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Question 16

The product of $7and6\frac{3}{4}$ is

(a) $42\frac{1}{4}$
(b) $47\frac{1}{4}$
(c) $42\frac{3}{4}$
(d) $47\frac{3}{4}$

AB is a line segment which is inclined to line XY, such that they intersect at point O. A line PQ is drawn which intersects the line XY at point P at the same angle of inclination as AB. Line PQ is _________ to line segment AB.

If you are asked to construct $△$APQ $\sim$ $△$ABC with the scale factor $\frac{3}{5}$, which of the following are correct? In $△ABC,AB=4cm$, $BC=3cm$ and $\angle ABC={90}^{\circ }$.​

Which term of the sequence 3, 8, 13, ........ is 78 ?

If A is involuntory matrix and I is unit matrix of same order, then (I-A)(I+A) is

In $△ABC$, right angled at C, AC=4cm and $\angle BAC={60}^o$, find the length of side BC

If sin (A + B) = 1 and cos (A - B) = $1,0^o<A+B\le {90}^o,A\ge B$ find A and B.

Find the sum:
(i) 2+4+6+...+200
(ii) 3+11+19+...+803
(iii) (-5)+(-8)+(-11)+...+(-230)
(iv) 1+3+5+7+...+199
(v) $7+10\frac{1}{2}+14+...+84$
(vi) 34+32+30+...+10
(vii) 25+28+31+...+100
(viii) $18+15\frac{1}{2}+13+...+(-49\frac{1}{2})$

If a and b can take values 1, 2, 3 and 4, then the number of equations of the form $a{x}^2+bx+1=0$ having real roots is _____.

The sum of the digits of a two-digit number is 15.The number obtained by interchanging the digits exceeds the given number by 9.The number is

(a) 96 (b) 69 (c) 87 (d)78

There are 25 trees at equal distances of 5 m in a line with a water tank, the distance of the water tank from the nearest tree being 10 m. A gardener waters all the trees separately, starting from the water tank and returning back to the water tank after watering each tree to get water for the next, Find the total distance covered by the gardener in order to water all the trees.

ABC is a right-angled triangle right angled at A. A circle is inscribed in it the lengths of the two sides containing the right angle are 6 cm and 8 cm. Find the radius of the circle. [4 MARKS]

In the given figure, find $a+b+c+d$.

D and E are points on the sides AB and AC respectively of a $△$ABC such that DE || BC

and divides $△$ABC into two parts, equal in area. Find $\frac{BD}{AB}$

Find the value of the trigonometric expression
$\cot \left(\frac{\pi }{20}\right)\cot \left(\frac{3\pi }{20}\right)\cot \left(\frac{5\pi }{20}\right)\cot \left(\frac{7\pi }{20}\right)\cot \left(\frac{9\pi }{20}\right)$.

If $\overrightarrow{a}$ and $\overrightarrow{b}$ are the position vectors of points A and B respectively, find the position vector of point C on AB produced such that $\overrightarrow{AC}=3\overrightarrow{AB}$

A coin is tossed. If the outcome is a head, a die is thrown. If the die shows up an even number, the die is thrown again. What is the sample space for the experiment?

Solve the inequality : $3-4x\ge x-22$ given that $x\in$ N.

abx² +(b²-ac) x-bc=0

How many terms of the series 54,51, 48, ..........be taken so that their sum is 513 ?

A man purchased 47 stamps of 20 p and 25 p for Rs.10.Find the number of each type of stamps.

What is the cumulative frequency of the modal class of the following distribution?

$\begin{array}{cccccccc}Class& 3-6& 6-9& 9-12& 12-15& 15-18& 18-2& 21-24\\ Frequency& 7& 13& 10& 23& 4& 21& 16\end{array}$

How many coins 1.75 cm in diameter and 2 mm thick must be melted to form a cuboid $11cm\times 10cm\times 7cm$ ?

Show that the system of equations $6x+5y=11,9x+\frac{15}{2}y=21$ has no solution.

A path of 4 m width runs round a semi-circular grassy plot whose circumference is $163\frac{3}{7}m$. Find:

(i) The area of the path
(ii) The cost of gravelling the path at the rate of Rs. 1.50 per square metre
(iii) The cost of turfing the plot at the rate of 45 paise per $m^2$.

What is the probability of a sure event?
(a) 0 (b) $\frac{1}{2}$ (c) 1 (d) less then 1

Find two consecutive odd positive integers, sum of whose squares is 970.

On dividing a polynomial p(x) by a nonzero polynomial q(x), let g(x) be the quotient and r(x) be the remainder then p(x) = q(x).g(x)+r(x), where

(a) r(x) = 0 always

(b) deg r(x) < deg g(x) always

(c) either r(x) = 0 or deg r(x) < deg g(x)

(d) r(x) = g(x)

In a circle of a radius 21 cm, an arc subtends an angle of ${60}^{\circ }$ at the centre. Find the length of the arc.

The median class for the following data is
$\begin{array}{cccccc}\text{Marks}& \text{Below 10}& \text{Below 20}& \text{Below 30}& \text{Below 40}& \text{Below 50}\\ \text{No. of students}& 5& 10& 23& 31& 40\end{array}$

Find four numbers in A.P. whose sum is 20 and the sum of whose squares is 120.

Using binomial theorem, find the value of $(99{)}^4$.

Find the coordinates of the centre of the circle passing through the points (0, 0), (–2, 1) and (–3, 2). Also, find its radius.

Solve the following quadric equations by factorization method only $4x^2-12x+25=0$

Every pair of positive integers a and b there exist a unique pair of whole numbers q and r such that a=bq+r give examples of a and b wherever possible satisfying.

a r=0

b q=0

c r>b

d If a<b what can be said about q and r.

A sum of money at simple interest amounts to Rs. 815 in 3 years and to Rs. 854 in 4 years. The sum is

Find the sum of odd interges from 1 to 2001 ,

Show that the function f: N$\to$N given by f(1) = f(2) = 1 and f(x) = x – 1, for every x $\ge$ 3, is onto but not one-one.

A tent is cylindrical to a height of 4 m and conical above it. If its diameter is 105 m and its slant height is 40 m, the total area of the canvas required is

The common ratio of the G.P 256,-128,64,-32.. is

Write in factorised form: $\frac{2}{x^2}-\frac{5}{x}+2=0$

The sum of the ages of a father and his son is 45 years. Five years ago, the product of their ages (in years) was 124. Determine their present ages.

Find the mean deviation about mean for the following data

38, 70, 48, 40, 42, 55, 63, 46, 54, 44