Let A = {1, 2, 3, 4} and B = {4, 8, 9, 10}. A function f: A ⟶ B given by f = {(1, 4), (2, 8), (3, 9), (4,10)} is a

If g = {(1,1), (2,3), (3,5), (4,7)} is a function given by g(x) = αx + β then the values of α and β are

If the order pairs (a, -1) and (5, b) blongs to {(x, y) | y = 2x + 3}, then a and b are __________

If f(x) = ax - 2, g(x) = 2x - 1 and fog = gof, the value of a is ___________

If f(x) = 2 - 3x, then f o f(1 - x) = ?

If f(x) + f(1 - x) = 2 then \(f\left( \frac { 1 }{ 2 } \right) \) is ___________

7^4k \(\equiv \) ________ (mod 100)

The first term of an arithmetic progression is unity and the common difference is 4. Which of the following will be a term of this A.P.

What is the HCF of the least prime and the least composite number?

Sum of infinite terms of G.P is 12 and the first term is 8. What is the fourth term of the G.P?

Graph of a linear equation is a ____________

For the given matrix A = \(\left( \begin{matrix} 1 \\ 2 \\ 9 \end{matrix}\begin{matrix} 3 \\ 4 \\ 11 \end{matrix}\begin{matrix} 5 \\ 6 \\ 13 \end{matrix}\begin{matrix} 7 \\ 8 \\ 15 \end{matrix} \right) \) the order of the matrix A^T is

Consider the following statements:
(i) The HCF of x+y and x⁸-y⁸ is x+y
(ii) The HCF of x+y and x⁸+y⁸ is x+y
(iii) The HCF of x-y nd x⁸+y⁸ is x-y
(iv) The HCF of x-y and x⁸-y⁸ is x-y

The real roots of the quardractic equation x²-x-1 are ___________

Axis of symmetry in the term of vertical line seperates parabola into ___________

If in \(\triangle\)ABC, DE || BC, AB = 3.6 cm, AC = 2.4 cm and AD = 2.1 cm then the length of AE is

In the adjacent figure \(\angle BAC\) = 90^o and AD\(\bot \)BC then 

The ratio of the areas of two similar triangles is equal to ____________

A line which intersects a circle at two distinct points ic called ____________

Two concentric circles if radii a and b where a>b are given. The length of the chord of the circle which touches the smaller circle is ____________

The area of triangle formed by the points (−5, 0), (0, −5) and (5, 0) is

The straight line given by the equation x = 11 is

Find the equation of the line passing the point which is parrallel to the y axis (5, 3) is ____________

The y-intercept of the line 3x - 4y + 8 = 0 is ___________

The angle of depression of the top and bottom of 20 m tall building from the top of a multistoried building are 30° and 60° respectively. The height of the multistoried building and the distance between two buildings (in metres) is

If (sin α + cosec α)² + (cos α + sec α)² = k + tan²α + cot²α, then the value of k is equal to

Given that sin ∝ = \(\frac{1}{2}\) and cos β = \(\frac{1}{2}\), then the value of (∝ + β) is ___________

If A is an assets angle of Δ ABC, right angle at 3, then the value of sin A T cos A is ___________

9 sec²A  - 9tan²A = ___________

The height of a right circular cone whose radius is 5 cm and slant height is 13 cm will be

A shuttle cock used for playing badminton has the shape of the combination of

How many balls, each of radius 1 cm, can be made from a solid sphere of lead of radius cm?

The material of a cone is converted into the shape of a cylinder of equal radius. If the height of the cylinder is 5 cm, then height of the cone is ___________

A spherical steel ball is melted to make 8 new identical balls. Then the radius each new ball is how much times the radius of the original ball?

If a letter is chosen at random from the English alphabets {a, b....,z}, then the probability that the letter chosen precedes x ____________

The range of the data 8, 8, 8, 8, 8. . . 8 is

Which of the following is incorrect?

The standard deviation is the ____ of variance 

If the smallest value and co-efficient of range a data are 25 and 0.5 respectively. Then the largest value is ___________

If the probability of non-happening of an event is, then probability of happening of the event is ___________

A relation ‘f’ \(X \rightarrow Y\) is defined by f(x) = x² - 2 where x \(\in \) {-2, -1, 0, 3} and Y = R
(i) List the elements of f
(ii) Is f a function?

In each of the following cases state whether the function is bijective or not. Justify your answer.
i. f : R ⟶ R defined by f(x) = 2x + 1
ii. f : R ⟶ R defined by f(x) = 3 - 4x²

Let A =  {1,2, 3, 4} and B = {-1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12} Let R = {(1, 3), (2, 6), (3, 10), (4, 9)} \(\subseteq \) A x B bea relation. Show that R is a function and find its domain, co-domain and the range of R.

Let A = {0, 1, 2, 3} and B = {1, 3, 5, 7, 9} be two sets. Let f: A \(\rightarrow\)B be a function given by  f(x) = 2x + 1. Represent this function as  a set of ordered pairs.

Let A = {0, 1, 2, 3} and B = {1, 3, 5, 7, 9} be two sets. Letf: A \(\rightarrow\)B be a function given by  f(x) = 2x + 1. Represent this function as  a table .

Check whether the following sequences are in A.P. or not?
 \(3\sqrt { 2 } ,5\sqrt { 2 } ,7\sqrt { 2 } ,9\sqrt { 2 } \),.....

Which of the following sequences are in G.P.?
4, 44, 444, 4444,...

