32581 + Interview Questions in Mathematics Page 648 InterviewSolution

32351.	If x=√a sinα and y=√a cosα. Find the value of y2 + x2. __
Answer» If $x = \sqrt{a} s i n α$ and $y = \sqrt{a} c o s α$ . Find the value of $y^{2}$ + $x^{2}$ . __

Discussion

32352.	The number of common roots of the equations x2 – 7x + 10 = 0 and x2 – 10x + 16 = 0 is
Answer» The number of common roots of the equations $x^{2}$ – 7x + 10 = 0 and $x^{2}$ – 10x + 16 = 0 is

Discussion

32353.	Show that 5−√3 is an irrational number.
Answer» Show that $5 - \sqrt{3}$ is an irrational number.

Discussion

32354.	The given distribution shows the number of wickets taken by the bowlers in one-day international cricket matches: Number of wicketsLess than 15Less than 30Less than 45Less than 60Less than 75Less than 90Less than 105Less than 120Number of bowlers2591739547080 Draw a 'less than type' ogive from the above data.Find the median.
Answer» The given distribution shows the number of wickets taken by the bowlers in one-day international cricket matches: $\begin{matrix} N u m b e r o f w i c k e t s & L e s s t h a n 15 & L e s s t h a n 30 & L e s s t h a n 45 & L e s s t h a n 60 & L e s s t h a n 75 & L e s s t h a n 90 & L e s s t h a n 105 & L e s s t h a n 120 N u m b e r o f b o w l e r s & 2 & 5 & 9 & 17 & 39 & 54 & 70 & 80 \end{matrix}$ Draw a 'less than type' ogive from the above data.Find the median.

32354.

The given distribution shows the number of wickets taken by the bowlers in one-day international cricket matches: Number of wicketsLess than 15Less than 30Less than 45Less than 60Less than 75Less than 90Less than 105Less than 120Number of bowlers2591739547080 Draw a 'less than type' ogive from the above data.Find the median.

Answer»

The given distribution shows the number of wickets taken by the bowlers in one-day international cricket matches:

$\begin{matrix} N u m b e r o f w i c k e t s & L e s s t h a n 15 & L e s s t h a n 30 & L e s s t h a n 45 & L e s s t h a n 60 & L e s s t h a n 75 & L e s s t h a n 90 & L e s s t h a n 105 & L e s s t h a n 120 N u m b e r o f b o w l e r s & 2 & 5 & 9 & 17 & 39 & 54 & 70 & 80 \end{matrix}$

Draw a 'less than type' ogive from the above data.Find the median.

Discussion

32355.	If ΔABC∼ΔDEF such that area of ΔABC is 9 cm2 and the area of ΔDEF is 16 cm2 and BC = 2.1 cm. Find the length of EF. [2 MARKS]
Answer» If $Δ A B C \sim Δ D E F$ such that area of $Δ A B C$ is $9 c m^{2}$ and the area of $Δ D E F$ is $16 c m^{2}$ and BC = 2.1 cm. Find the length of EF. [2 MARKS]

Discussion

32356.	The areas of two similar triangles are 12 cm2 and 48 cm2. If the height of the smaller one is 2.1 cm, then the corresponding height of the bigger one is
Answer» The areas of two similar triangles are $12 c m^{2}$ and $48 c m^{2}$ . If the height of the smaller one is $2.1 c m,$ then the corresponding height of the bigger one is

Discussion

32357.	If α and β are the zeros of 2x2+5x−9 then the value of αβ is (a) −52 (b) 52 (c)−92 (d)92
Answer» If $α a n d β$ are the zeros of $2 x^{2} + 5 x - 9$ then the value of $α β$ is (a) $\frac{- 5}{2}$ (b) $\frac{5}{2}$ (c) $\frac{- 9}{2}$ (d) $\frac{9}{2}$

32357.

If α and β are the zeros of 2x2+5x−9 then the value of αβ is (a) −52 (b) 52 (c)−92 (d)92

Answer»

If $α a n d β$ are the zeros of $2 x^{2} + 5 x - 9$ then the value of $α β$ is

(a) $\frac{- 5}{2}$ (b) $\frac{5}{2}$ (c) $\frac{- 9}{2}$ (d) $\frac{9}{2}$

Discussion

32358.	HCF of 1848, 3058 and 1331 is ___
Answer» HCF of 1848, 3058 and 1331 is ___

Discussion

32359.	State fundamental theorem of arithmetic.
Answer» State fundamental theorem of arithmetic.

Discussion

32360.	A chord of a circle is equal to the radius of the circle. Find the angle subtended by the chord at a point on the major arc.
Answer» A chord of a circle is equal to the radius of the circle. Find the angle subtended by the chord at a point on the major arc.

