32581 + Interview Questions in Mathematics

1.	A toy is in the shape of a right circular cylinder with a hemisphere on one end and a cone on the other. The radius and height of the cylindrical part are 5 cm and 13 cm respectively. The radii of the hemispherical and the conical parts are the same as that of the cylindrical part. Find the surface area of the toy, if the total height of the toy is 30 cm.
Answer» A toy is in the shape of a right circular cylinder with a hemisphere on one end and a cone on the other. The radius and height of the cylindrical part are 5 cm and 13 cm respectively. The radii of the hemispherical and the conical parts are the same as that of the cylindrical part. Find the surface area of the toy, if the total height of the toy is 30 cm.

Discussion

2.	In Fig. the square ABCD is divided into five equal parts, all having same area. The central part is circular and the lines AE, GC, BF and HD lie along the diagonals AC and BD of the square. If AB = 22 cm, find:
Answer» In Fig. the square ABCD is divided into five equal parts, all having same area. The central part is circular and the lines AE, GC, BF and HD lie along the diagonals AC and BD of the square. If AB = 22 cm, find:

Discussion

3.	A solid toy is in the form of a hemisphere surmounted by a right circular cone. The height of the cone is 4cm and diameter of the base is 8cm. Determine the volume of the toy. If a cube circumstances the toy, then find the difference of the volumes of cube and the toy. Also, find the total surface area of the toy.
Answer» A solid toy is in the form of a hemisphere surmounted by a right circular cone. The height of the cone is $4 c m$ and diameter of the base is $8 c m$ . Determine the volume of the toy. If a cube circumstances the toy, then find the difference of the volumes of cube and the toy. Also, find the total surface area of the toy.

Discussion

4.	The first term of an A.P. is 5, the common difference is 3 and the last term is 80; find the number of terms.
Answer» The first term of an A.P. is 5, the common difference is 3 and the last term is 80; find the number of terms.

Discussion

5.	Find the mean of the step deviations: Class intervalFrequency(fi)Class mark(xi)di=xi−aui=dih0−1004050−200−2100−20039150−100−1200−3003425000300−400303501001400−500454502002
Answer» Find the mean of the step deviations: $\begin{matrix} Class interval & Frequency (f_{i}) & Class mark (x_{i}) & d_{i} = x_{i} - a & u_{i} = \frac{d_{i}}{h} 0 - 100 & 40 & 50 & - 200 & - 2 100 - 200 & 39 & 150 & - 100 & - 1 200 - 300 & 34 & 250 & 0 & 0 300 - 400 & 30 & 350 & 100 & 1 400 - 500 & 45 & 450 & 200 & 2 \end{matrix}$

Discussion

6.

Question 2 (v) Multiply and reduce to lowest form (if possible): 13×158

Answer»

Question 2 (v)

Multiply and reduce to lowest form (if possible):

\frac{1}{3} \times \frac{15}{8}

Discussion

7.	In the given figure, PA is tangent to the circle. If PC intersects the circle at B and PB = 9 cm and BC =7cm, PA = ______ cm.
Answer» In the given figure, PA is tangent to the circle. If PC intersects the circle at B and PB = 9 cm and BC =7cm, PA = ______ cm.

Discussion

8.	The height of a tree is √3 times the length of its shadow. Find the angle of elevation of the sun. [1 MARK]
Answer» The height of a tree is $\sqrt{3}$ times the length of its shadow. Find the angle of elevation of the sun. [1 MARK]

Discussion

9.	In an AP with a = 3 and d = 12, find the term that will be 120 more than it's 21(st) term.
Answer» In an AP with a = 3 and d = 12, find the term that will be 120 more than it's $21^{(} s t)$ term.

Discussion

10.	If the sum of m terms of an A.P. is the same as the sum of its n terms, show that the sum of its (m + n) terms is zero.
Answer» If the sum of m terms of an A.P. is the same as the sum of its n terms, show that the sum of its (m + n) terms is zero.

Discussion

11.	Question 6 Write True or False and justify your answer : If AOB is a diameter of a circle and C is a point on the circle, then AC2+BC2=AB2
Answer» Question 6 Write True or False and justify your answer : If AOB is a diameter of a circle and C is a point on the circle, then $A C^{2} + B C^{2} = A B^{2}$

Discussion

12.	Show that any positive odd integer is of the form 6q + 1, or 6q + 3 or 6q + 5, where q is some integer.
Answer» Show that any positive odd integer is of the form 6q + 1, or 6q + 3 or 6q + 5, where q is some integer.

