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sin 25° sin 50° sin 90° sec 40° sec 65° = ___.

Question 127(iii)

An insect is on the 0 point of a number line, hopping towards 1. She covers half the distance from her current location to 1 with each hop.
So, she will be at $\frac{1}{2}$ after one hop, $\frac{3}{4}$ after two hops and so on.



Will the insect ever get to 1? Explain.

Identify the correct statements:

(i) A matrix with 3 columns and 2 rows is of order $3\times 2$.
(ii) A matrix with 5 columns and 8 rows is of order $8\times 5$
(iii) If the order of a matrix is $4\times 3$, then it has 12 elements.
(iv) If the order of a matrix is $5\times 3$, then it has 10 elements.

From a point q the length of the tangent to the tangent to a circle is 24 cm and the distance of q form the centre is 25 cm find the radius of the circle

A solid is in the form of a cone standing on a hemi-sphere with both their radii being equal to 8 cm and the height of cone is equal to its radius. Find, in terms of it, the volume of the solid.

Given, $tan(A+B)=\sqrt{3}$ and $tan(A-B)=\frac{1}{\sqrt{3}}$

If $B<A<{90}^{\circ }$, then,
A = ___
B = ___
(If your answer is ${20}^{\circ }$, then type 20).

The given table shows the Marks obtained by students in Mathematics.

$\begin{array}{cc}\text{Marks}& \text{No. of Students}\\ 0-10& 3\\ 10-20& 7\\ 20-30& 12\\ 30-40& 15\\ 40-50& 20\\ 50-60& 9\\ 60-70& 8\\ 70-80& 16\\ 80-90& 14\\ 90-100& 6\end{array}$

Using the table determine the Upper Quartile by drawing an ogive curve.

A line segment AB is divided in the ratio 4:9 by a point C.
Find the length AC (in cm) if AB=26 cm.

1. 8

Can two numbers have 18 as their HCF and 380 as their LCM?

Give reason.

Taylor purchased a rectangular plot of area $634m^2$. The length of the plot is $2m$ more than thrice its breadth. Find the length and breadth (approximate values).

What is the value of tan 75^o?

If the line y = mx + 8 contains the point (-4, 4), calculate the value of m.

The pair of linear equations x + y + 10 = 0 and x + y - 7 = 0 has:

1. \N

Three positive numbers form an increasing GP. If the middle term of the GP is doubled, then new numbers are in AP. Then, the common ratio of the GP is
(IIT JEE Main 2014)

The centre of a circle of radius 13 units is the point (2, 5). P (6, 8) is a point inside the circle. APB is a chord of the circle such that AP = PB. Calculate the length of AB.

A cubical vessel has a side with 'I' cm lenth contained a gas at a pressure of 'p'. when the side of the vessel is made $\frac{1}{2}$ cm, the pressure of gas becomes?

The distance between the points $(cos\theta ,sin\theta )$ and $(sin\theta ,-cos\theta )$ is

The perpendicular distance from the origin to a line is 7 and the perpendicular makes an angle of ${150}^{\circ }$ with the positive x-axis. Find the equation of the line.

The following data shows monthly savings of 100 families . Find the Mode of the Monthly Savings

$\begin{array}{cc}\text{Monthly savings(Rs)}& \text{Number of families}\\ 1000-2000& 14\\ 2000-3000& 15\\ 3000-4000& 21\\ 4000-5000& 27\\ 5000-6000& 25\end{array}$

Identify the Theorem:Every composite number can be expressed (factorised) as a product of primes, and this factorisation is unique, apart from the order in which the prime factors occur.

In the given figure, PAT is tangent to the circle with centre O, at point A on its circumference and is parallel to chord BC. If CDQ is a line segment, show that :

(i) $\angle$ BAP = $\angle$ ADQ

(ii) $\angle$ AOB = 2$\angle$ ADQ

(iii) $\angle$ ADQ = $\angle$ ADB.

Sangeeta invested rupees 16500 partly in 10% Rupees 100 share at rupees 130 and partly in 8% Rs 100 shares at Rs 120if her total annual income from this share is RS 1180 find her investment in each case

$\angle ABC=xand\angle ADC=2x$. Find $\angle COD$

Solve:
$4[1–si{n}^2\theta ][1+ta{n}^2\theta$]

The square of (5$x$ + 1) is equal to 16. What is$x$ ?

Find the total surface area of a cone, if its slant height is 21 m and diameter of its base is 24 m. $[Assume\pi =\frac{22}{7}]$

$\frac{sin{42}^{\circ }}{sec{48}^{\circ }}+\frac{cos{42}^{\circ }}{cosec{48}^{\circ }}-\frac{4}{3}si{n}^2{30}^{\circ }=$___

A student got an experiment to find the volume of a glass slab of fixed thickness using a screw gauge. The dimension of the base was found to be 2 cm $\times$ 5 cm. The screw gauge reading for the thickness is shown below. Find the volume of the glass slab. Given the least count of the screw gauge is 0.01 mm.

​

The radii of two circles are 8 cm and 6 cm respectively. The diameter of the circle having area equal to the sum of the areas of the two circles (in cm) is

If sec θ + tan θ = x then tan θ is equal to

If a cone is cut into two parts by a horizontal plane passing through the mid-point of its axis, then the ratio of the volumes of the upper part of the cone and the entire cone is:

The line through A(-2, 3) and B(4, b) is perpendicular to the line 2x - 4y = 5. Find the value of b.

The Yin-Yang symbol can be explained with the following dimensions. What would be area covered by the Yin (black) region? The radius of the larger circle is, R = 8 cm.

If the discriminant of the quadratic equation 4$x^2$ + px + 25 = 0 is 0, what is the value of p if p $>$ 0?

The following are the marks obtained in Science by students in class X.
The mean of the given data is 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?

$\begin{array}{cc}Marks& Frequency\\ 10-20& 1\\ 20-30& 0\\ 30-40& 0\\ 40-50& 0\\ 50-60& 1\\ 60-70& 5\\ 70-80& 15\\ 80-90& 20\\ 90-100& 3\end{array}$

Which of the following statement is correct?

Factorise $x^2+5x+6$ by using the Factor Theorem.

Find the value of k, if (x −1) is a factor of p(x) in each of the following cases:
$\left(i\right)p\left(x\right)=x^2+x+k$
$\left(ii\right)p\left(x\right)={2x}^2+kx+\sqrt{2}$ [4 MARKS]