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The LCM of two numbers is 1200. Show that the HCF of these numbers cannot be 500. Why?

A man invests Rs 1,680 in buying shares of nominal value Rs 24 and selling at 12% premium. The devidend on the shares is 15% per annum. Calculate :

(i) the number of shares he buys;

(ii) the dividend he receives annually.

Whats the factorization of $6x^2-\frac{11x}{2}+1$

A cylinder and a cone have equal radii of their bases and equal heights. Show that their volumes are in the ratio 3:1.

The ratio of the sum and the product of the roots of $5x^2–14x+8=0$ is

Question 133

An inch is approximately equal to 0.02543 metres. Write this distance in standard form.

Any two digit number can be represented as

If $t_n$ represents $n^{th}$ term of an A. P., $t_2+t_5-t_3=10$ and $t_2+t_9=17$ , find its first term and its common difference.

The quadrilateral formed by joining the angle bisectors of a cyclic quadrilateral is a

Without using tables, evaluate:
(i) sin ${53}^{\circ }÷cos{37}^{\circ }$
(ii) cos ${49}^{\circ }÷sin{41}^{\circ }$
(iii) tan ${66}^{\circ }÷cot{24}^{\circ }$

A point P (a, b) is reflected in the x-axis to P' (2, 3). Write down the values of a and b. P" is the image of P, reflected in the y-axis. Write down the co-ordinates of P". Find the co-ordinates of P", when P is reflected in the line, parallel to y-axis, such that x = 4.

Match the following:

$\begin{array}{cccc}& Point& & Invariantwithrespecttoline\\ a.& (-3,2)& \left(i\right)& y=4\\ b.& (2,-3)& \left(ii\right)& x=4\\ c.& (-1,4)& \left(iii\right)& y=2\\ d.& (4,-1)& \left(iv\right)& x=2\end{array}$

In a right angle triangle $△$ABC, a perpendicular BD is drawn on to the largest side from the opposite vertex. Which of the following does NOT give the ratios of the areas of $△$ABD and $△$BCD?

Find the sum of first 22 terms of an AP in which d = 7 and 22nd term is 149.

If the vertices of a triangle are (2,0), (0,2). (4,6), then the equation of the median through the vertex (2,0) is ___.

The length of the shadow of a tower standing on a level plane is found to be 2x metres longer when the sun's altitude is ${30}^{\circ }$ then when it is ${45}^{\circ }$. The height of the tower = ___ m.

The number of circles that can be drawn, touching all the vertices of a triangle is ___ .

Taylor purchased a rectangular plot of area $750m^2$. The length of the plot is 5 m more than its breadth. Find its length.

In the given figure, DE || BC and AD : DB = 5 : 4, then $\frac{areaof\Delta DOE}{areaof\Delta DCE}$ is

If sum of the zeroe of the polynomial Ky^2+2y-3K is twice their product of zeros then find the value of K

In the given figure $△ABC$ is isosceles with AB = AC and is inscribed in a circle. If DAE is a tangent to the circle, then which of the following statement is true?

If y is the mean proportional between x and z, prove that : $\frac{x^2-y^2+z^2}{x^{-2}-y^{-2}+z^{-2}}=y^4$

Find the common difference and ${99}^{th}$ term of the arithmetic progession :

$7\frac{3}{4},9\frac{1}{2},11\frac{1}{4},............$

Ram bought an article for ₹ 374 , which included a discount of 15 % on the marked price and a sales tax of 10 % on the reduced price. Find the marked price of the article

$5x+4>8x-11;xϵZ$

If (3,0), (2,a), and (b,6) are the vertices of ΔABC whose centroid is (2,5), then the values of a and b are

Out of a day's production, which is 1000 machine parts, 100 were found to be sub-standard. The probability that a part selected at random being up to the standard is

A wire is bent in the form of a circle of radius 28 cm. It is rebent to form a square. The length of the side of the square will be

PS is the diameter of a circle of radius 6 cm. Q and R are points on the diameter such that PQ, QR and RS are equal. Semicircles are drawn with PQ and QS as diameters, as shown in the figure. Find the perimeter of the shaded region.(take π = 3.14)

Calculate the ratio in which the line joining A(6, 5) and B(-4, 3) is divided by the line = 2.

In what ratio does the -axis divide the line segment joining (2, 3) and (3, –5)? Find the co-ordinates of the point of intersection.

A ladder is placed against a wall such that its foot is at a distance of $2.5m$ from the wall and its top reaches $6m$ above the ground. Find the length of the ladder.

___ m

30th term of the ap : 10,7,4

a) Distinguish between stock and supply.

b) Complete the following schedule:

$\begin{array}{cccc}\text{Units Produced}& \text{TPP(in Rs.)}& \text{APP(in Rs.)}& \text{MPP(in Rs.)}\\ 1& 100& & \\ 2& & & 140\\ 3& & 140& \\ 4& 480& & \end{array}$

Solve the following pairs of linear (simultaneous) equations using method of elimination by substitution:

$6x=7y+7$

$7y-x=8$

Median of the following data:

1, 3, 4, 6, 7, 8, 8, 9, 12, 15

Two cubes, each of side $4cm$ are joined end to end. Find the surface area of the resulting cuboid.

For the following distribution the modal class is

$△$ABC is a right angled triangle, right angled at B. BD is a perpendicular as shown. Which of the following is true?

Find the mode and median of the following frequency distribution:
$\begin{array}{ccccccc}x& 10& 11& 12& 13& 14& 15\\ f& 1& 4& 7& 5& 9& 3\end{array}$

Find the number of integers that lie between the roots of the equation $x^2+7x+12=0$

At $\theta ={90}^{\circ }$, which of the following angles are not defined?

If $\theta$ is an acute angle and $tan\theta +cot\theta =2$, then find the value of $ta{n}^7\theta +co{t}^7\theta$.

Indian cricket team won 4 more matches than it lost with New Zealand. If it won $\frac{3}{5}$ of its matches, how many matches did India play?