Discussion

13.	If 0∘<θ<90∘, √sec2θ+cosec2θ= ___.
Answer» If $0^{\circ} < θ < 90^{\circ}$ , $\sqrt{s e c^{2} θ + c o s e c^{2} θ} =$ ___.

Discussion

14.	Question 9 (iii) The adjoining figure represents a rectangular lawn with a circular flower bed in the middle. Find: The area of a lawn excluding the area of the flower bed.
Answer» Question 9 (iii) The adjoining figure represents a rectangular lawn with a circular flower bed in the middle. Find: The area of a lawn excluding the area of the flower bed.

14.

Question 9 (iii) The adjoining figure represents a rectangular lawn with a circular flower bed in the middle. Find: The area of a lawn excluding the area of the flower bed.

Answer»

Question 9 (iii)

The adjoining figure represents a rectangular lawn with a circular flower bed in the middle. Find:

The area of a lawn excluding the area of the flower bed.

Discussion

15.	The sum of the 4th and 8th terms of an AP is 24 and the sum of 6th and 10th terms is 44. Find the first three terms of the AP.
Answer» The sum of the $4^{t h}$ and $8^{t h}$ terms of an AP is 24 and the sum of $6^{t h}$ and $10^{t h}$ terms is 44. Find the first three terms of the AP.

Discussion

16.	__,50, 75, 100,125, ..... The first number in the above series is __.
Answer» __,50, 75, 100,125, ..... The first number in the above series is __.

Discussion

17.	5pens and one book together cost Rs.225. Cost of 10 pens is equal to cost of 1 book find the total cost of 3pens and 2 books
Answer» 5pens and one book together cost Rs.225. Cost of 10 pens is equal to cost of 1 book find the total cost of 3pens and 2 books

Discussion

18.	I left home for bringing milk between 7am and 8am. The angle between the hour-hand and the minute hand was 90∘. I returned home between 7 am and 8 am. Then also the angle between the minute-hand and hour-hand was 90∘. At what time (nearest to second) did I leave and return home?
Answer» I left home for bringing milk between 7am and 8am. The angle between the hour-hand and the minute hand was $90^{\circ}$ . I returned home between 7 am and 8 am. Then also the angle between the minute-hand and hour-hand was $90^{\circ}$ . At what time (nearest to second) did I leave and return home?

Discussion

19.	Solve the following pair of linear equation: (a - b)x + (a + b)y = a² - 2ab - b² ( a + b)(x + y)= a² +b²
Answer» Solve the following pair of linear equation: (a - b)x + (a + b)y = a² - 2ab - b² ( a + b)(x + y)= a² +b²

19.

Solve the following pair of linear equation: (a - b)x + (a + b)y = a² - 2ab - b² ( a + b)(x + y)= a² +b²

Answer»

Solve the following pair of linear equation:

(a - b)x + (a + b)y = a² - 2ab - b²

( a + b)(x + y)= a² +b²

Discussion

20.	James buys a chair listed at ₹ 1,500 and gets successive discounts of 20% and 10%. He spends ₹ 20 on transportation and sells it at a profit of 20%. Find the selling price of the chair ?
Answer» James buys a chair listed at ₹ 1,500 and gets successive discounts of 20% and 10%. He spends ₹ 20 on transportation and sells it at a profit of 20%. Find the selling price of the chair ?

Discussion

21.	Calculate the radius of a circle circumscribing a right-angled triangle the length of whose sides are 6 cm and 8 cm.
Answer» Calculate the radius of a circle circumscribing a right-angled triangle the length of whose sides are 6 cm and 8 cm.

Discussion

22.	Prove the uniqueness of q and r in Euclid division Lemma.i.e., let a and b be any two positive integers there exist unique integers q and r, a=bq+r,0≤r≤b.
Answer» Prove the uniqueness of $q$ and $r$ in Euclid division Lemma. i.e., let $a$ and $b$ be any two positive integers there exist unique integers $q$ and $r$ , $a = b q + r, 0 \leq r \leq b$ .

Discussion

23.	f(x) denotes the sum of the digits of the number x and g(x) denotes the product of the digits of the number x. How many three digit numbers are there for which f(x)=g(x), where x is a three digit number.
Answer» f(x) denotes the sum of the digits of the number x and g(x) denotes the product of the digits of the number x. How many three digit numbers are there for which f(x)=g(x), where x is a three digit number.