Discussion

32361.	From the given diagram find the values of sides AB and BC respectively.
Answer» From the given diagram find the values of sides AB and BC respectively.

32361.

From the given diagram find the values of sides AB and BC respectively.

Answer»

From the given diagram find the values of sides AB and BC respectively.

Discussion

32362.	Question 8 The value of c for which the pair of equations cx – y = 2 and 6x – 2y = 3 will have infinitely many solutions is (A) 3 (B) – 3 (C) –12 (D) no value
Answer» Question 8 The value of c for which the pair of equations cx – y = 2 and 6x – 2y = 3 will have infinitely many solutions is (A) 3 (B) – 3 (C) –12 (D) no value

Discussion

32363.	The point C divides the line segment AB in the ratio 3:7. Find the length of AB (in cm) if the line segment BC is 3.5 cm long - ___
Answer» The point C divides the line segment AB in the ratio 3:7. Find the length of AB (in cm) if the line segment BC is 3.5 cm long - ___

32363.

The point C divides the line segment AB in the ratio 3:7. Find the length of AB (in cm) if the line segment BC is 3.5 cm long - ___

Answer»

The point C divides the line segment AB in the ratio 3:7. Find the length of AB (in cm) if the line segment BC is 3.5 cm long -

___

Discussion

32364.	If (x+1) is a factor of x4−(p−3)x3−(3p−5)x2+(2p−7)x+6, then p =
Answer» If (x+1) is a factor of $x^{4} - (p - 3) x^{3} - (3 p - 5) x^{2} + (2 p - 7) x + 6$ , then p =

Discussion

32365.	D, E, F are the mid points of the sides BC, CA and AB respectively of an equilateral △ ABC. Then △ DEF is congruent to triangle –
Answer» D, E, F are the mid points of the sides BC, CA and AB respectively of an equilateral $△$ ABC. Then $△$ DEF is congruent to triangle –

32365.

D, E, F are the mid points of the sides BC, CA and AB respectively of an equilateral △ ABC. Then △ DEF is congruent to triangle –

Answer»

D, E, F are the mid points of the sides BC, CA and AB respectively of an equilateral $△$ ABC. Then $△$ DEF is congruent to triangle –

Discussion

32366.	Shriya and Vidya solved a quadratic equation. In solving it, Shriya made a mistake in the constant term and obtained the roots as 5, – 3 while Vidya made a mistake in the coefficient of x and obtained the roots as 1, –3. Which of the following are correct about the correct roots of the equation?
Answer» Shriya and Vidya solved a quadratic equation. In solving it, Shriya made a mistake in the constant term and obtained the roots as 5, – 3 while Vidya made a mistake in the coefficient of x and obtained the roots as 1, –3. Which of the following are correct about the correct roots of the equation?

Discussion

32367.	A circle is inserted inside a square, such that the edge of the circle touches the sides of the square.If X = 14 cm, the area of the shaded portion will be __sq.cm.
Answer» A circle is inserted inside a square, such that the edge of the circle touches the sides of the square.If X = 14 cm, the area of the shaded portion will be __sq.cm.

32367.

A circle is inserted inside a square, such that the edge of the circle touches the sides of the square.If X = 14 cm, the area of the shaded portion will be __sq.cm.

Answer»

A circle is inserted inside a square, such that the edge of the circle touches the sides of the square.If X = 14 cm, the area of the shaded portion will be __sq.cm.

Discussion

32368.	Mr Amit deposited Rs. 150 per month in a bank for 8 months under the recurring deposits scheme. What will be the maturiy value of his deposits, if the rate of interest is 8% per annum and interest is calculated at the end of every month?
Answer» Mr Amit deposited Rs. 150 per month in a bank for 8 months under the recurring deposits scheme. What will be the maturiy value of his deposits, if the rate of interest is 8% per annum and interest is calculated at the end of every month?

Discussion

32369.	Prove that the following is irrational : 7√5 [2 MARKS]
Answer» Prove that the following is irrational : $7 \sqrt{5}$ [2 MARKS]

Discussion

32370.	Divide x2−4x+11 by x -2 and find the sum of quotient and remainder.
Answer» Divide $x^{2} - 4 x + 11$ by x -2 and find the sum of quotient and remainder.

