32581 + Interview Questions in Mathematics

1.	A hemispherical bowl fits exactly on the open surface of a cone with height 5 cm and radius 3.5 cm.What is the volume of the solid formed?
Answer» A hemispherical bowl fits exactly on the open surface of a cone with height 5 cm and radius 3.5 cm.What is the volume of the solid formed?

Discussion

2.	Name the type of triangle formed by the points A(-5,6), B(-4,-2) and C(7,5).
Answer» Name the type of triangle formed by the points A(-5,6), B(-4,-2) and C(7,5).

Discussion

3.	Express the ratios of sin A and cos A respectively in terms of tan A.
Answer» Express the ratios of $s i n A$ and $c o s A$ respectively in terms of $t a n A$ .

Discussion

4.	Question 2 (iv) Write whether the following statements are true or false. Justify your answers. Every quadratic equation has at most two roots.
Answer» Question 2 (iv) Write whether the following statements are true or false. Justify your answers. Every quadratic equation has at most two roots.

Discussion

5.	Plot the points P(3, 2) & Q(-3, -2). From P & Q, draw ⏊s PM & QN on the – ais. Assign a special name to the geometrical figure PMQN and find its area.
Answer» Plot the points P(3, 2) & Q(-3, -2). From P & Q, draw ⏊s PM & QN on the – ais. Assign a special name to the geometrical figure PMQN and find its area.

5.

Plot the points P(3, 2) & Q(-3, -2). From P & Q, draw ⏊s PM & QN on the – ais. Assign a special name to the geometrical figure PMQN and find its area.

Answer»

Plot the points P(3, 2) & Q(-3, -2). From P & Q, draw ⏊s PM & QN on the – ais.

Assign a special name to the geometrical figure PMQN and find its area.

Discussion

6.	If a is the G.M. of 2 and 14, find a.
Answer» If a is the G.M. of 2 and $\frac{1}{4},$ find a.

Discussion

7.	Molar conductances of BaCl2,H2SO4 and HCl at infinite dilutions are x1,x2 and x3 respectively. Equivalent conductance of BaSO4 at infinite dilution will be :
Answer» Molar conductances of $B a C l_{2}, H_{2} S O_{4}$ and HCl at infinite dilutions are $x_{1}, x_{2}$ and $x_{3}$ respectively. Equivalent conductance of $B a S O_{4}$ at infinite dilution will be :

Discussion

8.	Question 7 If the 2nd term of an AP is 13 and 5th term is 25, what is its 7th term? A) 30 B) 33 C) 37 D) 38
Answer» Question 7 If the $2^{n d}$ term of an AP is 13 and $5^{t h}$ term is 25, what is its $7^{t h}$ term? A) 30 B) 33 C) 37 D) 38

Discussion

9.	Father's age is 3 times the sum of Ages of his two children . after 5 years his age will be twice the sum of Ages of two children find the age of father
Answer» Father's age is 3 times the sum of Ages of his two children . after 5 years his age will be twice the sum of Ages of two children find the age of father

Discussion

10.	If 45 students can consume a stock of food in 2 months, then for how many days the same stock of food will last for 27 students?
Answer» If 45 students can consume a stock of food in 2 months, then for how many days the same stock of food will last for 27 students?

Discussion

11.	The letters of the word "ASSASSAIN"are written down at random in a row.The probability that no 2 S occur together is what? 1.1/35. 2.1/14. 3.1/15 4.None of these. (Multiple options may be correct.) Pls explain how you did it,step by step.
Answer» The letters of the word "ASSASSAIN"are written down at random in a row.The probability that no 2 S occur together is what? 1.1/35. 2.1/14. 3.1/15 4.None of these. (Multiple options may be correct.) Pls explain how you did it,step by step.