Find the square root of the following polynomials by division method 16x⁴ + 8x² + 1

Determine the nature of roots for the following quadratic equations
2x² - 2x + 9 = 0

Is \(\triangle\)ABC ~ \(\triangle\)PQR?

D and E are respectively the points on the sides AB and AC of a \(\triangle\)ABC such that AB = 5.6 cm, AD = 1.4 cm, AC = 7.2 cm and AE = 1.8 cm, show that DE || BC

Show that the straight lines x - 2y + 3 = 0 and 6x + 3y + 8 = 0 are perpendicular.

What is the inclination of a line whose slope is 1

Find the equation of a line through the given pair of points (2, 3) and (-7, -1)

The horizontal distance between two buildings is 70 m. The angle of depression of the top of the first building when seen from the top of the second building is 45°. If the height of the second building is 120 m, find the height of the first building.

prove the following identitity tan⁴\(\theta \) + tan²\(\theta \) = sec⁴\(\theta \) - sec²\(\theta \) .

Find the diameter of a sphere whose surface area is 154 m².

The radius and height of a cylinder are in the ratio 5 : 7 and its curved surface area is 5500 sq.cm. Find its radius and height.

The standard deviation and mean of a data are 6.5 and 12.5 respectively. Find the coefficient of variation.

A and B are two events such that, P(A) = 0.42, P(B) = 0.48, P(A ∩ B) = 0.16. Find (i) P(not A) (ii) P(not B) (iii) P(A or B)

A functionf: [-7,6) \(\rightarrow\) R is defined as follows.

\(\cfrac { 4f(-3)+2f(4) }{ f(-6)-3f(1) } \)

If R = {(a, -2), (-5, b), (8, c), (d, -1)} represents the identity function, find the values of a, b, c and 

Which of the following list of numbers form an AP? If they form an AP, write the next two terms:
-2, 2, -2, 2, -2

At t minutes past 2 pm, the time needed to 3 pm is 3 minutes less than \(\frac {t^{2}}{4}\). Find t.

A = \(\left( \begin{matrix} 3 & 0 \\ 4 & 5 \end{matrix} \right) \), B = \(\left( \begin{matrix} 6 & 3 \\ 8 & 5 \end{matrix} \right) \), C = \(\left( \begin{matrix} 3 & 6 \\ 1 & 1 \end{matrix} \right) \) find the matrix D, such that CD – AB = 0

If A = \(\left[ \begin{matrix} 1 & 8 & 3 \\ 3 & 5 & 0 \\ 8 & 7 & 6 \end{matrix} \right] \), B = \(\left[ \begin{matrix} 8 & -6 & -4 \\ 2 & 11 & -3 \\ 0 & 1 & 5 \end{matrix} \right] \), C = \(\left[ \begin{matrix} 5 & 3 & 0 \\ -1 & -7 & 2 \\ 1 & 4 & 3 \end{matrix} \right] \) compute the following
3A + 2B - C

Find two consecutive natural numbers whose product is 20.

ABCD is a quadrilateral in which AB=AD, the bisector of \(\angle\)BAC and \(\angle\)CAD intersect the sides BC and CD at the points E and F respectively. Prove that EF||BD

PQ is a chord of length 8 cm to a circle of radius 5 cm. The tangents at P and Q intersect at a point T. Find the length of the tangent TP.

Find the equation of a straight line through the point of intersection of the lines 8x + 3y = 18, 4x + 5y = 9 and bisecting the line segment joining the points (5, –4) and (–7, 6).

prove that (cosec\(\theta \) - sin\(\theta \)) (sec\(\theta \) - cos\(\theta \)) (tan\(\theta \) + cot\(\theta \)) = 1

If x sin³\(\theta \) + ycos³\(\theta \) = sin\(\theta \) cos\(\theta \) and x sin\(\theta \) = ycos\(\theta \), then prove that x² + y² = 1.

A bird is flying from A towards B at an angle of 35°, a point 30 km away from A. At B it changes its course of flight and heads towards C on a bearing of 48° and distance 32 km away.
How far is B to the West of A? (sin 55° = 0.8192, cos 55° = 0.5736, sin 42° = 0.6691.cos 42° = 0.7431)

If ATB=90^o then prove that
\(\sqrt { \frac { tanA\quad tanB+tanA\quad cotB }{ sinA\quad secB } } -\frac { { Sin }^{ 2 }A }{ { Cos }^{ 2 }A } =tanA\)

Calculate the mass of a hollow brass sphere if the inner diameter is 14 cm and thickness is 1mm, and whose density is 17.3 g/ cm³.

A cylindrical glass with diameter 20 cm has water to a height of 9 cm. A small cylindrical metal of radius 5 cm and height 4 cm is immersed it completely. Calculate the raise of the water in the glass?

Find the number of coins, 1.5 cm in diameter and 2 mm thick, to be melted to form a right circular cylinder of height 10 cm and diameter 4.5 cm.

The marks scored by 10 students in a class test are 25, 29, 30, 33, 35, 37, 38, 40, 44, 48. Find the standard deviation.

The mean of the following frequency distribution is 62.8 and the sum of all frequencies is 50. Compute the missing frequencies f₁ and f₂.

Prices of peanut packets in various places of two cities are given below. In which city, prices were more stable?

Construct a \(\triangle\)PQR such that QR = 6.5 cm,\(\angle\)P = 60^oand the altitude from P to QR is of length 4.5 cm.

Draw the two tangents from a point which is 5 cm away from the centre of a circle of diameter 6 cm. Also, measure the lengths of the tangents