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The factors of x⁴ + x² + 25 are



(a) (x² + 3x + 5) (x² − 3x + 5)



(b) (x² + 3x + 5) (x² + 3x − 5)



(c) (x² + x +5) (x² − x + 5)



(d) none of these

If each edge of a cube is increased by $50\%$, then its total surface area is increased by .

An ant moves 3 units along the positive direction of the X-axis from the origin and reaches a point P, then moves 4 units from P along the negative direction of the Y-axis and reaches a point Q. What are the coordinates of points P and Q?

Two persons are ${}^{\prime }{a}^{\prime }$ metres apart and the height of one is double that of the other. If from the middle point of the line joining their feet, an observer who looks at the top of their head , finds the angular elevations to be complementary, then the height of the shorter person in metres is :

Question 86 (v)

Using suitable identities, evaluate the following:

$(1005{)}^2$

$\text{ABC is a triangle such that AB = 10 cm}\text{and AC = 3 cm. Which of the following}\text{statements are true?}$

Here AB $\parallel$ CD. If the altitude of $△$ACD is 6 cm and CD is 8 cm then the area of $△$BCD is:

Find out how many times did 4 or a greater than 4 number appeared.

$$\begin{array}{ccccccc}Dice& 1& 2& 3& 4& 5& 6\\ Frequency& 10& 12& 6& 4& 8& 10\end{array}$$

Find the HCF of 360 and 18144 by prime factorization.

In the given figure, QR is parallel to AB and DR is parallel to QB. If PD = 4 cm and PA = 9 cm, then find PQ.

Question 12

To warn ships for underwater rocks, a lighthouse spreads a red coloured light over a sector of angle ${80}^{\circ }$ to a distance of 16.5 km. Find the area of the sea over which the ships are warned.

$(Use\pi =3.14)$

Match the two columns.

$\begin{array}{ccc}& \text{Column-I}& \text{Column-II}\\ & \text{(A) Data which is collected for the first time by the statistical}& \text{(p) Secondary data}\\ & \text{investigator or with the help of his workers is called}& \\ & \text{(B) These are the data already collected by a person or a}& \text{(q) Variable}\\ & \text{society and these may be in published form.}& \\ & \text{These data should be carefully used.}& \\ & \text{(C) When the data is compiled in the same form and order in}& \text{(r) Primary Data}\\ & \text{which it is collected, it is known as}& \\ & \text{(D) A quantity which can vary from one individual to another is}& \text{(s) Raw Data}\\ & \text{called}& \end{array}$



Choose the correct option:

If (x-2) is the factor of x² + 2x+ a, find the value of 'a'.

If $lo{g}_{7}2=m,thenlo{g}_{49}28$ is equal to

Three angles of a quadrilateral are in the ratio 8 : 11 : 7. If fourth angle is 100°, then the other three angles of the quadrilateral are respectively ___.

A representation of data in which a circle is divided into different parts to represent the data is :

Which of the following is/are not the radical expression?

In $\Delta ABC$, $\angle B={105}^{\circ }$, $\angle C={50}^{\circ }$. Find $\angle A$. [1 MARK]

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.

$$\begin{array}{cccccc}ClassInterval& 0-10& 10-20& 20-30& 30-40& 40-50\\ Numberofstudents& 3& 4& 13& 15& 5\end{array}$$

1. 28.75

Find the remainder when $x^3+4x^2$ + 4x -3 is divided by x.

ABCD is a parallelogram, M is the mid-point of BD and BM bisects $\angle B$. Then $\angle AMB=$

The line through P (4, 3) intersects y – axis at Q.

$\sqrt{10}\times \sqrt{15}$ is equal to

In the figure, ABC is a quadrant of a circle of radius 14 cm and a semicircle is drawn with BC as diameter. Find the area of the shaded region. [2 MARKS]

Construct the angles of the following measurements:

(i) 30° (ii) (iii) 15°

Factorize $\frac{8}{27}{x}^3+1+\frac{4}{3}{x}^2+2x$

Three girls Ishita, Isha and Nisha are playing a game by standing on a circle of radius $20m$ drawn in a park. Ishita throws a ball to Isha, Isha to Nisha and Nisha to Ishita. If the distance between Ishita and Isha and between Isha and Nisha is $24m$ each, what is the distance between Ishita and Nisha?