Discussion

12.	4(sin⁴30+cos⁴60)-2/3(sin²60-cos²45)+1/2tan²60
Answer» 4(sin⁴30+cos⁴60)-2/3(sin²60-cos²45)+1/2tan²60

Discussion

13.	A circular tank of diameter 2 m is dug and the earth removed is spread uniformly all around the tank to form an embarkment 2 m in width and 1.6m in height find the depth of the circular tank.
Answer» A circular tank of diameter 2 m is dug and the earth removed is spread uniformly all around the tank to form an embarkment 2 m in width and 1.6m in height find the depth of the circular tank.

Discussion

14.	if one zero of the quadratic polynomial f(x)=4x^2-8kx-9 is negative of the other,Find the value of k.
Answer» if one zero of the quadratic polynomial f(x)=4x^2-8kx-9 is negative of the other,Find the value of k.

Discussion

15.	How many numbers divisible by 5 and lying between 4000 and 5000 can be formed from the digits 4,5,6,7 and 8?
Answer» How many numbers divisible by 5 and lying between 4000 and 5000 can be formed from the digits 4,5,6,7 and 8?

Discussion

16.	Which of the following should be the LAST sentence after rearrangement?
Answer» Which of the following should be the LAST sentence after rearrangement?

Discussion

17.	78=54;53=16;2*7=?
Answer» 78=54;53=16;2*7=?

Discussion

18.	Find out from amongst the four alternatives as to how the pattern would appear when the transparent sheet is folded at the dotted line
Answer» Find out from amongst the four alternatives as to how the pattern would appear when the transparent sheet is folded at the dotted line

18.

Find out from amongst the four alternatives as to how the pattern would appear when the transparent sheet is folded at the dotted line

Answer»

Find out from amongst the four alternatives as to how the pattern would appear when the transparent sheet is folded at the dotted line

Discussion

19.	A positive integer 'a'when divided by the smallest odd prime leaves a reminder ''r'which of the following cannot be 'r' ? A} 0 B}1. C}2. D}3
Answer» A positive integer 'a'when divided by the smallest odd prime leaves a reminder ''r'which of the following cannot be 'r' ? A} 0 B}1. C}2. D}3

19.

A positive integer 'a'when divided by the smallest odd prime leaves a reminder ''r'which of the following cannot be 'r' ? A} 0 B}1. C}2. D}3

Answer»

A positive integer 'a'when divided by the smallest odd prime leaves a reminder ''r'which of the following cannot be 'r' ?

A} 0 B}1. C}2. D}3

Discussion

20.	Two dice are rolled once. Find the probability of getting such numbers on two dice, whose product is a perfect square. OR A game consists of tossing a coin 3 times and noting its outcomes each time. Hanif wins if he gets three heads or three tails, and loses otherwise. Calculate the probability that Hanif will lose the game.
Answer» Two dice are rolled once. Find the probability of getting such numbers on two dice, whose product is a perfect square. OR A game consists of tossing a coin 3 times and noting its outcomes each time. Hanif wins if he gets three heads or three tails, and loses otherwise. Calculate the probability that Hanif will lose the game.

20.

Two dice are rolled once. Find the probability of getting such numbers on two dice, whose product is a perfect square. OR A game consists of tossing a coin 3 times and noting its outcomes each time. Hanif wins if he gets three heads or three tails, and loses otherwise. Calculate the probability that Hanif will lose the game.

Answer»

Two dice are rolled once. Find the probability of getting such numbers on two dice, whose product is a perfect square.

OR

A game consists of tossing a coin 3 times and noting its outcomes each time. Hanif wins if he gets three heads or three tails, and loses otherwise. Calculate the probability that Hanif will lose the game.

Discussion

21.	In an A.P. the sum of first n terms is 3n22+13n2. Find the 25th term. [3 MARKS]
Answer» In an A.P. the sum of first n terms is $\frac{3 n^{2}}{2} + \frac{13 n}{2}$ . Find the 25th term. [3 MARKS]

Discussion

22.	If secθ−tanθ=13, the value of secθ+tanθ is:
Answer» If $sec θ - tan θ = \frac{1}{3}$ , the value of $sec θ + tan θ$ is:

Discussion

23.	Why do we draw Q′Pm∥QPm+n, while constructing the section of the line PQ in the ratio m:n?
Answer» Why do we draw $Q^{'} P_{m} ∥ Q P_{m + n}$ , while constructing the section of the line PQ in the ratio $m : n$ ?