Discussion

24.	Three numbers that are co - prime to each other are such that the product of the first two is 551 and that of the last two is 1073. Find, the sum of all the three numbers.
Answer» Three numbers that are co - prime to each other are such that the product of the first two is 551 and that of the last two is 1073. Find, the sum of all the three numbers.

Discussion

25.	The following are the marks obtained in Science by students in class X. The mean was calculated to be 63.33. Is this mean an appropriate representation of the average marks obtained? If no, what would be the most appropriate measure of central tendency for the correct representation of the marks distribution? What is the value of this measure of central tendency for the given data? MarksFrequency10−20120−30030−40040−50050−60160−70570−801580−902090−1003
Answer» The following are the marks obtained in Science by students in class X. The mean was calculated to be 63.33. Is this mean an appropriate representation of the average marks obtained? If no, what would be the most appropriate measure of central tendency for the correct representation of the marks distribution? What is the value of this measure of central tendency for the given data? $\begin{matrix} Marks & Frequency 10 - 20 & 1 20 - 30 & 0 30 - 40 & 0 40 - 50 & 0 50 - 60 & 1 60 - 70 & 5 70 - 80 & 15 80 - 90 & 20 90 - 100 & 3 \end{matrix}$

Discussion

26.	I have some tables and chairs. If I place two chairs at each table, I have one extra chair. If I place three chairs at each table, I have one table with no chairs. What is the sum of the total number of tables and chairs?
Answer» I have some tables and chairs. If I place two chairs at each table, I have one extra chair. If I place three chairs at each table, I have one table with no chairs. What is the sum of the total number of tables and chairs?

Discussion

27.	If the polynomial f(x)=x4−6x3+16x2−25x+10 is divided by another polynomial x2−2x+k, the remainder comes out to be x+a, find k and a. [4 MARKS]
Answer» If the polynomial $f (x) = x^{4} - 6 x^{3} + 16 x^{2} - 25 x + 10$ is divided by another polynomial $x^{2} - 2 x + k$ , the remainder comes out to be $x + a$ , find k and a. [4 MARKS]

Discussion

28.	Question 10 Find whether 55 is a term of the AP 7, 10, 13 …. Or not. If yes, find which term it is.
Answer» Question 10 Find whether 55 is a term of the AP 7, 10, 13 …. Or not. If yes, find which term it is.

Discussion

29.	If the sum if the zeros of the polynomial kt^2 +2t +3k is equal to their product find the value of k
Answer» If the sum if the zeros of the polynomial kt^2 +2t +3k is equal to their product find the value of k

Discussion

30.	The co-ordinates of the centroid of a triangle PQR are (2, -5). If Q = (-6, 5) and R = (11, 8); calculate the co-ordinates of vertex P.
Answer» The co-ordinates of the centroid of a triangle PQR are (2, -5). If Q = (-6, 5) and R = (11, 8); calculate the co-ordinates of vertex P.

Discussion

31.	Which of the following sequences form an AP? (i) 2, 4, 8, 16…….. (ii) 2, 3, 5, 7, 11……. (iii) -1, -1.25, -1.5, -1.75…… (iv) 1, -1, -3, -5…………
Answer» Which of the following sequences form an AP? (i) 2, 4, 8, 16…….. (ii) 2, 3, 5, 7, 11……. (iii) -1, -1.25, -1.5, -1.75…… (iv) 1, -1, -3, -5…………

31.

Which of the following sequences form an AP? (i) 2, 4, 8, 16…….. (ii) 2, 3, 5, 7, 11……. (iii) -1, -1.25, -1.5, -1.75…… (iv) 1, -1, -3, -5…………

Answer»

Which of the following sequences form an AP?

(i) 2, 4, 8, 16……..

(ii) 2, 3, 5, 7, 11…….

(iii) -1, -1.25, -1.5, -1.75……

(iv) 1, -1, -3, -5…………

Discussion

32.	If an unbiased die is thrown 5 times and every throw resulted in a 6, what is the probability of getting a 6 on the sixth throw?
Answer» If an unbiased die is thrown 5 times and every throw resulted in a 6, what is the probability of getting a 6 on the sixth throw?

Discussion

33.	If R is a relation between A and B, then which of the following is correct?
Answer» If R is a relation between A and B, then which of the following is correct?

