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Solve the pair of linear equations using cross-multiplication method.5(x−2)=4(1−y)26x+3y+4=0

Which term of the AP=72,68,64,60, ...is 0?

In the follwoing distribution, if the mean of the distribution is 86 then the value of P is

Obtain all zeros of the polynomial f(x) = x4 − 3x3 − x2 + 9x − 6, if two of its zeros are -3 and 3

The expression 16x0 can also be written as .

The line segment A(-2, 9) and B(6, 3) is a diameter of a circle with centre C. Find the coordinates of C.

The length of direct common tangents to two circles touching each other of radii 3 cm and 12 cm is 16 cm . Calculate the distance between their centres.

If a1,a2,a3,a4 are terms of an AP, then the relation between them is

Question 12 Circumference of two circles are equal. Is it necessary that their areas be equal? Why?

Evaluation of ∫42x3dx using a 2-equal-segment trapezoidal rule gives value of 63

If two dice are rolled simultaneously , then what is the probability that the sum of numbers is a multiple of either 2 or 7?

What is the probability that a leap year has 52 Mondays?(a) 27(b) 47(c) 57(d) 67

The sum of digits of a two digit number is 12. the number obtained by interchanging the two digits exceeds the given number by 18. find the number.

The radii of the ends of a frustum of a cone 45cm high are 28 cm and 7cm. Find its volume, the curved surface area, and the total surface area (take π=227).

if U_n=2COSnθ then U_1U_n-U_{n-1}is equal to

An iron pillar consists of a cylindrical portion 2.8 m high and 20 cm in diameter and a cone 42 cm high is surmounting it. Find the weight of the pillar, given that 1 cubic cm of iron weighs 7.5 gm.

A card is drawn from a deck of 52 cards. Find the probability that the card drawn is neither a black card nor a jack.

P is a point on side BC of a parallelogram ABCD. If DP produced meets AB produced at point L, prove that : (i) DP:PL=DC:BL. (ii) DL:DP=AL:DC.

If sin A + cos A = m and sec A + cosec A = n, show that : n(m2−1)=2m

If 2a + 3b + 4c = 0, then the straight lines ax + by + c = 0 will always pass through the point ___________.

If l is the arc length of a sector of a circle of radius r and A is the area of the sector, then A : l = __________.

Slope of tangent(s) to y=(x−2)(x+3)(x+4) at point(s) where curve intersects the x−axis, is/are

On dividing 3x3+x2+2x+5 by a polynomial g(x), the quotient and remainder are (3x-5) and (9x+10) respectively. Find g(x).

Write the zeros of the polynomial x2 − x − 6

What is the square root of 81a4y3 ?

Find the quadratic equation whose roots are 6+√33 and 6−√33 .

From the following cumulative frequency table, estimate: (i) The median (ii) The semi-interquartile range.

Question 5Given sec θ = 1312, calculate all other trigonometric ratios.

46 Find four numbers in an AP whose sum is 20 and sum of whose square is 120.

Find the value of k for which the following system of equations has a unique solution:kx + 2y = 53x + y = 1

84. Prove that points (-2,5),(0,1) and (2,-3) are collinear??

shorts are fired from simul†an eously from top and bottom of a vertical cliff at an angle 30 and 60degree with horizontal.these shots hit an object simul†an eously if the horizontal dis†an ce of object from bottom of cliff is 10\sqrt2 thenheight of cliff i

Question 15Check whether p(x) is a multiple of g(x) or not:(i) p(x)=x3–5x2+4x–3, g(x)=x–2(ii) p(x)=2x3–11x2–4x+5, g(x)=2x+1

Non terminating and repeating rational number from among the following is .

On dividing x​​​​​​2​​​-3x​​2+x+2 by a polynomial g(x) ,the quotient and the remainder were x -2 and -2-+4 respectively. Find g(x).

If sec A+tanA=2 then let us determine the value of(secA-tanA)

Show that x2 minus y2 is a composite number

Two circular pieces of equal radii and maximum area, touching each other are cut out from a rectangular card board of dimensions 14 cm × 7 cm. Find the area of the remaining card board. (Use π = 22/7).

A 13 m ladder is leaned against a wall as shown in figure. Find the distance of foot of ladder from the wall.

The areas of two similar triangles are 81cm2 and 49cm2 respectively. Find the ratio i4their corresponding heights. What is the ratio of their corresponding medians?

Solve the equation x2 -5x -12 = 0 graphically.

Define a matrix.

Mark the correct alternative in the following question:What least number is to be subtracted from each term of the ratio 15 : 19 to make the ratio 3 : 4?(a) 3 (b) 5 (c) 6 (d) 9

The number of 4 digit numbers having the digits in non-decreasing order (from left to rigt constructed by using the digits belonging to it set {1, 2, 3} is _.

At one end A of a diameter AB of a circle of radius 5 cm, tangent XAY is drawn to the circle. Find the length of the chord CD which is parallel to XY and at a distance of 8 cm from A.

ABCD is a square of side 4 cm. If E is a point in the interior of the square such that ΔCED is equilateral, then area of Δ ACE is(a) 23-1 cm2(b) 43-1 cm2(c) 63-1 cm2(d) 83-1 cm2

a b c d e fg h i j k l

A lot consists of 144 ball pens of which 20 are defective and others good. Nutri will buy a pen if it is good, but will not buy if it is defective. the shopkeeper draws one pen at random and gives it to her. What is the probability that(i) She will buy it?(ii) She will not buy it?

A kite is attached to a string. Find the length of the string, when the height of the kite is 60 m. and the string makes an angle 30∘ with the ground. [2 MARKS]

Explain this how this is a cubic polynomial? (x+2)3=4-x3

On dividing x2-3x2+x+2 by a polynomial g(x) ,the quotient and the remainder were x -2 and -2-+4 respectively. Find g(x).