23.

Why do we draw Q′Pm∥QPm+n, while constructing the section of the line PQ in the ratio m:n?

Answer»

Why do we draw $Q^{'} P_{m} ∥ Q P_{m + n}$ , while constructing the section of the line PQ in the ratio $m : n$ ?

Discussion

24.	The square of (2x -1) is equal to 5. The values of x are
Answer» The square of (2 $x$ -1) is equal to 5. The values of $x$ are

Discussion

25.	A Flipkart delivery boy has to deliver the product to his customer. The delivery boy followed the below path to reach the customer from the Flipkart office. The delivery boy starts walking towards north. After walking 10 units he turns towards east. After walking 6 units he turns towards the north. After walking 4 units he turns west. Finally, after walking for 3 units he reached the customer house. If Flipkart office is at a point (3, -5) and customer house is at a point (x, y). The value of x + y is ___.
Answer» A Flipkart delivery boy has to deliver the product to his customer. The delivery boy followed the below path to reach the customer from the Flipkart office. The delivery boy starts walking towards north. After walking 10 units he turns towards east. After walking 6 units he turns towards the north. After walking 4 units he turns west. Finally, after walking for 3 units he reached the customer house. If Flipkart office is at a point (3, -5) and customer house is at a point (x, y). The value of x + y is ___.

Discussion

26.	Cards bearing numbers 3 to 20 are placed in a bag and mixed thoroughly. A card is taken out randomly from the bag. What is the probability that the number on the card is an even number?
Answer» Cards bearing numbers 3 to 20 are placed in a bag and mixed thoroughly. A card is taken out randomly from the bag. What is the probability that the number on the card is an even number?

Discussion

27.	If sec A=2√3, find the value of tan Acos A+1+sin Atan A
Answer» If $s e c A = \frac{2}{\sqrt{3}},$ find the value of $\frac{t a n A}{c o s A} + \frac{1 + s i n A}{t a n A}$

Discussion

28.	The simplest form of (x3–1)(x2–1) is
Answer» The simplest form of $\frac{(x^{3} - 1)}{(x^{2} - 1)}$ is

Discussion

29.	The sum of the 4th and 12th term of an arithmetic progression is 20. What is the sum of the first 15 terms of the arithmetic progression?
Answer» The sum of the $4^{t h}$ and $12^{t h}$ term of an arithmetic progression is $20$ . What is the sum of the first $15$ terms of the arithmetic progression?

29.

The sum of the 4th and 12th term of an arithmetic progression is 20. What is the sum of the first 15 terms of the arithmetic progression?

Answer»

The sum of the $4^{t h}$ and $12^{t h}$ term of an arithmetic progression is $20$ . What is the sum of the first $15$ terms of the arithmetic progression?

Discussion

30.	Calculate the mean of the following data, using direct method: Class25−3535−4545−5555−6565−75Frequency6108124
Answer» Calculate the mean of the following data, using direct method: $\begin{matrix} Class & 25 - 35 & 35 - 45 & 45 - 55 & 55 - 65 & 65 - 75 Frequency & 6 & 10 & 8 & 12 & 4 \end{matrix}$

Discussion

31.	Find the area of quadrilateral ABCD whose vertices are A(3, -1), B(9, -5), C(14, 0) and D(9, 19).
Answer» Find the area of quadrilateral ABCD whose vertices are A(3, -1), B(9, -5), C(14, 0) and D(9, 19).

Discussion

32.	In a rectangle, if the length is increased by 3 metres and breadth is decreased by 4 metres, the area of the rectangle is reduced by 67 square metres. If length is reduced by 1 metre and breadth is increased by 4 metres, the area is increased by 89 sq. metres. Find the dimensions of the rectangle.
Answer» In a rectangle, if the length is increased by 3 metres and breadth is decreased by 4 metres, the area of the rectangle is reduced by 67 square metres. If length is reduced by 1 metre and breadth is increased by 4 metres, the area is increased by 89 sq. metres. Find the dimensions of the rectangle.