Discussion

34.	Aparna has a cumulative deposit in Union bank for 4 years at 9% rate of interest per annum. She receives Rs 51,607.50 at the time of maturity. Find her monthly installment.
Answer» Aparna has a cumulative deposit in Union bank for 4 years at 9% rate of interest per annum. She receives Rs 51,607.50 at the time of maturity. Find her monthly installment.

Discussion

35.	The marks obtained by 40 students in class X of a certain school in a math paper of 100 marks total are presented in the table. Find the mean using direct method. Class Interval0−1010−2020−3030−4040−50Number of students341315528.75
Answer» The marks obtained by 40 students in class X of a certain school in a math paper of 100 marks total are presented in the table. Find the mean using direct method. $\begin{matrix} C l a s s I n t e r v a l & 0 - 10 & 10 - 20 & 20 - 30 & 30 - 40 & 40 - 50 N u m b e r o f s t u d e n t s & 3 & 4 & 13 & 15 & 5 \end{matrix}$ 28.75

35.

The marks obtained by 40 students in class X of a certain school in a math paper of 100 marks total are presented in the table. Find the mean using direct method. Class Interval0−1010−2020−3030−4040−50Number of students341315528.75

Answer»

The marks obtained by 40 students in class X of a certain school in a math paper of 100 marks total are presented in the table. Find the mean using direct method.

$\begin{matrix} C l a s s I n t e r v a l & 0 - 10 & 10 - 20 & 20 - 30 & 30 - 40 & 40 - 50 N u m b e r o f s t u d e n t s & 3 & 4 & 13 & 15 & 5 \end{matrix}$

28.75

Discussion

36.	The sum of first 8 terms of an a.p is 140 and the sum of first 24 terms is 996. Find the a.p.
Answer» The sum of first 8 terms of an a.p is 140 and the sum of first 24 terms is 996. Find the a.p.

Discussion

37.	If A=⎡⎢⎣123⎤⎥⎦ then AA' =
Answer» If $A = ⎡ ⎢ ⎣ \begin{matrix} 123 \end{matrix} ⎤ ⎥ ⎦$ then AA' =

Discussion

38.	In the above figure, CM is a tangent at point C. ABCD is a square. B is the centre of the circle. BM = 10 cm, CM = 8 cm. What is the value of AD?
Answer» In the above figure, CM is a tangent at point C. ABCD is a square. B is the centre of the circle. BM = 10 cm, CM = 8 cm. What is the value of AD?

38.

In the above figure, CM is a tangent at point C. ABCD is a square. B is the centre of the circle. BM = 10 cm, CM = 8 cm. What is the value of AD?

Answer»

In the above figure, CM is a tangent at point C. ABCD is a square. B is the centre of the circle. BM = 10 cm, CM = 8 cm. What is the value of AD?

Discussion

39.	2 women and 5 men together can finish an ebroidery work in 4 days,while 3 women and 6 men can finish it in 3 days.Find the time taken by 1 woman alone to finish the work, and also that taken by 1 man alone.
Answer» 2 women and 5 men together can finish an ebroidery work in 4 days,while 3 women and 6 men can finish it in 3 days.Find the time taken by 1 woman alone to finish the work, and also that taken by 1 man alone.

Discussion

40.	50 bells B1 , B2 , B3 ,.......B50 start ringing together. The bells ring after every 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.....50 sec respectively. Bells B11 , B22, B33 and B44 ring together in 22.a1.b1 sec. Which of the following is always true about a and b ?
Answer» 50 bells B1 , B2 , B3 ,.......B50 start ringing together. The bells ring after every 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.....50 sec respectively. Bells $B_{11}$ , $B_{22}$ , $B_{33}$ and $B_{44}$ ring together in $2^{2} . a^{1} . b^{1}$ sec. Which of the following is always true about a and b ?

Discussion

41.	In the given figure, PA and PB are two tangents drawn from an external point P. If ∠APB=40∘, then find ∠AOB.
Answer» $In the given figure, PA and PB are two tangents drawn from an external point P. If ∠ A P B = 40^{\circ}, then find ∠ A O B .$

Discussion

42.	Please give some tips for Mathematics Class 10th board exams like how to attempt the paper, from which section to start and what to do just before the exam.
Answer» Please give some tips for Mathematics Class 10th board exams like how to attempt the paper, from which section to start and what to do just before the exam.

