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Vertical cross-section of a right circular cylinder is always a

(a) square (b) rectangle

(c) rhombus (d) trapezium

Question 76

In the following question, state whether the given statements are true (T) or false (F).
The number of multiples of a given number is finite.

If sin $\alpha$ = 5/13 and sin $\beta$ = $\frac{4}{5}$ then the value of cos $\alpha$ cos $\beta$ - sin $\alpha$ sin $\beta$ is

If $\overrightarrow{a},\overrightarrow{b}$ and $\overrightarrow{c}$ are three non – coplanar vectors, then $(\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}).\left(\right(\overrightarrow{a}+\overrightarrow{b})\times (\overrightarrow{a}+\overrightarrow{c}\left)\right)$ equals

Compute the value of 'a' by adding the following pair of equations:

2a + b = 15

3a - b = 10

Question 8

If represent some integers on the number line, then descending order of these numbers is

_{​​​​​​​​​ Radha made a picture aeroplane with coloured paper as shown in the figure 12.15 find the total area of the paper used}

In the given figure, ABCD is a rhombus. If OB = 6 units, OC = 8 units and BE = 4 units. Find the length of CE. (CE is perpendicular to AB)

The decimal expansions that correspond to rational numbers is.

To represent 2.5162 which of the following method would be used.

The surface area of a cube is 864 cm². Its volume is

Without performing long division determine the type of decimal expansion of the rational number 171/3125.

The number of observations in a group is 40. If the mean of first 10 is 4.5 and that of the remaining 30 is 3.5, then the mean of the whole group is

In an equilateral triangle ABC; points P, Q and R are taken on the sides AB, BC and CA respectively such that AP= BQ = CR. Prove that triangle PQR is equilateral.

Which of the following options represents diagonal(s) to the given quadrilateral?

Prove that a triangle AC is isosceles, if:

(i) altitude AD bisects angle $\angle$ BAC, or

(ii) bisector of angle BAC is perpendicular to base BC.

The population of students of four major cities in India in a particular year is given below:

Choose the correct representation of the bar graph to represent the above data

In the figure, ∠ POR and ∠QOR form a linear pair. If a – b = 70^o the values of a and b are

The set of all $x$ satisfying $4^{x^2+2}-9\times 2^{x^2+2}+8=0$ consists of

You deposit Rs. 400 in a bank account paying $5\%$ simple interest per year. How much interest would you have earned after 3 years?

What is the remainder when q(x)= 2x³ – x² + x - 1 is divided by x+2?

Find the number of integers x which satisfies the inequality $\frac{3}{1+\sqrt{3}}$ < x < $\frac{3}{\sqrt{5}-\sqrt{3}}$

A container holds 500 mL of $C{O}_2$ at ${20}^{\circ }C$ and 742 torr. What will be the volume of the $C{O}_2$ if the pressure is increased to 795 torr?

The mid value of class range is 47.5 and the lower limit of the class range is 30. What will be the upper limit of this class range ?

Join the two sentences using the correct pronoun.

Ravi is going to the club. I am going to the club.

Ravi and __ are going to the club.

Distance between equal chords, $AB$ and $CD$ of a circle with centre, $O$ and radius, $5cm$ is $8cm$. Find the length of the the chords.

A chord 6 cm long is 1 cm away from the centre of the circle. What is the length of a chord which is 2 cm away from the centre?

Find the point that divides A(2, 4) and B(6, 8) in the ratio a : 1.

A hollow garden roller, $63cm$ wide with a girth of $440cm$, is made of $4cm$ thick iron. Find the volume of the iron.

In the adjoining figure, AOB is a straight line. If x : y : z=4:5 :6, then y =?

(a) ${60}^{\circ }$

(b) ${80}^{\circ }$

(c) ${48}^{\circ }$

(d) ${72}^{\circ }$

If $3^x=5^y=(75{)}^z,showthatz=\frac{xy}{2x+y}$

In the figure, $\angle PQR$$={100}^{\circ }$, where $P,Q,$ and $R$ are points on a circle with center $O.$ Find $\angle OPR.$

Question 53

State whether the given statement is True or False.

In a rational number, denominator always has to be a non-zero integer.

The sides of a quadrangular field taken in order are 26 m, 27 m, 7 m and 24 in respectively. The angle contained by the last two sides is a right angle. Find its area.

Two straight lines AB and CD intersect one another at the point O. If $\angle AOC+\angle COB+\angle BOD={274}^0$, then $\angle AOD$

$29,29,27,25,25,21,23,17,$__,__ complete the miscellaneous series.

A.$17,19$

B.$21,13$

C.$21,19$

D.$19,27$

$\frac{8a+2b}{8a-2b}=\frac{7}{1}$, then b : a =

If Rs 1750 amounts to Rs 1933.75 in a time period of 3 years, what is the rate of simple interest?

In the circle shown alongside,the chords AB and AC are of same length. The bisector of $\angle$A intersects the chord BC at D and meets the circle at E. Then which of the following is/are true?

If $\sqrt{10}=3.162$, then find the value of $\frac{1}{\sqrt{10}}$. [2 MARKS]

The linear equation 5x - y = 2x - 1 has

$\begin{array}{cc}\text{Assertion (A)}& \text{Reason (R)}\\ \text{The diagonals of a}||gm\text{bisect each}& \text{If the diagonals of a}||gm\text{are equal}\\ \text{other}& \text{and intersect at right angles then}\\ & \text{the parallelogram is a square.}\end{array}$

The correct answer is: (a)/(b)/(c)/(d).

If $p\left(x\right)=x^2-2\sqrt{2}x+1$ then $p\left(2\sqrt{2}\right)=?$
(a) $0$
(b) $1$
(c) $4\sqrt{2}$
(d) $-1$

$\text{A cone and a hemisphere have equal bases and equal volumes. The ratio of their heights is}\left(a\right)1:2\left(b\right)2:1\left(c\right)4:1\left(d\right)\sqrt{2}:1$