Discussion

32371.	A ladder 17 m long reaches a window of a building 15 m above the ground. Find the distance of the foot of the ladder from the building.
Answer» A ladder 17 m long reaches a window of a building 15 m above the ground. Find the distance of the foot of the ladder from the building.

Discussion

32372.	Angle between 2 planes ¯r.^n1=d1,¯r.^n2=d2, can always be given by
Answer» Angle between 2 planes $¯ r ._{1} = d_{1}, ¯ r ._{2} = d_{2}$ , can always be given by

Discussion

32373.	What is the probability of getting a king when a card is drawn from a well shuffled deck of 52 playing cards?
Answer» What is the probability of getting a king when a card is drawn from a well shuffled deck of 52 playing cards?

Discussion

32374.	The value of sin229∘+sin261∘ is
Answer» The value of $s i n^{2} 29^{\circ} + s i n^{2} 61^{\circ}$ is

Discussion

32375.	A 1.5 m tall boy is standing at some distance from a 30 m tall building. The angles of elevation from his eyes to the top of the building increase from 30∘ to 60∘ as he walks towards the building. The distance he walked towards the building is
Answer» A 1.5 m tall boy is standing at some distance from a 30 m tall building. The angles of elevation from his eyes to the top of the building increase from $30^{\circ}$ to $60^{\circ}$ as he walks towards the building. The distance he walked towards the building is

Discussion

32376.	The angle Of depression of the top and bottom of a building 50 m high as observed from the top of a tower at 30 and 60. find the height of the tower and also the horizontal distance between the building and the tower.
Answer» The angle Of depression of the top and bottom of a building 50 m high as observed from the top of a tower at 30 and 60. find the height of the tower and also the horizontal distance between the building and the tower.

Discussion

32377.	The speed of sound is 332 metres per second.A gun is fired.Describe the locus of all the people on the earth's surface,who hear the sound exactly after one second?
Answer» The speed of sound is 332 metres per second.A gun is fired.Describe the locus of all the people on the earth's surface,who hear the sound exactly after one second?

Discussion

32378.	In ΔABC,∠A=∠B=30∘,AB=12 cm, the area of the triangle will be equal to
Answer» In $Δ A B C, ∠ A = ∠ B = 30^{\circ}, A B = 12 c m$ , the area of the triangle will be equal to

32378.

In ΔABC,∠A=∠B=30∘,AB=12 cm, the area of the triangle will be equal to

Answer»

In $Δ A B C, ∠ A = ∠ B = 30^{\circ}, A B = 12 c m$ , the area of the triangle will be equal to

Discussion

32379.	sin(90∘−θ)cos(90∘−θ)cot(90∘−θ) + sin2θ = __
Answer» $\frac{s i n (90^{\circ} - θ) c o s (90^{\circ} - θ)}{c o t (90^{\circ} - θ)}$ + $s i n^{2} θ$ = __

Discussion

32380.	Question 2 In an AP, if a = 3.5, d = 0 and n = 101, then an will be: A) 0 B) 3.5 C) 103.5 D) 104.5
Answer» Question 2 In an AP, if a = 3.5, d = 0 and n = 101, then $a_{n}$ will be: A) 0 B) 3.5 C) 103.5 D) 104.5

Discussion

32381.	Consider two particles P and Q. Particle P moves from A to B and particle Q moves from C to D. If the displacement of particle P and Q be x, y respectively. Then:
Answer» Consider two particles $P$ and $Q$ . Particle $P$ moves from $A$ to $B$ and particle $Q$ moves from $C$ to $D$ . If the displacement of particle $P$ and $Q$ be $x$ , $y$ respectively. Then:

Discussion

32382.	If two rectangles ABCD and PQRS whose sides are parallel to the coordinate axes are drawn as shown in below figure then the coordinates of 'P' is ___
Answer» If two rectangles ABCD and PQRS whose sides are parallel to the coordinate axes are drawn as shown in below figure then the coordinates of 'P' is ___

32382.

If two rectangles ABCD and PQRS whose sides are parallel to the coordinate axes are drawn as shown in below figure then the coordinates of 'P' is ___

Answer»

If two rectangles ABCD and PQRS whose sides are parallel to the coordinate axes are drawn as shown in below figure then the coordinates of 'P' is ___

Discussion

32383.	If ax2 + bx + c is a monomial in x, what can be said about a, b and c?
Answer» If ax² + bx + c is a monomial in x, what can be said about a, b and c?