Discussion

33.	In fig. 10.37, find tan P and cot R. Is tan P=cot R ?
Answer» In fig. 10.37, find tan P and cot R. Is tan P=cot R ?

33.

In fig. 10.37, find tan P and cot R. Is tan P=cot R ?

Answer»

In fig. 10.37, find tan P and cot R. Is tan P=cot R ?

Discussion

34.	Evaluate each of the following sin 60∘ cos30∘ + cos 60∘ sin 30∘
Answer» Evaluate each of the following sin $60^{\circ}$ cos $30^{\circ}$ + cos $60^{\circ}$ sin $30^{\circ}$

34.

Evaluate each of the following sin 60∘ cos30∘ + cos 60∘ sin 30∘

Answer»

Evaluate each of the following

sin $60^{\circ}$ cos $30^{\circ}$ + cos $60^{\circ}$ sin $30^{\circ}$

Discussion

35.	Find the values of k for which the roots are real and equal in each of the following equations. (i)kx2+4x+1=0(ii)kx2−2√5x+4=0(iii)3x2−5x+2k=0(iv)4x2+kx+9=0(v)2kx2−40x+25=0(vi)9x2−24x+k=0(vii)4x2−2kx+1=0(viii)x2−2(5+2k)x+3(7+10k)=0(ix)(3k+1)x2+2(k+1)x+k=0(x)kx2+kx+1=−4x2−x(xi)(k+1)x2+2(k+3)x(k+8)=0(xii)x2−2kx+7k−12=0(xiii)(k+1)x2−2(3k+1)x+8k+1=0(xiv)5x2−4x+2+k(4x21−2x−1)=0(xv)(4−k)x2+(2k+4)x+(8k+1)=0(xvi)(2k+1)x2+2(k+3)x+(k+5)=0(xvii)4x2−2(k+1)x+(k+4)=0(xviii)4x2−2(k+1)x+(k+1)=0
Answer» Find the values of k for which the roots are real and equal in each of the following equations. $(i) k x^{2} + 4 x + 1 = 0 (i i) k x^{2} - 2 \sqrt{5} x + 4 = 0 (i i i) 3 x^{2} - 5 x + 2 k = 0 (i v) 4 x^{2} + k x + 9 = 0 (v) 2 k x^{2} - 40 x + 25 = 0 (v i) 9 x^{2} - 24 x + k = 0 (v i i) 4 x^{2} - 2 k x + 1 = 0 (v i i i) x^{2} - 2 (5 + 2 k) x + 3 (7 + 10 k) = 0 (i x) (3 k + 1) x^{2} + 2 (k + 1) x + k = 0 (x) k x^{2} + k x + 1 = - 4 x^{2} - x (x i) (k + 1) x^{2} + 2 (k + 3) x (k + 8) = 0 (x i i) x^{2} - 2 k x + 7 k - 12 = 0 (x i i i) (k + 1) x^{2} - 2 (3 k + 1) x + 8 k + 1 = 0 (x i v) 5 x^{2} - 4 x + 2 + k (4 x^{2} 1 - 2 x - 1) = 0 (x v) (4 - k) x^{2} + (2 k + 4) x + (8 k + 1) = 0 (x v i) (2 k + 1) x^{2} + 2 (k + 3) x + (k + 5) = 0 (x v i i) 4 x^{2} - 2 (k + 1) x + (k + 4) = 0 (x v i i i) 4 x^{2} - 2 (k + 1) x + (k + 1) = 0$

Discussion

36.	The equation (Cosp−1)x2+(Cosp)x+Sinp=0, where x is a variable with real roots. then the interval of p may be any one of the following.
Answer» The equation $(C o s p - 1) x^{2} + (C o s p) x + S i n p = 0,$ where x is a variable with real roots. then the interval of p may be any one of the following.