Discussion

43.	The points A(0, 6), B(-5, 3) and C(3, 1) are the vertices of a triangle which is
Answer» The points A(0, 6), B(-5, 3) and C(3, 1) are the vertices of a triangle which is

Discussion

44.	Which of the following options is equal to cot θ+cosec θ−1cot θ−cosec θ+1
Answer» Which of the following options is equal to $\frac{c o t θ + c o s e c θ - 1}{c o t θ - c o s e c θ + 1}$

Discussion

45.	If x51 + 51 is divided by x + 1, then the remainder is
Answer» If $x^{51} + 51$ is divided by $x + 1$ , then the remainder is

Discussion

46.	Prove that (i)sec2 θ+cosec2 θ=sec2 θ cosec2 θ (ii)tan2 θ−sin2 θ=tan2 θ sin2 θ (iii)tan2 θ+cot2 θ+2=sec2 θ cosec2 θ [3 MARKS]
Answer» Prove that $(i) s e c^{2} θ + c o s e c^{2} θ = s e c^{2} θ c o s e c^{2} θ$ $(i i) t a n^{2} θ - s i n^{2} θ = t a n^{2} θ s i n^{2} θ$ $(i i i) t a n^{2} θ + c o t^{2} θ + 2 = s e c^{2} θ c o s e c^{2} θ$ [3 MARKS]

Discussion

47.	The angle between two tangents to a circle may be 0∘.
Answer» The angle between two tangents to a circle may be $0^{\circ}$ .

Discussion

48.	If the sum of the 33 + 73 + 113 + 153 ...................20 terms is s20. Find the value of s20100 ___
Answer» If the sum of the $3^{3}$ + $7^{3}$ + $11^{3}$ + $15^{3}$ ...................20 terms is $s_{20}$ . Find the value of $\frac{s_{20}}{100}$ ___

Discussion

49.	The angle opposite to the base edge of a square pyramid on its lateral face is 30∘. If the slant height of the pyramid is 20cm, what is the lateral surface area of the pyramid? (Note that tan15∘=0.268)
Answer» The angle opposite to the base edge of a square pyramid on its lateral face is 30 $^{\circ}$ . If the slant height of the pyramid is 20 $c m$ , what is the lateral surface area of the pyramid? (Note that $t a n 15^{\circ} = 0.268$ )

Discussion

50.	If the square roots of 3 + 4i is ±(a+ib). Find the value of a + b. ___
Answer» If the square roots of 3 + 4i is $\pm (a + i b)$ . Find the value of a + b. ___

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

In Fig. the square ABCD is divided into five equal parts, all having same area. The central part is circular and the lines AE, GC, BF and HD lie along the diagonals AC and BD of the square. If AB = 22 cm, find:

The first term of an A.P. is 5, the common difference is 3 and the last term is 80; find the number of terms.

Find the mean of the step deviations: Class intervalFrequency(fi)Class mark(xi)di=xi−aui=dih0−1004050−200−2100−20039150−100−1200−3003425000300−400303501001400−500454502002

Question 2 (v) Multiply and reduce to lowest form (if possible): 13×158

In the given figure, PA is tangent to the circle. If PC intersects the circle at B and PB = 9 cm and BC =7cm, PA = ______ cm.

The height of a tree is √3 times the length of its shadow. Find the angle of elevation of the sun. [1 MARK]

In an AP with a = 3 and d = 12, find the term that will be 120 more than it's 21(st) term.

If the sum of m terms of an A.P. is the same as the sum of its n terms, show that the sum of its (m + n) terms is zero.

Question 6 Write True or False and justify your answer : If AOB is a diameter of a circle and C is a point on the circle, then AC2+BC2=AB2

Show that any positive odd integer is of the form 6q + 1, or 6q + 3 or 6q + 5, where q is some integer.

If 0∘&lt;θ&lt;90∘, √sec2θ+cosec2θ= ___.

Question 9 (iii) The adjoining figure represents a rectangular lawn with a circular flower bed in the middle. Find: The area of a lawn excluding the area of the flower bed.

The sum of the 4th and 8th terms of an AP is 24 and the sum of 6th and 10th terms is 44. Find the first three terms of the AP.

__,50, 75, 100,125, ..... The first number in the above series is __.

5pens and one book together cost Rs.225. Cost of 10 pens is equal to cost of 1 book find the total cost of 3pens and 2 books

I left home for bringing milk between 7am and 8am. The angle between the hour-hand and the minute hand was 90∘. I returned home between 7 am and 8 am. Then also the angle between the minute-hand and hour-hand was 90∘. At what time (nearest to second) did I leave and return home?