Discussion

32384.	A man on the top of a tower, standing on the sea shore, finds a boat coming towards him takes 10 minutes for the angle of depression to change from 30∘ to 60∘. How soon will the boat reach the sea-shore?
Answer» A man on the top of a tower, standing on the sea shore, finds a boat coming towards him takes 10 minutes for the angle of depression to change from $30^{\circ}$ to $60^{\circ}$ . How soon will the boat reach the sea-shore?

Discussion

32385.	Modal class of the following distribution is
Answer» Modal class of the following distribution is

32385.

Modal class of the following distribution is

Answer»

Modal class of the following distribution is

Discussion

32386.	Pinky scored 40 marks in a test getting 3 marks for each right answer and losing 1 mark for each wrong answer. Had 4 marks been awarded for each correct answer and 2 marks were deducted for each wrong answer, then Pinky again would have scored 40 marks. How many questions were there in the test?
Answer» Pinky scored 40 marks in a test getting 3 marks for each right answer and losing 1 mark for each wrong answer. Had 4 marks been awarded for each correct answer and 2 marks were deducted for each wrong answer, then Pinky again would have scored 40 marks. How many questions were there in the test?

Discussion

32387.	A boat goes 80 km upstream and 120 km downstream in 20 hours. In 15 hours, it can go 48 km upstream and 108 km down-stream. Determine the speed of the boat in still water and that of the stream. [4 MARKS]
Answer» A boat goes 80 km upstream and 120 km downstream in 20 hours. In 15 hours, it can go 48 km upstream and 108 km down-stream. Determine the speed of the boat in still water and that of the stream. [4 MARKS]

Discussion

32388.	In a quadrilateral ABCD, AB = 7 cm, BC = 5 cm, AC = 9 cm, AD = 6 cm, CD = 2 cm. Which of the following options is true about the construction of a quadrilateral ABCD?
Answer» In a quadrilateral ABCD, AB = 7 cm, BC = 5 cm, AC = 9 cm, AD = 6 cm, CD = 2 cm. Which of the following options is true about the construction of a quadrilateral ABCD?

Discussion

32389.	In an auditorium, 600 tickets were sold. The total sale of tickets was rupees 4250. If the tickets denominations were ₹ 2.5, ₹ 5.0 and ₹ 10.0. how many of each denominations were sold ?
Answer» In an auditorium, 600 tickets were sold. The total sale of tickets was rupees 4250. If the tickets denominations were ₹ 2.5, ₹ 5.0 and ₹ 10.0. how many of each denominations were sold ?

Discussion

32390.	Find the equation of the line which passes through the point (3, 4) and the sum of its intercepts on the axes is 14.
Answer» Find the equation of the line which passes through the point (3, 4) and the sum of its intercepts on the axes is 14.

Discussion

32391.	In the given figure ABCD is quadrilateral circumscribing a circle with centre O. If ∠B = 900, AD = 23 cm, AB = 29 cm and DS = 5 cm, then the radius of the circle is ___ cm.
Answer» In the given figure ABCD is quadrilateral circumscribing a circle with centre O. If $∠$ B = $90^{0}$ , AD = 23 cm, AB = 29 cm and DS = 5 cm, then the radius of the circle is ___ cm.

32391.

In the given figure ABCD is quadrilateral circumscribing a circle with centre O. If ∠B = 900, AD = 23 cm, AB = 29 cm and DS = 5 cm, then the radius of the circle is ___ cm.

Answer»

In the given figure ABCD is quadrilateral circumscribing a circle with centre O. If $∠$ B = $90^{0}$ , AD = 23 cm, AB = 29 cm and DS = 5 cm, then the radius of the circle is ___ cm.

Discussion

32392.	Find the ratio of AE: EC in the shown figure if straight line drawn through the mid-point of one side AB of the triangle parallel of another side (BC).
Answer» Find the ratio of AE: EC in the shown figure if straight line drawn through the mid-point of one side AB of the triangle parallel of another side (BC).

32392.

Find the ratio of AE: EC in the shown figure if straight line drawn through the mid-point of one side AB of the triangle parallel of another side (BC).

Answer»

Find the ratio of AE: EC in the shown figure if straight line drawn through the mid-point of one side AB of the triangle parallel of another side (BC).

