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#1 Class 10 Mathematics Probability 2027 Long 4M CBSE
A labourer prints 400 T-shirts in a day. The supervisor checked the T-shirts and found that 312 prints were good, 54 prints were with minor defects and the rest of the prints were of major defects. Harish, a customer,...
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#2 Class 10 Mathematics Arithmetic Progressions 2027 Long 4M CBSE
Delhi's pollution is a severe, often seasonal issue caused by a combination of factors like high vehicular and industrial emissions, dust from construction, and crop burning in surrounding states. In a school, student...
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#3 Class 10 Mathematics Areas Related to Circles 2027 Long 4M CBSE
A motion sensor (or motion detector) is an electronic device that is designed to detect and measure movement. The motion detector can detect movement over a sector of angle $\theta = 70^\circ$ to a distance of 24 m. (...
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#4 Class 10 Mathematics Some Applications of Trigonometry 2027 Long 5M CBSE
A statue standing on a pedestal is 1.6 m tall. From a point on the ground, the angles of elevation of the top and bottom of the statue are $60^\circ$ and $45^\circ$ respectively. Find the height of the pedestal.
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#5 Class 10 Mathematics Some Applications of Trigonometry 2027 Long 5M CBSE
To assist an ambulance, a drone is hovering over an accident site at a constant height on a highway. The angle of depression of the ambulance, approaching the accident site, observed from the drone is $30^\circ$. Twel...
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#6 Class 10 Mathematics Surface Areas and Volumes 2027 Long 5M CBSE
The largest possible hemisphere is drilled out of a wooden cubical block of side 21 cm such that the base of the hemisphere is on one of the faces of the cube. Then, find i. the volume of the wood left in the block. i...
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#7 Class 10 Mathematics Quadratic Equations 2027 Long 5M CBSE
John and Jivanti together have 45 marbles. Both of them lost 5 marbles each, and the product of the number of marbles they now have is 124. Find the number of marbles they had with them in the beginning.
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#8 Class 10 Mathematics Quadratic Equations 2027 Long 5M CBSE
A train travels a distance of 360 km at a uniform speed. If the speed had been 5 km/h more, then it would have taken 1 hour less to cover the same distance. Find the speed of the train.
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#9 Class 10 Mathematics Pair of Linear Equations in Two Variables 2027 Short 3M CBSE
The sum of the digits of a two-digit number is 9. Also, nine times this number is twice the number obtained by reversing the order of the digits. Find the number.
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#10 Class 10 Mathematics Statistics 2027 Short 3M CBSE
The distribution below gives the weight of 50 students of class X. Find the modal weight of the students. Weight (in kg) 35 – 45 45 – 55 55 – 65 65 – 75 75 – 85 Number of students 5 10 20 12 3
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#11 Class 10 Mathematics Statistics 2027 Short 3M CBSE
The mean of the following distribution is 48 and the sum of all the frequencies is 50. Find the missing frequencies $x$ and $y$. Class 20 – 30 30 – 40 40 – 50 50 – 60 60 – 70 Frequency 8 6 $x$ 11 $y$
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#12 Class 10 Mathematics Introduction to Trigonometry 2027 Short 3M CBSE
Consider $\triangle ACB$, right-angled at $C$, in which $AB = 29$ units, $BC = 21$ units and $\angle ABC = \theta$. Determine the values of i. $1 + \tan^2\theta$ ii. $\cos^2\theta - \sin^2\theta$
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#13 Class 10 Mathematics Coordinate Geometry 2027 Short 3M CBSE
Determine the ratio in which the point $(-6, y)$ divides the line segment joining the points $A(-3, -1)$ and $B(-8, 9)$. Also, find the value of $y$.
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#14 Class 10 Mathematics Circles 2027 Short 3M CBSE
$AX$, $AY$ and $BC$ are tangents to a circle with $P$, $R$ and $Q$ as the respective points of contact ($B$ lies on $AX$ and $C$ lies on $AY$). Prove that $AP = \dfrac{1}{2}(AB + BC + CA)$.
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#15 Class 10 Mathematics Real Numbers 2027 Short 3M CBSE
Given that $\sqrt{5}$ is irrational, prove that $2 + 3\sqrt{5}$ is irrational.
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#16 Class 10 Mathematics Coordinate Geometry 2027 Short 2M CBSE
Find a linear relation between $x$ and $y$ such that $P(x, y)$ is equidistant from the points $A(1, 4)$ and $B(-1, 2)$.
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#17 Class 10 Mathematics Coordinate Geometry 2027 Short 2M CBSE
Points $A(3, 1)$, $B(5, 1)$, $C(a, b)$ and $D(4, 3)$ are vertices of a parallelogram $ABCD$. Find the values of $a$ and $b$.
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#18 Class 10 Mathematics Circles 2027 Short 2M CBSE
$PA$ is a common tangent to two circles touching them at $A$, where $A$ lies between $P$ and $Q$. $QB$ is the tangent from $Q$ to the smaller circle and $PC$ is the tangent from $P$ to the larger circle. If $QB = 5$ c...
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#19 Class 10 Mathematics Polynomials 2027 Short 2M CBSE
If one zero of the quadratic polynomial $2x^2 - 3x + p$ is 3, find the value of $p$. Also, find the other zero.
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#20 Class 10 Mathematics Introduction to Trigonometry 2027 Short 2M CBSE
If $3\sin\theta = 4\cos\theta$, find the value of $\sin\theta + \cos^2\theta - 1$.
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