Discussion

37.	If A=[abba]and A2=[αββα], then
Answer» $If A = [\begin{matrix} a & b b & a \end{matrix}] and A^{2} = [\begin{matrix} α & β β & α \end{matrix}], then$

Discussion

38.	If a=22.3.x and b=2.32.y ; LCM=22.32.52 and HCF = 2.3.5, which of the following is true?
Answer» If $a = 2^{2} .3 . x$ and $b = {2.3}^{2} . y$ ; $L C M = 2^{2} {.3}^{2} {.5}^{2}$ and HCF = 2.3.5, which of the following is true?

Discussion

39.	Question 27 In the trapezium ABCD, the measure of ∠D is a) 55∘ b) 115∘ c) 135∘ d) 125∘
Answer» Question 27 In the trapezium ABCD, the measure of $∠ D$ is a) $55^{\circ}$ b) $115^{\circ}$ c) $135^{\circ}$ d) $125^{\circ}$

Discussion

40.	Question 8 Δ ABC is isosceles with AB = AC = 7.5 cm and BC = 9 cm. The height AD from A to BC is 6 cm. Find the area of Δ ABC. What will be the height from C to AB i.e. CE?
Answer» Question 8 $Δ$ ABC is isosceles with AB = AC = 7.5 cm and BC = 9 cm. The height AD from A to BC is 6 cm. Find the area of $Δ$ ABC. What will be the height from C to AB i.e. CE?

40.

Question 8 Δ ABC is isosceles with AB = AC = 7.5 cm and BC = 9 cm. The height AD from A to BC is 6 cm. Find the area of Δ ABC. What will be the height from C to AB i.e. CE?

Answer»

Question 8

$Δ$ ABC is isosceles with AB = AC = 7.5 cm and BC = 9 cm. The height AD from A to BC is 6 cm. Find the area of $Δ$ ABC. What will be the height from C to AB i.e. CE?

Discussion

41.	Question 30 State whether the given statements are true (T) or false (F). The ratio of 5 : 4 is different from the ratio 4 : 5
Answer» Question 30 State whether the given statements are true (T) or false (F). The ratio of 5 : 4 is different from the ratio 4 : 5

41.

Question 30 State whether the given statements are true (T) or false (F). The ratio of 5 : 4 is different from the ratio 4 : 5

Answer»

Question 30

State whether the given statements are true (T) or false (F).

The ratio of 5 : 4 is different from the ratio 4 : 5

Discussion

42.	What is the value of k if one of the zeroes of (k−2)x2+kx+1 is -4 ? [2 MARKS]
Answer» What is the value of k if one of the zeroes of $(k - 2) x^{2} + k x + 1$ is -4 ? [2 MARKS]

Discussion

43.	How many of the following are consistent with the axiomatic definition of probability ___ 1) The probability of sample space is 1 2) P(A) belongs to the set [0,1] for any event A 3) P(A∪B)=P(A)+P(B) if A and B are mutually exclusive events
Answer» How many of the following are consistent with the axiomatic definition of probability ___ 1) The probability of sample space is 1 2) P(A) belongs to the set [0,1] for any event A 3) $P (A \cup B) = P (A) + P (B)$ if A and B are mutually exclusive events

Discussion

44.	Which of the following is a factor of 49x2−1?
Answer» Which of the following is a factor of $49 x^{2} - 1$ ?

Discussion

45.	Without solving, examine the nature of roots of the equations 2x2 – 5x + 5 = 0
Answer» Without solving, examine the nature of roots of the equations 2 $x^{2}$ – 5x + 5 = 0

Discussion

46.	A vessel is in the form of a hollow hemisphere mounted by a hollow cylinder. The diameter of the hemisphere is 14 cm and the total height of the vessel is 13 cm. Find the inner surface area of the vessel( in cm2).
Answer» A vessel is in the form of a hollow hemisphere mounted by a hollow cylinder. The diameter of the hemisphere is 14 $c m$ and the total height of the vessel is 13 $c m$ . Find the inner surface area of the vessel( in $c m^{2}$ ).

