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A man completes 3/8 of a job in 12 days. At this rate, how many more days will it take him to finish the job?

Find the sum of :
(i) the first 1000 positive integers

(ii) the first n positive integers

Find all the zeros of the polynomial $2x^3+x^2-6x-3,$ if two of its zeros are $-\sqrt{3}$ and $\sqrt{3}$.

Question 88

Area of an isosceles triangle is $48c{m}^2.$ If the altitudes corresponding to the base of the triangle is 8 cm, find the perimeter of the triangle.

In the given figure 'O' is the center of the circle. SP and TP are the two tangents at S and T respectively. $\angle SPT$ is ${50}^{\circ }$, the value of $\angle SQT$ is:

A pole has to be erected at a point on the boundary of a circular park of diameter 17 meters in such a way that the difference of its distances from two diametrically opposite fixed gates A and B on the boundary is 7 metres. Is it the possible to do so? If yes, at what distances from the two gates should the pole be erected?

Sales tax depends on?

Which of the following cannot be the probability of an event?
(a) $\frac{1}{3}$
(b) $0.1$
(c) $3\%$
(d) $\frac{17}{16}$

If $y=\sqrt{\sqrt{7}+7+\sqrt{8+2\sqrt{7}}}-\sqrt{7}$, then the value of y will be:

Two different dice are thrown together. Find the probability that the numbers obtained have

(i) even sum (ii) even product.

If the sum of first m terms of an AP is n and the sum of first n terms is m , then show that sum of first (m+n) term is -(m+n).

If 4/5 , a, 2 are three consecutive terms of an A.P., then the value of a is:

If a digit is chosen at random from the digits 1, 2, 3, 4, 5, 6, 7, 8, 9 then the probability that it is odd is

If log 5 = x, find the value of log 625.

Show that 12 raise to n cannot end with the digit 0 or 5 for any natural number n

What is the quotient when 2m^2-m+3 is divided by (2-m) leaving a remainder 9

If α is the negative root of the equation 1006 $x^2$ + 1008x - 2014 = 0, find 1006α + 2015=

A square matrix $\left(a_{ij}\right)$ where $a_{ij}$= 0 for i $\ne$ j and $a_{ij}$= k (constant) for i = j is called __

Using the concept of slope, prove that the points (a, b +c), (b,c+a) and (c, a+b) are in a straight line.

Find the proportionality constant of the following table.

$$\begin{array}{ccccccc}No.ofworkers\left(x\right)& 3& 4& 6& 8& 9& 16\\ No.ofdays\left(y\right)& 96& 72& 48& 36& 32& 18\end{array}$$

The position of the centre of gravity of a (i) Rectangular lamina and (ii) cylinder is

What is G.C.D?

Solve for x and give the answer correct to 2 decimal places $2x^2-10x+5=0$

Given that () is a factor of ³ – ² + + 2, factorise the expression completely.

A card is drawn at random from a well- suffled deck of 52 cards. Find the probability of getting
(i) a queen (ii) a diamond
(iii) a king or an ace (iv) a red ace.

An A. P. consists of 50 terms of which $3^{rd}$ term is 12 and the last term is 106. Find the ${29}^{th}$ term of the A. P.

$f:R\to R$ is defined as $f\left(x\right)=x^4-6x^2+12$. The range of f(x) is

In the given figure, AB and AC are tangents to a circle with centre O and radius 8 cm. If OA = 17 cm, then the length of AC (in cm) is

(a) 9 (b) 15 (c) $\sqrt{353}$ (d) 25

A 36-m-long,15-m-broad verandah is to be paved with stones, each measuring 6 dm by 5 dm. How many stones will be required?

The difference between the circumference and radius of a circle is 37 cm. The area of the circle is

(a) 111${cm}^2\left(b\right)184{cm}^2\left(c\right)154{cm}^2\left(d\right)259c{m}^2$

In Figure a $\Delta$ ABC is drawn to circumscribe a circle of radius 4 cm such that the segments BD and DC are of lengths 8 cm and 6 cm respectively. Find the lengths of sides AB and AC, when area of $\Delta$ ABC is 84 $c{m}^2$.

What is the ratio of the sum of all observations to the number of observations called?

What length of a solid cylinder 2 cm in diameter must be taken to recast into a hollow cylinder of length 16 cm, external diameter 20 cm and thickness 2.5 mm?

$\frac{sin\theta }{(1+cos\theta )}+\frac{1+cos\theta }{sin\theta }=2cosec\theta$

A circle is inscribed inside a right-angled triangle. If BC = a, CA= b and AB = c, then the radius of the circle is ____.

find x if ${\log }_2(x-5)>3$

tan38°-cot22°=?

Choose the option which contains set of prime numbers.

A cylindrical tub of radius 12 cm contains water to a depth of 20 cm. A spherical form ball of radius 9 cm is dropped into the tub and thus the level of water is raised by h cm. What is the value of h ?

Solve each of the following quadratic equations:
$6x^2+x-12=0$

Ramesh travels 760 km to his home partly by train and partly by car. He takes 8 hours if he travels 160 km. by train and the rest by car.He takes 12 minutes more if the travels 240 km by train and the rest by car. Find the speed of the train and car respectively.

A container of length $4\text{m}$, width $2\text{m}$ and height $3\text{m}$ is kept on a horizontal floor. A bee enters the container from a hole at bottom-most corner $\left(A\right)$ and comes out of the hole$\left(B\right)$ at diagonally opposite corner. If the displacement of bee is maximum when it comes out, what is its displacement ?

One of the factors of $(25x^2-1)+(1+5x{)}^2$ is

A) $5+x$
B) $5-x$
C) $5x-1$
​​​​​​​D) $10x$

Find all pairs if consecutive odd positive integers,both of which are smaller than 10,such that their sum is more than 11.