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A trader buys an article for Rs. 3000. He spent Rs. 1000 on transportation of the articles. If he wants to make a profit of 14% ,the selling price of the article including the 8% sales tax is Rs. ___

Find the roots of the quadratic equation $\sqrt{2}{x}^2+7x+5\sqrt{2}=0$ using factorization method

What is the hcf and lcm of 90 and 126

Question 1 (iv)
Which of the following pairs of linear equations has a unique solution, no solution or infinitely many solutions? In case there is a unique solution, find it by using cross multiplication method.
x - 3y - 7 = 0 ; 3x - 3y - 15= 0

Question 73

Find two numbers, whose sum is 100 and whose ratio is 9 : 16.

A conical dome of a palace is supported by a cylindrical pillar, both having the same radius. If the ratio of the height of cylinder to cone is 4:3, the ratio of their volume is

\text{(B) Chord ED is parallel to the diameter AC of the circle.}\text{If} \angle CBE = 55^\circ, \text{then calculate} \angle DEC\)

The water in a cubical tank of side 10 m is transferred to completely fill a cuboidal tank of length 5 m, breadth 10 m and height h. Then the height of the cuboidal tank (in metres) is ___

Question 155(ii)

What happens when 1 cm worms are sent through these hook-ups?

Find the number of elements which satisfies the given inequalities.

$\frac{-5}{2}+2x\le \frac{4x}{3}\le \frac{4}{3}+2x$, where, x $ϵ$ whole number.

A chord of a circle of radius 15 cm subtends an angle of ${60}^{\circ }$ at the centre. Find the areas in $c{m}^2$ of the corresponding minor and major segments of the circle.(Use $\pi =3.14$ and $\sqrt{3}=1.73$) [3 MARKS]

If A=$\left[\begin{array}{c}1\\ -2\end{array}\right],B=\left[\begin{array}{c}2\\ 2\end{array}\right]andC=\left[\begin{array}{c}-1\\ 2\end{array}\right]$, find 2A+B-5C

Triangle PQR is an isosceles right triangle right angled at Q.If PR= .What is the value of each of the equal sides?

If tan theta = 12/5, then find the value of 1+sin theta/ 1- sin theta

The angle of elevation of the top of a tower from two points at a distance of 4 m and 9 m from the base of the tower and in the same straight line with it are complementary. prove that the height of the tower is 6 metres .

In a traingle $ABC,2a^2+4b^2+c^2=4ab+2ac,$ then numerical value of $\cos B$ is equal to

If the point$(x,y)$ is equidistant from points (3, 5) and (7, 1) , then $y$ = _____.

Question 13
In the given figure, l||m and line segments AB, CD and EF are concurrent at point P. Prove that
$\frac{AE}{BF}=\frac{AC}{BD}=\frac{CE}{FD}$.

Use Euclid division lemma show that the cube of any positive integer is of the form8m,8m+1,8m+3,8m+5,8m+7

Find the equation of pair of tangents drawn to the circle $x^2+y^2-4x+4y=0$ from the point (2, 2)

If $A=\left(\begin{array}{cc}-6& -1\\ 9& 1\end{array}\right),B=\left(\begin{array}{cc}2& 0\\ -3& 5\end{array}\right)\text{and}C=\left(\begin{array}{cc}-1& 8\\ 7& -7\end{array}\right)$
Find A+B-C

A dice is thrown once. What is the probability that the

i) number is even

ii) number is greater than 2?

A gas obeys the equation of state P(V-b) = RT (The parameter b is constant). The slope for an isochore will be:

The sum of ages of M, N and 0 is 50 yr. What is N's age? I. N is 10 yr older than M. II. 0 is 30 yr old.

The 16th term of an AP is 5 times its 3rd term. If its 10th term is 41, find the sum of its first 15 terms.

The equivalent conductance of NaCl at concentration C and at infinite dilution are ${\lambda }_C$ and ${\lambda }_{\infty }$ respectively. The correct relationship between ${\lambda }_{C}and{\lambda }_{\infty }$ is given as (where, the constant B is positive)

For what value of k does the system of equations x+2y=3,5x+ky+7=0 have(i) a unique solution,(ii) no solution?

Also,show that there is no value of k for which the given system of equations has infinitely many solutions.

A chord of a circle of radius 10 cm subtends a right angle at the centre. Find the area of the minor segment.

[ Use $\pi$ = 3.14]

In the given figure, PQ = 24 cm, PR = 7 cm and O is the centre of the circle. Find the area of the shaded region. [Take $\pi =3.14$]

If the product of two numbers is 1050 and thier HCF is 25, find their LCM.

A box contains 25 bulbs. It is known that 13 of these bulbs are defective. Now I draw out one bulb from the box. This bulb is found to be defective. Now I again draw out one bulb in random from the box. What is the probability that a bulb is defective during this second draw too?

If tan (A - B) = $\frac{1}{\sqrt{3}}$ and tan $(A+B)=\sqrt{3},0^{\circ }<(A+B)<{90}^{\circ }$ and A > B then find A and B.

A box contains 25 cards numbered from 1 to 25. A card is drawn at random from the bag. Find the probability that the number on the drawn card is (i) divisible by 2 or 3, (ii) prime number.

Find the least number of square tiles required to pave the ceiling of a room 15 m 17 cm long and 9 m 2 cm broad.

A chord AB of a circle, of radius 14 cm makes an angle of ${60}^{\circ }$ at the centre of the circle. Find the area of the minor segment of the circle. (Use $\pi =\frac{22}{7}$)

By what number should ${\left(\frac{-3}{2}\right)}^{-3}$be divided so that the quotient may be ${\left(\frac{4}{27}\right)}^{-2}$?

Verify that 3, -2, 1 are the zeros of the cubic polynomial $p\left(x\right)=x^3-2x^2-5x+6$ and verify the relation betweeen its zeros and coefficients.

Show that: $\frac{cot({90}^{\circ }-\theta )}{cose{c}^2\theta }$.$\frac{sec\theta .co{t}^3\theta }{si{n}^2({90}^{\circ }-\theta )}$ = $\sqrt{ta{n}^2\theta +1}$

Which one of the following species has a square planar structure?