Discussion

47.	100 surnames were randomly picked up from a local telephone directory and the frequency distribution of the number of letters in the English alphabets in the surnames was obtained as follows: Number of lettersNumber of surnames1−464−7307−104010−131613−16416−194 Determine the median number of letters in the surnames. Find the mean number of letters in the surnames. Also, find the modal size of the surnames. [4 MARKS]
Answer» 100 surnames were randomly picked up from a local telephone directory and the frequency distribution of the number of letters in the English alphabets in the surnames was obtained as follows: $\begin{matrix} N u m b e r o f l e t t e r s & N u m b e r o f s u r n a m e s 1 - 4 & 6 4 - 7 & 30 7 - 10 & 40 10 - 13 & 16 13 - 16 & 4 16 - 19 & 4 \end{matrix}$ Determine the median number of letters in the surnames. Find the mean number of letters in the surnames. Also, find the modal size of the surnames. [4 MARKS]

Discussion

48.	Find the value of sgn(-1) + sgn(0) + sgn(1), where sgn(x) is the signum function ___.
Answer» Find the value of sgn(-1) + sgn(0) + sgn(1), where sgn(x) is the signum function ___.

Discussion

49.	The coordinates of the point of trisection of the line segment joining the points A(4, 8) and B(-2, 4) are
Answer» The coordinates of the point of trisection of the line segment joining the points A(4, 8) and B(-2, 4) are

49.

The coordinates of the point of trisection of the line segment joining the points A(4, 8) and B(-2, 4) are

Answer»

The coordinates of the point of trisection of the line segment joining the points A(4, 8) and B(-2, 4) are

Discussion

50.	Question 1 (ii) Which of the following pairs of linear equations has a unique solution, no solution or infinitely many solutions? In case there is a unique solution, find it by using cross multiplication method. 2x + y = 5 ; 3x +2y =8
Answer» Question 1 (ii) Which of the following pairs of linear equations has a unique solution, no solution or infinitely many solutions? In case there is a unique solution, find it by using cross multiplication method. 2x + y = 5 ; 3x +2y =8

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

A hemispherical bowl fits exactly on the open surface of a cone with height 5 cm and radius 3.5 cm.What is the volume of the solid formed?

Name the type of triangle formed by the points A(-5,6), B(-4,-2) and C(7,5).

Express the ratios of sin A and cos A respectively in terms of tan A.

Question 2 (iv) Write whether the following statements are true or false. Justify your answers. Every quadratic equation has at most two roots.

Plot the points P(3, 2) &amp; Q(-3, -2). From P &amp; Q, draw ⏊s PM &amp; QN on the – ais. Assign a special name to the geometrical figure PMQN and find its area.

If a is the G.M. of 2 and 14, find a.

Molar conductances of BaCl2,H2SO4 and HCl at infinite dilutions are x1,x2 and x3 respectively. Equivalent conductance of BaSO4 at infinite dilution will be :

Question 7 If the 2nd term of an AP is 13 and 5th term is 25, what is its 7th term? A) 30 B) 33 C) 37 D) 38

Father's age is 3 times the sum of Ages of his two children . after 5 years his age will be twice the sum of Ages of two children find the age of father

If 45 students can consume a stock of food in 2 months, then for how many days the same stock of food will last for 27 students?

The letters of the word "ASSASSAIN"are written down at random in a row.The probability that no 2 S occur together is what? 1.1/35. 2.1/14. 3.1/15 4.None of these. (Multiple options may be correct.) Pls explain how you did it,step by step.

4(sin⁴30+cos⁴60)-2/3(sin²60-cos²45)+1/2tan²60

A circular tank of diameter 2 m is dug and the earth removed is spread uniformly all around the tank to form an embarkment 2 m in width and 1.6m in height find the depth of the circular tank.

if one zero of the quadratic polynomial f(x)=4x^2-8kx-9 is negative of the other,Find the value of k.