Solve the following pair of linear equation: (a - b)x + (a + b)y = a² - 2ab - b² ( a + b)(x + y)= a² +b²

James buys a chair listed at ₹ 1,500 and gets successive discounts of 20% and 10%. He spends ₹ 20 on transportation and sells it at a profit of 20%. Find the selling price of the chair ?

Calculate the radius of a circle circumscribing a right-angled triangle the length of whose sides are 6 cm and 8 cm.

Prove the uniqueness of q and r in Euclid division Lemma.i.e., let a and b be any two positive integers there exist unique integers q and r, a=bq+r,0≤r≤b.

f(x) denotes the sum of the digits of the number x and g(x) denotes the product of the digits of the number x. How many three digit numbers are there for which f(x)=g(x), where x is a three digit number.

Three numbers that are co - prime to each other are such that the product of the first two is 551 and that of the last two is 1073. Find, the sum of all the three numbers.

I have some tables and chairs. If I place two chairs at each table, I have one extra chair. If I place three chairs at each table, I have one table with no chairs. What is the sum of the total number of tables and chairs?

If the polynomial f(x)=x4−6x3+16x2−25x+10 is divided by another polynomial x2−2x+k, the remainder comes out to be x+a, find k and a. [4 MARKS]

Question 10 Find whether 55 is a term of the AP 7, 10, 13 …. Or not. If yes, find which term it is.

If the sum if the zeros of the polynomial kt^2 +2t +3k is equal to their product find the value of k

The co-ordinates of the centroid of a triangle PQR are (2, -5). If Q = (-6, 5) and R = (11, 8); calculate the co-ordinates of vertex P.

Which of the following sequences form an AP? (i) 2, 4, 8, 16…….. (ii) 2, 3, 5, 7, 11……. (iii) -1, -1.25, -1.5, -1.75…… (iv) 1, -1, -3, -5…………

If an unbiased die is thrown 5 times and every throw resulted in a 6, what is the probability of getting a 6 on the sixth throw?

If R is a relation between A and B, then which of the following is correct?

Aparna has a cumulative deposit in Union bank for 4 years at 9% rate of interest per annum. She receives Rs 51,607.50 at the time of maturity. Find her monthly installment.

The marks obtained by 40 students in class X of a certain school in a math paper of 100 marks total are presented in the table. Find the mean using direct method. Class Interval0−1010−2020−3030−4040−50Number of students341315528.75

The sum of first 8 terms of an a.p is 140 and the sum of first 24 terms is 996. Find the a.p.

If A=⎡⎢⎣123⎤⎥⎦ then AA' =

In the above figure, CM is a tangent at point C. ABCD is a square. B is the centre of the circle. BM = 10 cm, CM = 8 cm. What is the value of AD?

2 women and 5 men together can finish an ebroidery work in 4 days,while 3 women and 6 men can finish it in 3 days.Find the time taken by 1 woman alone to finish the work, and also that taken by 1 man alone.

50 bells B1 , B2 , B3 ,.......B50 start ringing together. The bells ring after every 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.....50 sec respectively. Bells B11 , B22, B33 and B44 ring together in 22.a1.b1 sec. Which of the following is always true about a and b ?

In the given figure, PA and PB are two tangents drawn from an external point P. If ∠APB=40∘, then find ∠AOB.

Please give some tips for Mathematics Class 10th board exams like how to attempt the paper, from which section to start and what to do just before the exam.

The points A(0, 6), B(-5, 3) and C(3, 1) are the vertices of a triangle which is

Which of the following options is equal to cot θ+cosec θ−1cot θ−cosec θ+1

If x51 + 51 is divided by x + 1, then the remainder is

Prove that (i)sec2 θ+cosec2 θ=sec2 θ cosec2 θ (ii)tan2 θ−sin2 θ=tan2 θ sin2 θ (iii)tan2 θ+cot2 θ+2=sec2 θ cosec2 θ [3 MARKS]

The angle between two tangents to a circle may be 0∘.

If the sum of the 33 + 73 + 113 + 153 ...................20 terms is s20. Find the value of s20100 ___

The angle opposite to the base edge of a square pyramid on its lateral face is 30∘. If the slant height of the pyramid is 20cm, what is the lateral surface area of the pyramid? (Note that tan15∘=0.268)

If the square roots of 3 + 4i is ±(a+ib). Find the value of a + b. ___

If 0∘<θ<90∘, √sec2θ+cosec2θ= ___.

,50, 75, 100,125, ..... The first number in the above series is .