question_answer1) What is the common difference of an A.P in which \[{{a}_{21}}-{{a}_{7}}=84\]?
View Answer play_arrowquestion_answer2) If the angle between two tangents drawn from an external point P to a circle of radius a and centre O, is \[60{}^\circ \], then find the length of OP.
View Answer play_arrowquestion_answer3) If a tower 30 m high, casts a shadow \[10\sqrt{3}\] long on the ground, then what is the angle of elevation of the sun?
View Answer play_arrowquestion_answer4) The probability of selecting a rotten apple randomly from a heap of 900 apples is 0 ? 18. What is the number of rotten apples in the heap?
View Answer play_arrowquestion_answer5) Find the value of p, for which one root of the quadratic equation \[p{{x}^{2}}-14x+8=0\] is 6 times the other.
View Answer play_arrowquestion_answer6) Which term of the progression \[20,19\frac{1}{4},18\frac{1}{2},17\frac{3}{4},\] ?? is the first negative term?
View Answer play_arrowquestion_answer7) Prove that the tangents drawn at the end points of a chord of a circle make equal angles with the chord.
View Answer play_arrowquestion_answer8) A circle touches all the four sides of a quadrilateral ABCD. Prove that \[AB+CD=BC+DA\]
View Answer play_arrowquestion_answer9) A line intersects the y ? axis and x ? axis at the points P and Q respectively. If (\[2,\text{ }\text{ }5\]) is the mid-point of PQ, then find the co-ordinates of P and Q.
View Answer play_arrowquestion_answer10) If the distances of P(x, y), from A(5,1) and B(\[1,\text{ }5\]) are equal, then prove that \[3x=2y\].
View Answer play_arrowquestion_answer11) If \[ad\ne bc,\]then prove that the equation \[({{a}^{2}}+{{b}^{2}}){{x}^{2}}+2(ac+bd)x+({{c}^{2}}+{{d}^{2}})=0\]has no real roots.
View Answer play_arrowquestion_answer12) The first term of an A.P. is 5, the last term is 45 and the sum of all its terms is 400. Find the number of terms and the common difference of the A.P.
View Answer play_arrowquestion_answer13) On a straight line passing through the foot of a tower, two points C and D are at distances of 4 m and 16 m from the foot respectively. If the angles of elevation from C and D of the top of the tower are complementary, then find the height of the tower.
View Answer play_arrowquestion_answer14) A bag contains 15 white and some black balls. If the probability of drawing a black ball from the bag is thrice that of drawing a white ball, find the number of black balls in the bag.
View Answer play_arrowquestion_answer15)
In what ratio does the point \[\left( \frac{24}{11},y \right)\] divide the line segment joining the points \[P(2,-2)\] and \[Q(3,7)\]? Also find the value of y. |
question_answer16)
Three semicircles each of diameter 3 cm, a circle of diameter 4.5 cm and a semicircle of radius 4.5 cm are drawn in the given figure. Find the area of the shaded region. |
question_answer17)
In the given figure, two concentric circles with centre O have radii 21 cm and 42 cm. If \[\angle AOB=~60{}^\circ \], find the area of the shaded region. [Use \[\pi =\frac{22}{7}\]] |
question_answer18) Water in a canal, 5.4 m wide and 1.8 m deep, is flowing with a speed of 25 km/hour. How much area can it irrigate in 40 minutes, if 10 cm of standing water is required for irrigation?
View Answer play_arrowquestion_answer19) The slant height of a frustum of a cone is 4 cm and the perimeters of its circular ends are 18 cm and 6 cm. Find the curved surface area of the frustum.
View Answer play_arrowquestion_answer20) The dimensions of a solid iron cuboid are \[4.4\text{ }m\times 2.6\text{ }m\times 1.0\text{ }m\]. It is melted and recast into a hollow cylindrical pipe of 30 cm inner radius and thickness 5 cm. Find the length of the pipe.
View Answer play_arrowquestion_answer21) Solve for x: \[\frac{1}{x+1}+\frac{3}{5x+1}=\frac{5}{x+4},x\ne -1,-\frac{1}{5},-4\]
View Answer play_arrowquestion_answer22) Two taps running together can fill a tank in \[3\frac{1}{13}\] hours. If one tap takes 3 hours more than the other to fill the tank, then how much time will each tap take to fill the tank?
View Answer play_arrowquestion_answer23) If the ratio of the sum of the first n terms of two A.P.s is \[(7n+1):(4n+27)\], then find the ratio of their 9th terms.
View Answer play_arrowquestion_answer24) Prove that the lengths of two tangents drawn from an external point to a circle are equal.
View Answer play_arrowquestion_answer25)
In the given figure, XY and X?Y? are two parallel tangents to a circle with centre O and another tangent AB with point of contact C, is intersecting XY at A and X?Y? at B. Prove that \[\angle AOB=90{}^\circ \]. |
question_answer26) Construct a triangle ABC with side\[BC=7\text{ }cm,\text{ }\angle B=45{}^\circ ,\text{ }\angle A=105{}^\circ \]. Then construct another triangle whose sides are \[\frac{3}{4}\] times the corresponding sides of the \[\Delta \text{ }ABC\].
View Answer play_arrowquestion_answer27) An aeroplane is flying at a height of 300 m above the ground. Flying at this height, the angles of depression from the aeroplane of two points on both banks of a river in opposite directions are \[45{}^\circ \] and \[60{}^\circ \] respectively. Find the width of the river. [Use\[\sqrt{3}=1.732\]]
View Answer play_arrowquestion_answer28) If the points \[A(k+1,2k),B(3k,2k+3)\] and \[C(5k-1,5k)\] are collinear, then find the value of k.
View Answer play_arrowquestion_answer29)
Two different dice are thrown together. Find the probability that the numbers obtained have |
(i) even sum, and |
(ii) even product. |
question_answer30)
In the given figure, ABCD is a rectangle of dimensions \[21\,cm\times 14\text{ }cm\]. A semicircle is drawn with BC as diameter. Find the area and the perimeter of the shaded region in the figure. |
question_answer31) In a rain-water harvesting system, the rain-water from a roof of \[22\text{ }m\times 20\text{ }m\] drains into a cylindrical tank having diameter of base 2 m and height 3.5 m. If the tank is full, find the rainfall in cm. Write your views on water conservation.
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