How many numbers divisible by 5 and lying between 4000 and 5000 can be formed from the digits 4,5,6,7 and 8?

Which of the following should be the LAST sentence after rearrangement?

7*8=54;5*3=16;2*7=?

Find out from amongst the four alternatives as to how the pattern would appear when the transparent sheet is folded at the dotted line

A positive integer 'a'when divided by the smallest odd prime leaves a reminder ''r'which of the following cannot be 'r' ? A} 0 B}1. C}2. D}3

In an A.P. the sum of first n terms is 3n22+13n2. Find the 25th term. [3 MARKS]

If secθ−tanθ=13, the value of secθ+tanθ is:

Why do we draw Q′Pm∥QPm+n, while constructing the section of the line PQ in the ratio m:n?

The square of (2x -1) is equal to 5. The values of x are

Cards bearing numbers 3 to 20 are placed in a bag and mixed thoroughly. A card is taken out randomly from the bag. What is the probability that the number on the card is an even number?

If sec A=2√3, find the value of tan Acos A+1+sin Atan A

The simplest form of (x3–1)(x2–1) is

The sum of the 4th and 12th term of an arithmetic progression is 20. What is the sum of the first 15 terms of the arithmetic progression?

Calculate the mean of the following data, using direct method: Class25−3535−4545−5555−6565−75Frequency6108124

Find the area of quadrilateral ABCD whose vertices are A(3, -1), B(9, -5), C(14, 0) and D(9, 19).

In a rectangle, if the length is increased by 3 metres and breadth is decreased by 4 metres, the area of the rectangle is reduced by 67 square metres. If length is reduced by 1 metre and breadth is increased by 4 metres, the area is increased by 89 sq. metres. Find the dimensions of the rectangle.

In fig. 10.37, find tan P and cot R. Is tan P=cot R ?

Evaluate each of the following sin 60∘ cos30∘ + cos 60∘ sin 30∘

The equation (Cosp−1)x2+(Cosp)x+Sinp=0, where x is a variable with real roots. then the interval of p may be any one of the following.

If A=[abba]and A2=[αββα], then

If a=22.3.x and b=2.32.y ; LCM=22.32.52 and HCF = 2.3.5, which of the following is true?

Question 27 In the trapezium ABCD, the measure of ∠D is a) 55∘ b) 115∘ c) 135∘ d) 125∘

Question 8 Δ ABC is isosceles with AB = AC = 7.5 cm and BC = 9 cm. The height AD from A to BC is 6 cm. Find the area of Δ ABC. What will be the height from C to AB i.e. CE?

Question 30 State whether the given statements are true (T) or false (F). The ratio of 5 : 4 is different from the ratio 4 : 5

What is the value of k if one of the zeroes of (k−2)x2+kx+1 is -4 ? [2 MARKS]

How many of the following are consistent with the axiomatic definition of probability ___ 1) The probability of sample space is 1 2) P(A) belongs to the set [0,1] for any event A 3) P(A∪B)=P(A)+P(B) if A and B are mutually exclusive events

Which of the following is a factor of 49x2−1?

Without solving, examine the nature of roots of the equations 2x2 – 5x + 5 = 0

A vessel is in the form of a hollow hemisphere mounted by a hollow cylinder. The diameter of the hemisphere is 14 cm and the total height of the vessel is 13 cm. Find the inner surface area of the vessel( in cm2).

Find the value of sgn(-1) + sgn(0) + sgn(1), where sgn(x) is the signum function ___.

The coordinates of the point of trisection of the line segment joining the points A(4, 8) and B(-2, 4) are

Question 1 (ii) Which of the following pairs of linear equations has a unique solution, no solution or infinitely many solutions? In case there is a unique solution, find it by using cross multiplication method. 2x + y = 5 ; 3x +2y =8

Plot the points P(3, 2) & Q(-3, -2). From P & Q, draw ⏊s PM & QN on the – ais. Assign a special name to the geometrical figure PMQN and find its area.

78=54;53=16;2*7=?