Discussion

32393.	Question 20 Suppose you drop a die at random on the rectangular region shown in the given figure. What is the probability that it will land inside the circle with diameter 1 m?
Answer» Question 20 Suppose you drop a die at random on the rectangular region shown in the given figure. What is the probability that it will land inside the circle with diameter 1 m?

Discussion

32394.	Steps to draw an ogive.
Answer» Steps to draw an ogive.

Discussion

32395.	If cloth costs ₹10/m2 then find the total cost to build a cloth pyramid of base edge 10 m and slant height 10 m.
Answer» If cloth costs $₹ 10 / m^{2}$ then find the total cost to build a cloth pyramid of base edge 10 m and slant height 10 m.

Discussion

32396.	In the given figure, ABCD is a cyclic Quadrilateral. O is the centre of the circle and ∠BOD=160∘, find the measure of ∠BPD.
Answer» In the given figure, ABCD is a cyclic Quadrilateral. O is the centre of the circle and $∠ B O D = 160^{\circ}$ , find the measure of $∠ B P D .$

32396.

In the given figure, ABCD is a cyclic Quadrilateral. O is the centre of the circle and ∠BOD=160∘, find the measure of ∠BPD.

Answer»

In the given figure, ABCD is a cyclic Quadrilateral. O is the centre of the circle and $∠ B O D = 160^{\circ}$ , find the measure of $∠ B P D .$

Discussion

32397.	Question 6 If two positive integers a and b are written as a=x3y2 and b=xy2 where x, y are prime numbers, then HCF (a, b) is A) xy B) xy2 C) x3y3 D) x2y2
Answer» Question 6 If two positive integers a and b are written as $a = x^{3} y^{2} a n d b = x y^{2}$ where x, y are prime numbers, then HCF (a, b) is A) $x y$ B) $x y^{2}$ C) $x^{3} y^{3}$ D) $x^{2} y^{2}$

Discussion

32398.	How many tangents can be drawn to a circle through the points A, B and C as shown?
Answer» How many tangents can be drawn to a circle through the points A, B and C as shown?

Discussion

32399.	A die and a coin are tossed simultaneously. If a head on the coin is taken to be 1 and a tail is taken to be 0, find the number of outcomes where sum of numbers on the die and the coin is greater than 4.
Answer» A die and a coin are tossed simultaneously. If a head on the coin is taken to be 1 and a tail is taken to be 0, find the number of outcomes where sum of numbers on the die and the coin is greater than 4.

Discussion

32400.	Two coins are tossed simultaneously once. Find the probability of getting at least one head and one tail.
Answer» Two coins are tossed simultaneously once. Find the probability of getting at least one head and one tail.

Discussion

Explore topic-wise InterviewSolutions in .

If x=√a sinα and y=√a cosα. Find the value of y2 + x2. __

The number of common roots of the equations x2 – 7x + 10 = 0 and x2 – 10x + 16 = 0 is

Show that 5−√3 is an irrational number.

If ΔABC∼ΔDEF such that area of ΔABC is 9 cm2 and the area of ΔDEF is 16 cm2 and BC = 2.1 cm. Find the length of EF. [2 MARKS]

The areas of two similar triangles are 12 cm2 and 48 cm2. If the height of the smaller one is 2.1 cm, then the corresponding height of the bigger one is

If α and β are the zeros of 2x2+5x−9 then the value of αβ is (a) −52 (b) 52 (c)−92 (d)92

HCF of 1848, 3058 and 1331 is ___

State fundamental theorem of arithmetic.

A chord of a circle is equal to the radius of the circle. Find the angle subtended by the chord at a point on the major arc.

From the given diagram find the values of sides AB and BC respectively.

Question 8 The value of c for which the pair of equations cx – y = 2 and 6x – 2y = 3 will have infinitely many solutions is (A) 3 (B) – 3 (C) –12 (D) no value

The point C divides the line segment AB in the ratio 3:7. Find the length of AB (in cm) if the line segment BC is 3.5 cm long - ___

If (x+1) is a factor of x4−(p−3)x3−(3p−5)x2+(2p−7)x+6, then p =

D, E, F are the mid points of the sides BC, CA and AB respectively of an equilateral △ ABC. Then △ DEF is congruent to triangle –

A circle is inserted inside a square, such that the edge of the circle touches the sides of the square.If X = 14 cm, the area of the shaded portion will be __sq.cm.

