General Instructions:
(i) This question paper comprises four sections – A, B, C and D. This question paper carries 40 questions. All questions are compulsory.
(ii) Section A: Q. No.1 to 20 comprises of 20 questions of one mark each.
(iii) Section B: Q. No. 21 to 26 comprises of 6 questions of two mark each.
(iv) Section C: Q. No. 27 to 34 comprises of 8 questions of three mark each.
(v) Section D: Q. No. 35 to 40 comprises of 6 questions of four mark each.
(vi) Use of Calculators are not permitted.
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If one of the zeroes of the polynomial \(x^2+3x+k \) is \( 2\), the value of \(k \) is
The total number of factors of a prime number is
one and the number itself
The quadratic polynomial, the sum of whose zeroes is -5 and their product is 6 is
The value of k for which the system of equation \(x+y-4=0 \) and \(2x+ky=3 \) has no solution is
The HCF and LCM of 12, 21, 15 are
HCF of 12, 21 and 15 = 3
LCM
The value of \(x \) for which \(2x,x+10 \) and \(3x+2 \) are \(3 \) consecutive terms of an AP is
The first term of an AP is p and common difference is q then its \(10^{\text{th}} \) term is
The distance between the points \((a\cos\theta+b\sin\theta,0) \) and \(0,a\sin\theta-b\cos\theta \) is
If the point \(p(k,0) \) divides the line segment joining the point \(A(2-2) \) and \(B(-7,4) \) in the ratio \(1:2 \) the value of \(k \) is
The value of P for which the points \(A(3,1),B(5,P) \) and \(C(7,-5) \) are collinear is
In figure, \(\triangle \)ABC is circumscribing a circle the length of BC is
Given \(\triangle ABC\sim\triangle PQR \), is \(\dfrac{AB}{PQ}=\dfrac{1}{3} \) then \(\dfrac{ar(\triangle ABC)}{ar(\triangle PQR)}= \)
ABC is an equilateral \(\triangle \) of side \(2a \) the length of one of its altitude is
\(\dfrac{\cos80^o}{\sin10^o}+\cos5a^o\ \text{cosec}\ 31^o= \)
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The value of \(\sin^2\theta+\dfrac{1}{1+\tan^2\theta}= \)
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The ratio of the length of a vertical rod and the length of its shadow is \(1:\sqrt3 \). Find the angle of elevation of the sun at that moment
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Two cones have their heights in the ratio \(1:3 \) and radii in the ratio \(3:1 \). What is the ratio of their volumes?
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Ratio
A letter of English alphabet is chosen at random. What is the probability that the chosen letter is a consonant?
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P(consonant)
A die is thrown once. What is the probability of getting a number less than 3?
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P(number less than 3)
If the mean of first n natural numbers is 15. Find n
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Show that \((a-b)^2,(a^2+b^2) \) and \((a+b)^2 \) are in AP
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As the common difference is same, so they are in AP
If \(DE||AC \) and \(DC||AP \), prove that \(\dfrac{BE}{EC}=\dfrac{BC}{CP} \)
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In
So, (Basic proportionality theorem)…(1)
In
So, ….(2)
From equation (1) and (2) we get
(Proved)
The rod AC of a TV disc antenna is fixed at right angle to the wall AB and a rod CD is supporting the disc. If AC = 1.5 m long and CD = 3 m
Find (i) \(\tan\theta \)
(ii) \(\sec\theta+\text{cosec}\theta \)
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(i)
(ii)
A piece of wire 22 cm long is but into the form of an arc of circle subtending an angle of \(60^o \) at its centre. Find the radius of the circle. \(\left(\text{use}\ \pi=\dfrac{22}{7}\right) \))
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If a number X is chosen at random from the numbers -3, -2, -1, 0, 1, 2, 3. What is the probability that \(x^2\leqslant4 \)?
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Total number of outcomes
Favourable outcomes
Find the mean of the following distribution
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Find the quadratic polynomial whose zeroes are reciprocal of the zeroes of the polynomial \(f(x)=ax^2+bx+c\ a\ne0,c\ne0 \)
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Required quadratic polynomial
If 4 is the zero of the cubic polynomial \(x^3-3x^2-10x+24 \), find its other two zeroes
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other two zeroes are -3 and 2
In a fight of 600 km, an aircraft was slowed due to bad weather. Its average speed for the trip was reduced to 200 km/hr and time of flight increased by 30 minutes. Find the original duration of flight
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Let the speed of aircraft be km/hr
Speed of aircraft km/hr
Duration of flight hour
Find the area of triangle \(PQR \) formed by the points \(P(-5,7),Q(-4,-5) \) and \(R(4,5) \)
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In the figure \(\angle D=\angle E \) and \(\dfrac{AD}{DB}=\dfrac{AE}{EC} \), prove that \(BAC \) is an isosceles triangle
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So, is an isosceles triangle
If the point \(C(-1, 2) \) divides internally the line segment joining \(A(2,5) \) and \(B(x,y) \) in the ratio \(3:4 \). Find the coordinates of \(B \)
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The coordinates of are
If \(\sin\theta+\cos\theta=\sqrt3 \) then prove that \(\tan\theta+\cot\theta=1 \)
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A cone of base radius 4 cm is divided into 2 parts by drawing a plane through the mid-point of its height and parallel to its base compare the volume of two parts
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Ratio of volume
Show that the square of any positive integer cannot be of form \((5q+2) \) or \((5q+3) \) for any integer \( q\)
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Let be any positive integer
Case -1
Case -2
Case – 3
Case – 4
Case – 5
So, square of any positive integer cannot be of the form or
for any integer
The sum of four consecutive numbers in AP is 32 and ratio of the product of first and last terms to the product of two middle terms is \(7:15 \). Find the numbers
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Let four consecutive numbers be
Four numbers are
Solve \(1+4+7+10+….+x=287 \)
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A vertical tower stands on a horizontal plane and is surmounted by a vertical flag-staff of height 6m. At a point on the plane, the angle of elevation of the bottom and top of the flag-staff are \(30^o \) and \(45^o \) respectively. Find the height of the tower. \((\sqrt3=1.73) \)
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A bucket in the form of a frustum of a cone of height 30 cm with radii of its lower end and upper ends are 10 cm and 20 cm respectively. Find the capacity of the bucket
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Capacity
The following table gives production yield per hectare (in quintals) of wheat of 100 farms of a village change the distribution to ‘more than’ type distribution and draw its ogive
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