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The length and breadth of a cuboid are 2 m and 5 m respectively. What is the difference between total surface area and curved surface area ?

The sum of the squares of two consecutive multiples of 7 is 1225. Find the multiples.

Find the maximum number of zeroes and degree of the polynomial P(x) = 11$x^6$ + $x^5$ + 3$x^4$ + $x^3$ + $x^2$ + x +1.

The distance between the points $(\text{a}cos{35}^{\circ },0)\&(0,\text{a}cos{55}^{\circ })$ is

Q. Prove that for any positive integer n, n^{​​​​​​3}​- n is divisible by 6.

In the figure, given below, the medians BD and CE of a triangle ABC meet at G. Prove that : (i) $\Delta$ EGD~ $\Delta$ CGB and (ii) BG=2 GD from (i) above.

If $x+1,3x$ and $4x+2$ are the first three terms of an AP, then its $5^{\text{th}}$ term is ___.

If $\frac{AD}{BD}=\frac{3}{5}$, AC = 14 cm and $DE\parallel BC$ Find EC.

A shooter can hit a given target with probability $\frac{1}{4}.$ She keeps firing a bullet at the target until she hits it successfully three times and then she stops firing. The probability that she fires exactly six bullets lies in the interval

In an AP, the sum of the first ten terms is -80 and the sum of the next ten terms is -280. Find the AP.

In a school there are two sections $A$ and $B$ there are $32$ students in section A and $36$ students in section $B$. Determine the minimum number of books required for library so that it can be distributed equally among the children.

If $A$ is a square matrix of order $n,$ such that $|\text{adj(adj}A)|=|A{|}^9,$ then $n$ is

Sheela went to a bank to withdraw ₹ 2000. She asked the cashier to give her ₹ 50 and ₹ 100 notes only. Meena got 25 notes in all. Find how many notes of ₹ 50 and ₹ 100 she received.

1. 24

Find the middle term of the A.P. 213,205,197,...,37.

If $x=acosec\theta$ and $y=bcot\theta$, then which of the following equations is true ?

In each of the following, determine whether the given values are solutions (roots) of the equation or not :
(i) $3x^2–2x–1$ = 0; x = 1
(ii) $x^2+6x+5$ = 0; x = – 1, x = – 5
(iii) $x^2+x–4=0$; x = – 2

If the angle of elevation of a point on the ground to the top of a 100 m tower is 30°, then the point is at a distance of ___ m from the tower.

Prove that the perimeter of a right triangle is equal to the sum of the diameter of its incircle and twice the diameter of its circumcircle.

The probability of certain (sure) event is ___ .

B. Ltd. issued debentures at 94% for Rs 4,00,000 on April 01, 2011 repayable by five equal drawings of Rs 80,000 each. The company prepares its final accounts on March 31 every year.

Indicate the amount of discount to be written-off every accounting year assuming that the company decides to write-off the debentures discount during the life of debentures. (Amount to be written-off: 2012 Rs 8,000; 2013 Rs 6,400; 2014 Rs 4,800; 2015 Rs 2,000; 2016 Rs 1,600).

In the figure given below, PA and PB are tangents to the circle from point P. Which of the following is the correct relation between PA and PB?

Two tangents are drawn from an external point P that touches the circle at points Q and R respectively. The centre of the circle is O. The lines OQ and OR are drawn to complete the quadrilateral OQPR. The resulting quadrilateral is a ________necessarily.

Which of the following points lie at a distance of 3 units from the y axis: (1,1), (-1,-3), (3,3), (2,0), (-2,3)?

The tops of two poles of height 14 m and 20 m are connected by a wire which makes an angle of 30° with the horizontal. What is the length of the wire?

Question 99

A river 2 m deep and 45 m wide is flowing at the rate of 3 km per hour. Find the amount of water in cubic metres that runs into the sea per minute.