prove that 3+2√5 is irrational. [4 MARKS]

If the replacement set is a set of integers (I or Z), between -6 and 9, find the solution set of 6x−1≥9+x

If x+a is a factor of 2x²+2ax+6x+10 find a

What is the probability of getting a 'composite number' when a die is rolled?

A card is chosen from a well-shuffled deck of 52 cards. Calculate the probability that a card randomly picked will not be an ace.

A two-digit number is 3 more than 4 times the sum of its digits.If 18is added to the number,its digits are reversed.Find the number. (Answer:35)

The prime factorization of 184 is

The radius of the base of a right circular cone is 21 cm and its height is 20 cm. Find its volume.

√(a−b)2+√(b−a)2 is:

A circle C is inscribed in the quadrilateral ABCD. The quadrilateral ABCD can possibly be a

Fill in the blank. Price100755025Number6080240

In the given figure PQ and RS are the perpendicular diameters of the circle whose centre is O and radius = 14 cm. the area of the shaded region is

Split the middle term for x2-x-2

The order of matrix A=⎡⎢⎢⎢⎢⎢⎢⎢⎢⎣2−243109−3−1000500−200−7−1−100−51−1−2000⎤⎥⎥⎥⎥⎥⎥⎥⎥⎦ is ___

The quadratic polynomial having product of zeroes −1 and sum of zeroes 12 is ____

In theoretical probability approach, the outcomes are

The HCF of numbers is 11 and their LCM is 12100. If one of the numbers is a perfect of smallest two digit prime number, then find the other number.

Find the mid value of the class having highest frequency in the table given below. HeightNumber of students150−1544155−1593160−1642165−1691170−1742

Mohan has a recurring deposit account in a bank for 2 years at 6% p.a. simple interest. If he gets Rs 1,200 as interest at the time of maturity, find : (i) the monthly instalment (ii) the amount of maturity.

Solve 6x+3y=6xy, 2x+4y=5xy.

Mrs. Jhaluka deposits ₹1000 every month in a recurring deposit account for a time period of 3 years at 8% interest per annum. What is the Maturity Amount?

If one zero of the quadratic polynomial x​​​​​​2 +:3x + k is 2, then find the value of k

X is a number selected from a group of numbers -3,-2,-1,0,1,2,3.find probability that |x|=&lt;2.in this qustions answer how are there only 3 favourable outcomes.wont-2and -3 be considered as a favourable outcome

In the following figure, a circle is inscribed in the quadrilateral ABCD. If BC = 38 cm, QB = 27 cm, DC = 25 cm and that AD is perpendicular to DC, find the radius of the circle.

The sum of the digit of two digit number is 12.if the new number formed by reversing the digits is greater than the original number by 54.find the original number.

Using euclids division algorithm find whether 847 and 2160 are co prime or not.

A dice is thrown four times and its four different positions are shown below. Find the number on the face opposite the face showing 2.

The distance between points (a + b, b + c) and (a – b, c – b) is ____ units.

If one zero of the quadratic polynomial x2 +:3x + k is 2, then find the value of k

X is a number selected from a group of numbers -3,-2,-1,0,1,2,3.find probability that |x|=<2.in this qustions answer how are there only 3 favourable outcomes.wont-2and -3 be considered as a favourable outcome