Mr Amit deposited Rs. 150 per month in a bank for 8 months under the recurring deposits scheme. What will be the maturiy value of his deposits, if the rate of interest is 8% per annum and interest is calculated at the end of every month?

Prove that the following is irrational : 7√5 [2 MARKS]

Divide x2−4x+11 by x -2 and find the sum of quotient and remainder.

A ladder 17 m long reaches a window of a building 15 m above the ground. Find the distance of the foot of the ladder from the building.

Angle between 2 planes ¯r.^n1=d1,¯r.^n2=d2, can always be given by

What is the probability of getting a king when a card is drawn from a well shuffled deck of 52 playing cards?

The value of sin229∘+sin261∘ is

A 1.5 m tall boy is standing at some distance from a 30 m tall building. The angles of elevation from his eyes to the top of the building increase from 30∘ to 60∘ as he walks towards the building. The distance he walked towards the building is

The angle Of depression of the top and bottom of a building 50 m high as observed from the top of a tower at 30 and 60. find the height of the tower and also the horizontal distance between the building and the tower.

The speed of sound is 332 metres per second.A gun is fired.Describe the locus of all the people on the earth's surface,who hear the sound exactly after one second?

In ΔABC,∠A=∠B=30∘,AB=12 cm, the area of the triangle will be equal to

sin(90∘−θ)cos(90∘−θ)cot(90∘−θ) + sin2θ = __

Question 2 In an AP, if a = 3.5, d = 0 and n = 101, then an will be: A) 0 B) 3.5 C) 103.5 D) 104.5

Consider two particles P and Q. Particle P moves from A to B and particle Q moves from C to D. If the displacement of particle P and Q be x, y respectively. Then:

If two rectangles ABCD and PQRS whose sides are parallel to the coordinate axes are drawn as shown in below figure then the coordinates of 'P' is ___

If ax2 + bx + c is a monomial in x, what can be said about a, b and c?

A man on the top of a tower, standing on the sea shore, finds a boat coming towards him takes 10 minutes for the angle of depression to change from 30∘ to 60∘. How soon will the boat reach the sea-shore?

Modal class of the following distribution is

Pinky scored 40 marks in a test getting 3 marks for each right answer and losing 1 mark for each wrong answer. Had 4 marks been awarded for each correct answer and 2 marks were deducted for each wrong answer, then Pinky again would have scored 40 marks. How many questions were there in the test?

A boat goes 80 km upstream and 120 km downstream in 20 hours. In 15 hours, it can go 48 km upstream and 108 km down-stream. Determine the speed of the boat in still water and that of the stream. [4 MARKS]

In a quadrilateral ABCD, AB = 7 cm, BC = 5 cm, AC = 9 cm, AD = 6 cm, CD = 2 cm. Which of the following options is true about the construction of a quadrilateral ABCD?

In an auditorium, 600 tickets were sold. The total sale of tickets was rupees 4250. If the tickets denominations were ₹ 2.5, ₹ 5.0 and ₹ 10.0. how many of each denominations were sold ?

Find the equation of the line which passes through the point (3, 4) and the sum of its intercepts on the axes is 14.

In the given figure ABCD is quadrilateral circumscribing a circle with centre O. If ∠B = 900, AD = 23 cm, AB = 29 cm and DS = 5 cm, then the radius of the circle is ___ cm.

Find the ratio of AE: EC in the shown figure if straight line drawn through the mid-point of one side AB of the triangle parallel of another side (BC).

Question 20 Suppose you drop a die at random on the rectangular region shown in the given figure. What is the probability that it will land inside the circle with diameter 1 m?

Steps to draw an ogive.

If cloth costs ₹10/m2 then find the total cost to build a cloth pyramid of base edge 10 m and slant height 10 m.

In the given figure, ABCD is a cyclic Quadrilateral. O is the centre of the circle and ∠BOD=160∘, find the measure of ∠BPD.

Question 6 If two positive integers a and b are written as a=x3y2 and b=xy2 where x, y are prime numbers, then HCF (a, b) is A) xy B) xy2 C) x3y3 D) x2y2

How many tangents can be drawn to a circle through the points A, B and C as shown?

A die and a coin are tossed simultaneously. If a head on the coin is taken to be 1 and a tail is taken to be 0, find the number of outcomes where sum of numbers on the die and the coin is greater than 4.

Two coins are tossed simultaneously once. Find the probability of getting at least one head and one tail.